Experimental Realization of an Exact Solution to the Vlasov Equations for an Expanding Plas
Quantum spin liquid emerging in 2D correlated Dirac fermions
磁共振(磁谐振耦合)无线充电技术鼻祖级文章-英文原文
Wireless Power Transfer via Strongly Coupled Magnetic ResonancesAndré Kurs,1* Aristeidis Karalis,2 Robert Moffatt,1 J. D. Joannopoulos,1 Peter Fisher,3Marin Soljačić11Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. 2Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. 3Department of Physics and Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.*To whom correspondence should be addressed. E-mail: akurs@Using self-resonant coils in a strongly coupled regime, we experimentally demonstrate efficient non-radiative power transfer over distances of up to eight times the radius of the coils. We demonstrate the ability to transfer 60W with approximately 40% efficiency over distances in excess of two meters. We present a quantitative model describing the power transfer which matches the experimental results to within 5%. We discuss practical applicability and suggest directions for further studies. At first glance, such power transfer is reminiscent of the usual magnetic induction (10); however, note that the usual non- resonant induction is very inefficient for mid-range applications.Overview of the formalism. Efficient mid-range power transfer occurs in particular regions of the parameter space describing resonant objects strongly coupled to one another. Using coupled-mode theory to describe this physical system (11), we obtain the following set of linear equationsIn the early 20th century, before the electrical-wire grid, Nikola Tesla (1) devoted much effort towards schemes to a&m(t)=(iωm-Γm)a m(t)+∑iκmn a n(t)+F m(t)n≠m(1)transport power wirelessly. However, typical embodiments (e.g. Tesla coils) involved undesirably large electric fields. During the past decade, society has witnessed a dramatic surge of use of autonomous electronic devices (laptops, cell- phones, robots, PDAs, etc.) As a consequence, interest in wireless power has re-emerged (2–4). Radiative transfer (5), while perfectly suitable for transferring information, poses a number of difficulties for power transfer applications: the efficiency of power transfer is very low if the radiation is omnidirectional, and requires an uninterrupted line of sight and sophisticated tracking mechanisms if radiation is unidirectional. A recent theoretical paper (6) presented a detailed analysis of the feasibility of using resonant objects coupled through the tails of their non-radiative fields for mid- range energy transfer (7). Intuitively, two resonant objects of the same resonant frequency tend to exchange energy efficiently, while interacting weakly with extraneous off- resonant objects. In systems of coupled resonances (e.g. acoustic, electro-magnetic, magnetic, nuclear, etc.), there is often a general “strongly coupled” regime of operation (8). If one can operate in that regime in a given system, the energy transfer is expected to be very efficient. Mid-range power transfer implemented this way can be nearly omnidirectional and efficient, irrespective of the geometry of the surrounding space, and with low interference and losses into environmental objects (6).Considerations above apply irrespective of the physical nature of the resonances. In the current work, we focus on one particular physical embodiment: magnetic resonances (9). Magnetic resonances are particularly suitable for everyday applications because most of the common materials do not interact with magnetic fields, so interactions with environmental objects are suppressed even further. We were able to identify the strongly coupled regime in the system of two coupled magnetic resonances, by exploring non-radiative (near-field) magnetic resonant induction at MHzfrequencies. where the indices denote the different resonant objects. The variables a m(t) are defined so that the energy contained in object m is |a m(t)|2, ωm is the resonant frequency of thatisolated object, and Γm is its intrinsic decay rate (e.g. due to absorption and radiated losses), so that in this framework anuncoupled and undriven oscillator with parameters ω0 and Γ0 would evolve in time as exp(iω0t –Γ0t). The κmn= κnm are coupling coefficients between the resonant objects indicated by the subscripts, and F m(t) are driving terms.We limit the treatment to the case of two objects, denoted by source and device, such that the source (identified by the subscript S) is driven externally at a constant frequency, and the two objects have a coupling coefficient κ. Work is extracted from the device (subscript D) by means of a load (subscript W) which acts as a circuit resistance connected to the device, and has the effect of contributing an additional term ΓW to the unloaded device object's decay rate ΓD. The overall decay rate at the device is therefore Γ'D= ΓD+ ΓW. The work extracted is determined by the power dissipated in the load, i.e. 2ΓW|a D(t)|2. Maximizing the efficiency η of the transfer with respect to the loading ΓW, given Eq. 1, is equivalent to solving an impedance matching problem. One finds that the scheme works best when the source and the device are resonant, in which case the efficiency isThe efficiency is maximized when ΓW/ΓD= (1 + κ2/ΓSΓD)1/2. It is easy to show that the key to efficient energy transfer is to have κ2/ΓSΓD> 1. This is commonly referred to as the strongcoupling regime. Resonance plays an essential role in thisDS S D'' power transfer mechanism, as the efficiency is improved by approximately ω2/ΓD 2 (~106 for typical parameters) compared to the case of inductively coupled non-resonant objects. Theoretical model for self-resonant coils. Ourexperimental realization of the scheme consists of two self- resonant coils, one of which (the source coil) is coupled inductively to an oscillating circuit, while the other (the device coil) is coupled inductively to a resistive load (12) (Fig. 1). Self-resonant coils rely on the interplay between distributed inductance and distributed capacitance to achieve resonance. The coils are made of an electrically conducting wire of total length l and cross-sectional radius a wound into Given this relation and the equation of continuity, one finds that the resonant frequency is f 0 = 1/2π[(LC )1/2]. We can now treat this coil as a standard oscillator in coupled-mode theory by defining a (t ) = [(L /2)1/2]I 0(t ).We can estimate the power dissipated by noting that the sinusoidal profile of the current distribution implies that the spatial average of the peak current-squared is |I 0|2/2. For a coil with n turns and made of a material with conductivity σ, we modify the standard formulas for ohmic (R o ) and radiation (R r ) µ0ω l a helix of n turns, radius r , and height h . To the best of our knowledge, there is no exact solution for a finite helix in the literature, and even in the case of infinitely long coils, the solutions rely on assumptions that are inadequate for our R o = 2σ 4πa µ πωr 42 ωh 2 (6)system (13). We have found, however, that the simple quasi- R =0 n 2 + (7)static model described below is in good agreementr ε 12 c3π3 c(approximately 5%) with experiment.We start by observing that the current has to be zero at the ends of the coil, and make the educated guess that the resonant modes of the coil are well approximated bysinusoidal current profiles along the length of the conducting wire. We are interested in the lowest mode, so if we denote by s the parameterization coordinate along the length of the conductor, such that it runs from -l /2 to +l /2, then the time- dependent current profile has the form I 0 cos(πs /l ) exp(i ωt ). It follows from the continuity equation for charge that the linear charge density profile is of the form λ0 sin(πs /l ) exp(i ωt ), so the two halves of the coil (when sliced perpendicularly to its axis) contain charges equal in magnitude q 0 = λ0l /π but opposite in sign.As the coil is resonant, the current and charge density profiles are π/2 out of phase from each other, meaning that the real part of one is maximum when the real part of the other is zero. Equivalently, the energy contained in the coil is 0The first term in Eq. 7 is a magnetic dipole radiation term(assuming r << 2πc /ω); the second term is due to the electric dipole of the coil, and is smaller than the first term for our experimental parameters. The coupled-mode theory decay constant for the coil is therefore Γ = (R o + R r )/2L , and its quality factor is Q = ω/2Γ.We find the coupling coefficient κDS by looking at the power transferred from the source to the device coil,assuming a steady-state solution in which currents and charge densities vary in time as exp(i ωt ).P =⎰d rE (r )⋅J (r ) =-⎰d r (A&S (r )+∇φS (r ))⋅J D (r ) at certain points in time completely due to the current, and at other points, completely due to the charge. Usingelectromagnetic theory, we can define an effective inductance L and an effective capacitance C for each coil as follows:=-1⎰⎰d r d r ' µJ &S(r ')+ρS(r ') 4π |r -r |ε0≡-i ωMI S I Dr '-r|r '-r |3⋅J D (r )(8)L =µ04π |I 0 |⎰⎰d r d r 'J (r )⋅J (r ')|r -r '|where the subscript S indicates that the electric field is due to the source. We then conclude from standard coupled-mode theory arguments that κDS = κSD = κ = ωM /2[(L S L D )1/2]. When 1 1 ρ(r )ρ(r ') the distance D between the centers of the coils is much larger= C 4πε 0 |q 0 | ⎰⎰d r d r ' |r -r '|(4)than their characteristic size, κ scales with the D -3dependence characteristic of dipole-dipole coupling. Both κ and Γ are functions of the frequency, and κ/Γ and the where the spatial current J (r ) and charge density ρ(r ) are obtained respectively from the current and charge densities along the isolated coil, in conjunction with the geometry of the object. As defined, L and C have the property that the efficiency are maximized for a particular value of f , which is in the range 1-50MHz for typical parameters of interest. Thus, picking an appropriate frequency for a given coil size, as we do in this experimental demonstration, plays a major role in optimizing the power transfer.1 2Comparison with experimentallydeterminedU =2 L |I 0 |parameters. The parameters for the two identical helical coils built for the experimental validation of the power 1 2 transfer scheme are h = 20cm, a = 3mm, r = 30 cm, and n = =2C|q 0 | (5)5.25. Both coils are made of copper. The spacing between loops of the helix is not uniform, and we encapsulate theuncertainty about their uniformity by attributing a 10% (2cm) uncertainty to h . The expected resonant frequency given these22dimensions is f0 = 10.56 ± 0.3MHz, which is about 5% off from the measured resonance at 9.90MHz.The theoretical Q for the loops is estimated to be approximately 2500 (assuming σ = 5.9 × 107 m/Ω) but the measured value is Q = 950±50. We believe the discrepancy is mostly due to the effect of the layer of poorly conductingcopper oxide on the surface of the copper wire, to which the current is confined by the short skin depth (~20μm) at this frequency. We therefore use the experimentally observed Q and ΓS= ΓD= Γ = ω/2Q derived from it in all subsequent computations.We find the coupling coefficient κ experimentally by placing the two self-resonant coils (fine-tuned, by slightly adjusting h, to the same resonant frequency when isolated) a distance D apart and measuring the splitting in the frequencies of the two resonant modes. According to coupled-mode theory, this splitting should be ∆ω = 2[(κ2-Γ2)1/2]. In the present work, we focus on the case where the two coils are aligned coaxially (Fig. 2), although similar results are obtained for other orientations (figs. S1 and S2).Measurement of the efficiency. The maximum theoretical efficiency depends only on the parameter κ/[(L S L D)1/2] = κ/Γ, which is greater than 1 even for D = 2.4m (eight times the radius of the coils) (Fig. 3), thus we operate in the strongly- coupled regime throughout the entire range of distances probed.As our driving circuit, we use a standard Colpitts oscillator whose inductive element consists of a single loop of copper wire 25cm in radius(Fig. 1); this loop of wire couples inductively to the source coil and drives the entire wireless power transfer apparatus. The load consists of a calibrated light-bulb (14), and is attached to its own loop of insulated wire, which is placed in proximity of the device coil and inductively coupled to it. By varying the distance between the light-bulb and the device coil, we are able to adjust the parameter ΓW/Γ so that it matches its optimal value, given theoretically by (1 + κ2/Γ2)1/2. (The loop connected to the light-bulb adds a small reactive component to ΓW which is compensated for by slightly retuning the coil.) We measure the work extracted by adjusting the power going into the Colpitts oscillator until the light-bulb at the load glows at its full nominal brightness.We determine the efficiency of the transfer taking place between the source coil and the load by measuring the current at the mid-point of each of the self-resonant coils with a current-probe (which does not lower the Q of the coils noticeably.) This gives a measurement of the current parameters I S and I D used in our theoretical model. We then compute the power dissipated in each coil from P S,D=ΓL|I S,D|2, and obtain the efficiency from η = P W/(P S+ P D+P W). To ensure that the experimental setup is well described by a two-object coupled-mode theory model, we position the device coil such that its direct coupling to the copper loop attached to the Colpitts oscillator is zero. The experimental results are shown in Fig. 4, along with the theoretical prediction for maximum efficiency, given by Eq. 2. We are able to transfer significant amounts of power using this setup, fully lighting up a 60W light-bulb from distances more than 2m away (figs. S3 and S4).As a cross-check, we also measure the total power going from the wall power outlet into the driving circuit. The efficiency of the wireless transfer itself is hard to estimate in this way, however, as the efficiency of the Colpitts oscillator itself is not precisely known, although it is expected to be far from 100% (15). Still, the ratio of power extracted to power entering the driving circuit gives a lower bound on the efficiency. When transferring 60W to the load over a distance of 2m, for example, the power flowing into the driving circuit is 400W. This yields an overall wall-to-load efficiency of 15%, which is reasonable given the expected efficiency of roughly 40% for the wireless power transfer at that distance and the low efficiency of the Colpitts oscillator.Concluding remarks. It is essential that the coils be on resonance for the power transfer to be practical (6). We find experimentally that the power transmitted to the load drops sharply as either one of the coils is detuned from resonance. For a fractional detuning ∆f/f0 of a few times the inverse loaded Q, the induced current in the device coil is indistinguishable from noise.A detailed and quantitative analysis of the effect of external objects on our scheme is beyond the scope of the current work, but we would like to note here that the power transfer is not visibly affected as humans and various everyday objects, such as metals, wood, and electronic devices large and small, are placed between the two coils, even in cases where they completely obstruct the line of sight between source and device (figs. S3 to S5). External objects have a noticeable effect only when they are within a few centimeters from either one of the coils. While some materials (such as aluminum foil, styrofoam and humans) mostly just shift the resonant frequency, which can in principle be easily corrected with a feedback circuit, others (cardboard, wood, and PVC) lower Q when placed closer than a few centimeters from the coil, thereby lowering the efficiency of the transfer.When transferring 60W across 2m, we calculate that at the point halfway between the coils the RMS magnitude of the electric field is E rms= 210V/m, that of the magnetic field isH rms= 1A/m, and that of the Poynting vector is S rms=3.2mW/cm2 (16). These values increase closer to the coils, where the fields at source and device are comparable. For example, at distances 20cm away from the surface of the device coil, we calculate the maximum values for the fields to be E rms= 1.4kV/m, H rms= 8A/m, and S rms= 0.2W/cm2. The power radiated for these parameters is approximately 5W, which is roughly an order of magnitude higher than cell phones. In the particular geometry studied in this article, the overwhelming contribution (by one to two orders of magnitude) to the electric near-field, and hence to the near- field Poynting vector, comes from the electric dipole moment of the coils. If instead one uses capacitively-loaded single- turn loop design (6) - which has the advantage of confining nearly all of the electric field inside the capacitor - and tailors the system to operate at lower frequencies, our calculations show (17) that it should be possible to reduce the values cited above for the electric field, the Poynting vector, and the power radiated to below general safety regulations (e.g. the IEEE safety standards for general public exposure(18).) Although the two coils are currently of identical dimensions, it is possible to make the device coil small enough to fit into portable devices without decreasing the efficiency. One could, for instance, maintain the product of the characteristic sizes of the source and device coils constant, as argued in (6).We believe that the efficiency of the scheme and the power transfer distances could be appreciably improved by silver-plating the coils, which should increase their Q, or by working with more elaborate geometries for the resonant objects (19). Nevertheless, the performance characteristics of the system presented here are already at levels where they could be useful in practical applications.References and Notes1. N. Tesla, U.S. patent 1,119,732 (1914).2.J. M. Fernandez, J. A. Borras, U.S. patent 6,184,651(2001).3.A. Esser, H.-C. Skudelny, IEEE Trans. Indust. Appl. 27,872(1991).4.J. Hirai, T.-W. Kim, A. Kawamura, IEEE Trans. PowerElectron. 15, 21(2000).5.T. A. Vanderelli, J. G. Shearer, J. R. Shearer, U.S. patent7,027,311(2006).6.A. Karalis, J. D. Joannopoul os, M. Soljačić, Ann. Phys.,10.1016/j.aop.2007.04.017(2007).7.Here, by mid-range, we mean that the sizes of the deviceswhich participate in the power transfer are at least a few times smaller than the distance between the devices. For example, if the device being powered is a laptop (size ~ 50cm), while the power source (size ~ 50cm) is in thesame room as the laptop, the distance of power transfer could be within a room or a factory pavilion (size of the order of a fewmeters).8. T. Aoki, et al., Nature 443, 671 (2006).9.K. O’Brien, G. Scheible, H. Gueldner, 29th AnnualConference of the IEEE 1, 367(2003).10.L. Ka-Lai, J. W. Hay, P. G. W., U.S. patent7,042,196(2006).11.H. Haus, Waves and Fields in Optoelectronics(Prentice- Supporting Online Material/cgi/content/full/1143254/DC1SOM TextFigs. S1 to S530 March 2007; accepted 21 May 2007Published online 7 June 2007; 10.1126/science.1143254 Include this information when citing this paper.Fig. 1. Schematic of the experimental setup. A is a single copper loop of radius 25cm that is part of the driving circuit, which outputs a sine wave with frequency 9.9MHz. S and D are respectively the source and device coils referred to in the text. B is a loop of wire attached to the load (“light-bulb”). The various κ’s represent direct couplings between the objects indicated by the arrows. The angle between coil D and the loop A is adjusted to ensure that their direct coupling is zero, while coils S and D are aligned coaxially. The direct couplings between B and A and between B and S are negligible.Fig. 2. Comparison of experimental and theoretical values for κ as a function of the separation between coaxially aligned source and device coils (the wireless power transfer distance.) Fig. 3. Comparison of experimental and theoretical values for the parameter κ/Γ as a function of the wireless power transfer distance. The theory values are obtained by using the theoretical κ and the experimentally measured Γ. The shaded area represents the spread in the theoretical κ/Γ due to the 5% uncertainty in Q.Fig. 4. Comparison of experimental and theoretical efficiencies as functions of the wireless power transfer distance. The shaded area represents the theoretical prediction for maximum efficiency, and is obtained by inserting theHall, Englewood Cliffs, NJ, 1984).12.The couplings to the driving circuit and the load donot theoretical values from Fig. 3 into Eq. 2 [with Γκ2/Γ2 1/2 W /ΓD= (1 +have to be inductive. They may also be connected by awire, for example. We have chosen inductive coupling in the present work because of its easier implementation. 13.S. Sensiper, thesis, Massachusetts Institute of Technology(1951).14.We experimented with various power ratings from 5W to75W.15.W. A. Edson, Vacuum-Tube Oscillators (Wiley, NewYork,1953).16.Note that E ≠cμ0H, and that the fields are out of phaseand not necessarily perpendicular because we are not in a radiativeregime.17.See supporting material on Science Online.18.IEEE Std C95.1—2005 IEEE Standard for Safety Levelswith Respect to Human Exposure to Radio FrequencyElectromagnetic Fields, 3 kHz to 300 GHz (IEEE,Piscataway, NJ,2006).19. J. B. Pendry, Science 306, 1353 (2004).20. The authors would like to thank John Pendry forsuggesting the use of magnetic resonances, and Michael Grossman and Ivan Čelanović for technical assistance.This work was supported in part by the Materials Research Science and Engineering Center program of the National Science Foundation under Grant No. DMR 02-13282, by the U.S. Department of Energy under Grant No. DE-FG02-99ER45778, and by the Army Research Officethrough the Institute for Soldier Nanotechnologies under Contract No. DAAD-19-02-D0002.) ]. The black dots are the maximum efficiency obtained from Eq. 2 and the experimental values of κ/Γ from Fig. 3. The red dots present the directly measured efficiency,as described in thetext.。
关于2023十大科技成就英语作文高中
2023年十大科技成就：引领未来的创新之路In the year 2023, the world witnessed remarkable advancements in various fields of technology, marking a significant milestone in human progress. From the depths of the ocean to the vast expanse of space, from artificial intelligence to medical breakthroughs, the year was filled with groundbreaking achievements. Here are the top ten technological advancements that shaped our world in 2023.1. The Mapping of the Human Brain Cell AtlasIn 2023, scientists achieved a remarkable feat by creating the most comprehensive atlas of human brain cells. Published in leading journals such as Science, Science Advances, and Science Translational Medicine, the 21 articles detailing this atlas revealed the characteristics of over 3,000 types of brain cells. This advancement offers profound insights into the unique complexity of the human brain and holds promise for advancing research on brain diseases and cognitive capabilities.2. Artificial Intelligence Generates Original ProteinsIn January 2023, researchers at a US institution published their findings in Nature Biotechnology, introducing an artificial intelligence (AI) system capable of generating novel enzymes from scratch. This breakthrough demonstrates that AI can learn the principles of biology, suggesting its potential to revolutionize protein development. Scientists believe that this technology, potentially more powerful than the Nobel Prize-winning "protein design technology - directed evolution," could accelerate the discovery of new proteins.3. The Operationalization of the Largest Experimental Fusion ReactorIn December 2023, the European Fusion Energy Organization announced the successful operation of the JT-60SA fusion reactor, a joint project between Europe and Japan. The reactor, which completed assembly in 2020, achieved first plasma in October 2023. As part of the International Thermonuclear Experimental Reactor (ITER) program, also known as the "Artificial Sun" project, JT-60SA represents a crucial step towards the realization of fusion energy.4. The Release of GPT-4 by OpenAIIn March 2023, OpenAI unveiled GPT-4, the latest version of its large language model. With enhanced image recognition capabilities, an expanded text input limit of 25,000 words, and improved accuracy, GPT-4 can generate lyrics, creative text, and achieve stylistic variations. Its performance across various professional tests and academic benchmarks is impressive, marking a significant leap in AI technology.5. Solar Energy Transmission from Space Proves Viability of Space-Based EnergyIn June 2023, California Institute of Technology announced the successful transmission of microwave energy from a satellite to Earth-based receivers. This demonstration验证了天基太阳能利用技术的可行性，作为一种清洁、可再生的能源技术，被认为是实现零碳排放的重要途径。
Ecole Polytechnique F ed erale
Entanglement of the orbital angular momentum states of photons
15.Zhu,X.K.,O'Nions,R.K.,Guo,Y.&Reynolds,B.C.Secular variation of iron isotopes in NorthAtlantic deep water.Science287,2000±2002(2000).16.Belshaw,N.S.,Zhu,X.K.,Guo,Y.&O'Nions,R.K.High precision measurement of iron isotopes byplasma source mass spectrometry.Int.J.Mass.Spectrom.197,191±195(2000).17.Marechal,C.N.,T elouk,P.&AlbareÁde,F.Precise analysis of copper and zinc isotopic compositions byplasma-source mass spectrometry.Chem.Geol.156,251±273(1999).18.Clayton,R.N.&Mayeda,T.K.Formation of ureilites by nebular processes.Geochim.Cosmochim.Acta52,1313±1318(1988).19.Clayton,R.N.&Mayeda,T.K.Oxygen isotope studies of achondrites.Geochim.Cosmochim.Acta60,1999±2017(1996).20.Clayton,R.N.Mayeda,T.K.,Goswami,J.N.&Olsen,E.J.Oxygen isotope studies of ordinarychondrites.Geochim.Cosmochim.Acta55,2317±2337(1991).21.Volkening,J.&Papanastassiou,D.A.Iron isotope anomaly.Astrophys.J.347,L43±L46(1989).22.Volkening,J.&Papanastassiou,D.A.Zinc isotope anomaly.Astrophys.J.358,L29±L32(1990).23.Birck,J.L.&Lugmair,G.W.Nickel and chromium isotopes in Allende inclusions.Earth Planet.Sci.Lett.90,131±143(1988).24.Rotaru,M.,Birck,J.L.&AlleÁgre,C.J.Clue to early solar system history from chromium isotopes incarbonaceous chondrites.Nature358,465±470(1992).25.Podosek,F.A.et al.Thoroughly anomalous chromium in Orgueil.Meteorit.Planet.Sci.32,617±627(1997).26.Niemeyer,S.&Lugmair,G.W.Titanium isotopic anomalies in meteorites.Geochim.Cosmochim.Acta48,1401±1416(1984).27.Niemeyer,S.&Lugmair,G.W.Ubiquitous isotopic anomalies in Ti from normal Allende inclusions.Earth Planet.Sci.Lett.53,211±225(1981).28.Papanastassiou,D.A.Chromium isotopic anomalies in the Allende meteorite.Astrophys.J.308,L27±L30(1986).AcknowledgementsWe thank N.S.Belshaw for assistance with mass spectrometry;A.Galy for discussions and for providing solution aliquots of some samples analysed;G.Turner and F.AlbareÁde for comments on the manuscript;and M.Price for providing samples of the Mt and OUM series.This work was supported by the Natural Environment Research Council. Correspondence and requests for materials should be addressed to X.K.Z.(e-mail:xiangz@). ................................................................. Entanglement of the orbital angular momentum states of photonsAlois Mair*,Alipasha Vaziri,Gregor Weihs&Anton ZeilingerInstitut fuÈr Experimentalphysik,UniversitaÈt Wien,Boltzmanngasse5,1090Wien, Austria .............................................................................................................................................. Entangled quantum states are not separable,regardless of the spatial separation of their components.This is a manifestation of an aspect of quantum mechanics known as quantum non-locality1,2.An important consequence of this is that the measure-ment of the state of one particle in a two-particle entangled state de®nes the state of the second particle instantaneously,whereas neither particle possesses its own well-de®ned state before the measurement.Experimental realizations of entanglement have hitherto been restricted to two-state quantum systems3±6,involv-ing,for example,the two orthogonal polarization states of photons.Here we demonstrate entanglement involving the spatial modes of the electromagnetic®eld carrying orbital angular mo-mentum.As these modes can be used to de®ne an in®nitely dimensional discrete Hilbert space,this approach provides a practical route to entanglement that involves many orthogonal quantum states,rather than just two Multi-dimensional entangled states could be of considerable importance in the®eld of quantum information7,8,enabling,for example,more ef®cient use of communication channels in quantum cryptography9±11. Multi-dimensional entanglement is a wayÐin addition to multi-particle entanglementÐto extend the usual two-dimensional two-particle state.There have been suggestions12,13(and only a proof-of-*Present address:Harvard-Smithsonian Center for Astrophysics,60Garden Street,Cambridge,Massa-chusetts02138,USA.principle experiment14)as to how to realize higher-order entangle-ment via multiport beam splitters.Here we present an experiment in which we used the spatial modes of the electromagnetic®eld carrying orbital angular momentum to create multi-dimensional entanglement.The advantage of using these modes to create entanglement is that they can be used to de®ne an in®nitely dimensional discrete(because of the quantization of angular momentum)Hilbert space.The experimental realization proceeded in the following two steps.First,we con®rmed that spontaneous parametric down-conversion conserves the orbital angular momentum of photons. This was done for pump beams carrying orbital angular momenta of2~,0and ~per photon,respectively.Second,we showed that the state of the down-converted photons can not be explained by assuming classical correlationÐin the sense that the photon pairs produced are just a mixture of the combinations allowed by conservation of angular momentum.We proved that,in contrast, they are a coherent superposition of these combinations,and hence they have to be considered as entangled in their orbital angular momentum.After completion of the experimental work presented here,related theoretical work was brought to our attention15,16. We will now discuss in order the two steps mentioned above.For paraxial light beams,Laguerre±gaussian(LG)modes(Fig.1)de®ne a possible set of basis vectors.As predicted17and observed18,LG modes carry an orbital angular momentum for linearly polarized light that is distinct from the intrinsic angular momentum of photons associated with their polarizations.This external angular momentum of the photon states is the reason why they have been suggested for gearing micromachines,and it has been shown that they can be used as optical tweezers19±21.Figure1Laguerre±gaussian(LG l p)or`doughnut'mode.The index l is referred to as the winding number,and p 1 is the number of radial nodes.Here we only consider cases of p 0.The customary gaussian mode can be viewed as an LG mode with l 0.The handedness of the helical wave fronts of the LG modes is linked to the sign of the index l,and can be chosen by convention.The azimuthal phase term exp il f of the LG modes results in helical wave fronts.The phase variation along a closed path C around the beam centre is2p l. Therefore,in order to ful®l the wave equation,the intensity has to vanish in the centre of the beam.To demonstrate the conservation of the orbital angular momen-tum carried by the LG modes in spontaneous parametric down-conversion,we investigated three different casesÐfor pump photons possessing orbital angular momenta of2~,0and ~ per photon,respectively.As a pump beam,we used an argon-ion laser(wavelength351nm)which we could operate either with a simple gaussian mode pro®le(l 0)or in the®rst-order LG modes (l 61)after astigmatic mode conversion(for a description of this technique,see ref.22).Spontaneous parametric down-conver-sion was done in a1.5-mm-thick BBO(b-barium borate)crystal cut for type-I phase matching(that is,both photons carry the same linear polarization).The crystal cut was chosen so as to produce down-converted photons at a wavelength of702nm at an angle of48 off the pump direction.The mode detection of the down-converted photons was per-formed for gaussian and LG modes.The gaussian mode(l 0)was identi®ed using mono-mode®bres(Fig.2)in connection with avalanche detectors.All other modes have a larger spatial extension, and therefore cannot be coupled into the mono-mode®bre.The LG modes(lÞ0)were identi®ed using mode detectors consisting of computer-generated holograms and mono-mode optical®bres (Fig.2).Computer-generated holograms have often been exploited for creating LG modes of various orders23.Our holograms were phase gratings5mm35mm in size,with20lines mm-1,which we®rst recorded on holographic®lms and bleached afterwards to increase the transmission ef®ciency(Fig.2).We made holograms that had one or two dislocations in the centre,and designed them to have their maximum intensity in the®rst diffraction order.This enabled us to distinguish between LG modes l 22;21;0;1;2using all holograms in the®rst diffraction orderÐfor which they have been blazed.For analysing an LG mode with a negative index,the holograms were rotated by1808around the axis perpendicular to the grating lines.The total transmission ef®ciency of all our holograms was about80%,and they diffracted18%of the incoming beam into the desired®rst order.These characteristics were meas-ured at632nm wavelength because a laser source at702nm was not available.The diffraction ef®ciency is not the only loss that occurs.We also have to account for Fresnel losses at all optical surfaces(95% transmission),imperfect coupling into the optical®bres(70%for a gaussian beam),non-ideal interference®lters(75%centre trans-mission),and the ef®ciency of the detectors(30%).A conservative estimate of all the losses yields an overall collection ef®ciency of2±3%.Comparing the unnormalized(l pump l1 l2 0)coin-cidence rates of about2,000s-1to the single count rates of about 100,000s-1we deduce an ef®ciency of2%,in agreement with the above estimation.The mode analysis was performed in coincidence for all cases where mode®lter1was prepared for analysing LG modes l1 0;1;2 and mode®lter2for those with l2 22;21;0;1;2.For analys-ing an LG mode with mode index l 0Ðthat is,a gaussian modeÐthe dislocation of the hologram was shifted out of the beam path.Thus the beam was sent through the border of the hologram where it acts as a conventional grating without changing the photons'angular momentum.The results are shown in Fig.3for different values of orbital angular momenta of the pump beam.Within experimental accuracy,coincidences were only observed in those cases where the sum of the orbital angular momenta of the down-converted photons was equal to the pump beam's orbital angular momentum.However,the absolute count rates of these cases are not equal.This is probably due to unequal emission probabilities of the photons into the different modes in the down-conversion process.These results con®rm conservation of the orbital angular momentum in parametric down-conversion.The signal-to-noise ratios achieved were as high as V 0:97660:038and V 0:91660:009for pump beams with and without orbital angular momentum,respectively.V is de®ned as I out2I in = I out I in ,where I in and I out denote the maximum and the mini-mum of the coincidences with the dislocation of the hologram respectively in and out of the beam.It is only by using a coincidence measurement that we could show that the conservation of the orbital angular momentum holds for each single photon pair.In contrast,cumulative detection methods using many photons result in an incoherent pattern24,becauseFigure2Experimental set-up for single-photon mode detection.After parametric down-conversion,each of the photons enters a mode detector consisting of a computer-generated hologram and a mono-mode optical®bre.By diffraction at the hologram,the incoming mode undergoes a mode transformation in such a way that an LG mode can be transformed into a gaussian mode.As it has a smaller spatial extension than all LG modes, only the gaussian mode can be coupled into the mono-mode®bre.Thus observation of a click projects the mode incident on the®bre coupler into the gaussian mode.The hologram is a phase grating with D m dislocations in the centre blazed for®rst-order diffraction.An incoming gaussian laser beam passing through the dislocation of the hologram is diffracted by the grating,and the n th diffraction order becomes an LG mode with an index l n D m and vice versa.Intuitively speaking,the phase dislocation exerts a `torque'onto the diffracted beam because of the difference of the local grating vectors in the upper and lower parts of the grating.This`torque'depends on the diffraction order n and on D m.Consequently the right and left diffraction orders gain different handedness. Reversing this process,a photon with angular momentum D m~before the grating can be detected by the mono-mode®bre detector placed in the®rst diffraction order.A photon with zero angular momentum(gaussian mode)is detected by diffracting the beam at the border of the hologram far away from the dislocation.All our measurements were performed in coincidence detection between the two down-converted photons.each beam from parametric down-conversion by itself is an inco-herent mixture.Therefore some previous workers24using these classical detection methodsÐwhich are in principle unsuitable at the single photon levelÐwere led to believe that the orbital angular momentum is not conserved in spontaneous parametric down-conversion.Given this experimental veri®cation of the conservation of orbital angular momentum,entanglement between the two photons pro-duced in the conversion process might be expected.But to explain the conservation of the orbital angular momentum,the photons do not necessarily have to be entangled:it would be suf®cient to assume classical correlation.But further experimental results(see below) showed that the two-photon state goes beyond classical correlation, and indeed,we were able to prove the entanglement for photon states with phase singularities.To con®rm entanglement,we have to demonstrate that the two-photon state is not just a mixture but a coherent superposition of product states of the various gaussian and LG modes which obey angular momentum conservation.For simplicity,we restricted ourselves to superpositions of two basis states only.An important distinction between coherent superposition and incoherent mixture of gaussian and LG modes is that the latter possess no phase singularity.This is because adding the spatial intensity distributions of these two modes will yield a®nite intensity everywhere in the resulting pattern.In contrast,in a coherent superposition the amplitudes are added,and therefore the phase singularity must remain and is displaced to an eccentric location(Fig.4).It will appear at that location where the amplitudes of the two modes are equal,with opposite phase.Therefore the radial distance of the singularity from the beam centre is a measure of the amplitude ratio of the gaussian to the LG components,whereas the angular position of the singularity is determined by their relative phase.Intuitively speaking,the position of the dislocation with respect to the beam is equivalent to the orientation of a polarizer. Superpositions of LG and gaussian modes can be realized experi-mentally by shifting the dislocation of the hologram out of the centre of the beam by a certain(small)amount.Hence in order to detect a photon having an orbital angular momentum that is a superposition of the gaussian and the LG mode,the hologram was placed in a position such that the dislocation was slightly displaced from the beam centre.In the intensity pattern these modes possess an eccentric singularity(Fig.4).To demonstrate the entanglement, we therefore shifted one of the holograms and scanned the gaussian mode®lter on the other side while recording the coincidences. The results shown in Fig.4verify the correlation in superposition bases of the LG(l 62)and gaussian(l 0)modes.A closer analysis shows that there are two conditions necessary to obtain the measured curves.First,the shifted hologram has to work as described above,and second,the source must emit an angular-momentum-entangled state.Assume that the source only emits classically correlated but not entangled singularities.Then on the side with the shifted hologram,the various terms of the classical mixture would be projected onto a state with displaced singularity leaving the total state again in a mixture.Respecting the conserva-tion of angular momentum we would then have to sum the probabilities of the various components on the other side,resulting Figure3photon1and photon2in15possible combinations of orthogonal states were performed.This was done for a pump beam having an orbital angular momentum of2~,0and ~per photon,respectively.Coincidences were observed in all cases where the sum of thethe pump beam'sorbital angular momentum.The coincidence counts for each®xed value of the orbitalangular momentum of photon1were normalized by the total number of coincidencesvarying the orbital angular momentum of photon2.–750+75Detector position (µm)Experimental evidence(left;right,simulation)of entanglementwith phase singularities.The dislocation of the hologram in the beam of photon1is shiftedout of the beam centre step by step(top,middle,bottom).In these positions,thishologramÐtogether with the mono-mode®bre detectorÐprojects the state of photon1into a coherent superposition of LG and gaussian modes.The mode®lter for photon2withthe hologram taken out makes a scan of the second photon's intensity distribution(detector position)in order to identify the location of its singularity with respect to the beamcentre.The coincidences show that the second photon is also detected in a superpositionof LG and gaussian modes.Classical correlation would yield a coincidence picture whichis just a mixture of gaussian and LG modes.In that case,the intensity minimum wouldremain in the beam centre but would become washed out.In the experiment a hologramwith two dislocations in the®rst diffraction order was used.in a coincidence pattern not containing any intensity zeroes.Such a coincidence pattern would also be observed if a shifted hologram together with a mono-mode detector were not able to analyse for superposition states.An entangled state represents correctly both the correlation of the eigenmodes and the correlations of their superpositions.Having experimentally con®rmed the quantum superposition for l 0and l 62,it is reasonable to expect the quantum superposition will also occur for the other states.Nevertheless,ultimate con®rmation of entanglement will be a Bell inequality experiment generalized to more states25.Such an experiment will be a major experimental challenge,and we are preparing to perform it.For a pump beam with zero angular momentum,the emitted state must then be represented byw C0;0j0i j0i C1;21j1i j21i C21;1j21i j1iC2;22j2i j22i C22;2j22i j2i ¼¼1as the LG modes form an in®nite dimensional basis.Here the numbers in the brackets represent the indices l of the LG modes, and the C i,j denote the corresponding probability amplitude for measuring j i i j j i.The state(1)is a multi-dimensional entangled state for two photons,which in general will also contain terms with radial mode index pÞ0.It means neither photon in state (1)possesses a well-de®ned orbital angular momentum after parametric down-conversion.The measurement of one photon de®nes its orbital angular momentum state,and projects the second one into the corresponding orbital angular momentum state.It is conceivable that these states could in the future be extended to multi-dimensional multi-particle entanglement.A growing body of theoretical work calls for entanglement of quantum systems of higher dimensions7,8.These states have applications in quantum cryptography with higher alphabets and in quantum teleportation. As such states increase the¯ux of information,it is conceivable that they could be important for many other applications in quantum communication and in quantum information.The possibility of using these photon states to drive micromachines,and the applica-tion of these states as optical tweezers,make them versatile and potentially suitable for future technologies19±21.M Received12March;accepted5June2001.1.SchroÈdinger,E.Die gegenwaÈrtige Situation in der Quantenmechanik.Naturwissenschaften23,807±812;823±828;844±849(1935).2.SchroÈdinger,E.Discussion of probability relations between separated systems.Proc.Camb.Phil.Soc.31,555±563(1935).3.Bouwmeester,D.,Pan,J.-W.,Daniell,M.,Weinfurter,H.&Zeilinger,A.Observation of a three-photon Greenberger-Horne-Zeilinger state.Phys.Rev.Lett.82,1345±1349(1999).4.Pan,J.-W.,Bouwmeester,D.,Daniell,M.,Weinfurter,H.&Zeilinger,A.Experimental test of quantumnonlocality in three-photon Greenberger-Horne-Zeilinger entanglement.Nature403,515±519 (2000).5.Sackett,C.A.et al.Experimental entanglement of four particles.Nature404,256±259(2000).6.Pan,J.-W.,Daniell,M.,Gasparoni,S.,Weihs,G.&Zeilinger,A.Experimental demonstration of four-photon entanglement and high-®delity teleportation.Phys.Rev.Lett.86,4435±4438(2001).7.DiVincenzo,D.P.,More,T.,Shor,P.W.,Smolin,J.A.&Terhal,B.M.Unextendible product bases,uncompletable product bases and bound entanglement.Preprint quant-ph/9908070ath i(1999).8.Bartlett,S.D.,de Guise,H.&Sanders,B.C.Quantum computation with harmonic oscillators.Preprint quant-ph/0011080at h i(2000).9.Bechmann-Pasquinucci,H.&Peres,A.Quantum cryptography with3-state systems.Phys.Rev.Lett.85,3313±3316(2000).10.Bechmann-Pasquinucci,H.&Tittel,W.Quantum cryptography using larger alphabets.Phys.Rev.A61,62308±62313(2000).11.Bourennane,M.,Karlsson,A.&BjoÈrk,G.Quantum key distribution using multilevel encoding.Phys.Rev.A(in the press).12.Reck,M.,Zeilinger,A.,Bernstein,H.J.&Bertani,P.Experimental realization of any discrete unitaryoperator.Phys.Rev.Lett.73,58±61(1994).13.Zukowski,M.,Zeilinger,A.&Horne,M.Realizable higher-dimensional two-particle entanglementsvia multiport beam splitters.Phys.Rev.A55,2564±2579(1997).14.Reck,M.Quantum Interferometry with Multiports:Entangled Photons in Optical Fibers.Thesis,Univ.Innsbruck(1996).15.Arnaut,H.H.&Barbosa,G.A.Orbital and angular momentum of single photons andentangled pairs of photons generated by parametric down-conversion.Phys.Rev.Lett.85,286±289 (2000).16.Franke-Arnold,S.,Barnett,S.M.,Padgett,M.J.&Allen,L.Two-photon entanglement of orbitalangular momentum states.Phys.Rev.A(in the press).17.Allen,L.,Beijersbergen,M.W.,Spreeuw,R.J.C.&Woerdman,J.P.Orbital angular momentumof light and the transformation of laguerre-gaussian laser modes.Phys.Rev.A45,8185±8189 (1992).18.He,H.,Fries,M.,Heckenberg,N.&Rubinsztein-Dunlop,H.Direct observation of transfer of angularmomentum to absorbtive particles from a laser beam with a phase singularity.Phys.Rev.Lett.75,826±829(1995).19.Simpson,N.B.,Dholakia,K.,Allen,L.&Padgett,M.J.Mechanical equivalence of spin and orbitalangular momentum of light:An optical spanner.Opt.Lett.22,52±54(1997).20.Galajda,P.&Ormos,plex micromachines produced and driven by light.Appl.Phys.Lett.78,249±251(2001).21.Friese,M.E.J.,Enger,J.,Rubinsztein-Dunlop,H.&Heckenberg,N.Optical angular-momentumtransfer to trapped absorbing particles.Phys.Rev.A54,1593±1596(1996).22.Bejersbergen,M.W.,Allen,L.,van der Veen,H.E.L.O.&Woerdman,J.P.Astigmatic laser modeconverters and transfer of orbital angular mun.96,123±132(1993).23.Arlt,J.,Dholakia,K.,Allen,L.&Padgett,M.J.The production of multiringed laguerre-gaussianmodes by computer-generated holograms.J.Mod.Opt.45,1231±1237(1998).24.Arlt,J.,Dholakia,K.,Allen,L.&Padgett,M.Parametric down-conversion for light beams possessingorbital angular momentum.Phys.Rev.A59,3950±3952(1999).25.Kaszlikowski,D.,Gnacinski,P.,Zukowski,M.,Miklaszewski,W.&Zeilinger,A.Violation of localrealism by two entangled n-dimensional systems are stronger than for two qubits.Phys.Rev.Lett.85, 4418±4421(2000).AcknowledgementsThis work was supported by the Austrian Fonds zur FoÈrderung der wissenschaftlichen Forschung(FWF).Correspondence and requests for materials should be addressed to A.Z.(e-mail:anton.zeilinger@univie.ac.at).................................................................. Superconductivity in the non-magnetic state of iron under pressureKatsuya Shimizu*²,Tomohiro Kimura*,Shigeyuki Furomoto*,Keiki Takeda*,Kazuyoshi Kontani*,Yoshichika Onuki³&Kiichi Amaya*²*Department of Physical Science,Graduate School of Engineering Science, Osaka University,Toyonaka,Osaka560-8531,USA²Research Center for Materials Science at Extreme Conditions,Osaka University, Toyonaka,Osaka560-8531,Japan³Department of Physics,Graduate School of Science,Osaka University, Osaka560-0043,Japan .............................................................................................................................................. Ferromagnetism and superconductivity are thought to compete in conventional superconductors,although in principle it is possible for any metal to become a superconductor in its non-magnetic state at a suf®ciently low temperature.At pressures above10GPa, iron is known to transform to a non-magnetic structure1,2and the possibility of superconductivity in this state has been predicted3,4. Here we report that iron does indeed become superconducting at temperatures below2K at pressures between15and30GPa.The transition to the superconducting state is con®rmed by both a drop in resistivity and observation of the Meissner effect.An iron sample with purity of99.995%(Johnson Matthey)was puri®ed further and degassed by heating close to the melting point in an ultra-high-vacuum chamber.The sample was cut into a rectangular shape of0:0430:16030:07mm3and placed in the sample chamber of a non-magnetic diamond-anvil cell(DAC)made of BeCu alloy.For electrical resistivity measurements the BeCu metal gasket was covered with a thin Al2O3layer for electrical insulation.Electrical resistivity measurements are performed using the a.c.four-terminal method with a typical measuring current of0:131026A at low temperatures below10K.The sample chamber was®lled with NaCl as the pressure-transmitting medium(Fig.1a).Several ruby chips of less than0.002mm in diameter were located around the sample and the applied pressure。
量子身份认证系统
and the distribution of a common secret string is achieved by means of quantum key distribution ͑QKD͒. QKD, based on the Bennett and Brassard 1984 ͑BB84͒ protocol ͓7͔, has recently been proved secure against any collective attack allowed by quantum mechanics ͓8,9͔, and thus it offers unconditional protection even against eavesdroppers possessing unlimited computational and technological power. QKD is capable of providing two users with a random shared secret string, whose secrecy is guaranteed by the fundamental laws of quantum mechanics. Many papers have already been devoted to quantum cryptography.them ͓7,10–15͔ and the survey ͓16͔. A large bibliography may also be found in ͓17͔.
In all these instances, cryptography proves very helpful. One of the basic cryptographic tasks is to certify the identities of the legitimate users of a communications line ͑traditionally called Alice and Bob͒ so that no third party monitoring their identification can impersonate either of them. Moreover, the system must be designed in such a way that after a successful mutual identification, even Bob cannot later on pretend to someone else to be Alice and vice versa.
异性材料方解石制备的隐身斗篷macroscopic invisibility cloaking of visible light
© 2011 Macmillan Publishers Limited. All rights reserved.
nature communications | DOI: 10.1038/ncomms1176
T
height H2 and filled with an isotropic material of permittivity ε and µ (µ = 1; blue region in Fig. 1a) is mapped to a quadrilateral region in the physical space with anisotropic electromagnetic properties ε′ and µ′ (brown region in Fig. 1b). Thus, the cloaked region is defined by the small grey triangle of height H1 and half-width d. Mathematically, the transformation is defined by
ARTICLE
Received 15 Sep 2010 | Accepted 4 Jan 2011 | Published 1 Feb 2011
DOI: 10.1038/ncomms1176
Macroscopic invisibility cloaking of visible light
Xianzhong Chen1, Yu Luo2, Jingjing Zhang3, Kyle Jiang4, John B. Pendry2 & Shuang Zhang1
program-分会7-冷原子物理与量子模拟pdf
冷原子物理与量子模拟20日下午，地点：208，主持人：朱诗亮，南京大学 时 间 报告人 报告题目13：30-14：00张天才山西大学Full control and measurement of singleatom in micro-trap and micro-cavity14：00-14：30 史保森中科大Entanglement between a collective Rydbergexcitation and a ground-state spin wave14：30-15：00颜辉华南师大Narrowband single photons: Generation andApplication休息20日下午，地点：208，主持人：张天才，山西大学15：20-15：50 管习文物数所Luttinger liquid and beyond in one-dimensionalspin-1/2 Heisenberg antiferromagnet CuPzN15：50 -16:20钱静华东师大Non-equilibrium quantum phases in ultracold Rydberg atoms with strong blockadeeffect16：20-16：40金家森大连理工Steady-state phase diagram of a drivenQED-cavity array with cross-Kerrnonlinearities16：40-17：00魏世杰清华大学Duality Quantum Computer Simulates Open QuantumSystems Efficiently17：00-17：20周增荣清华大学The efficient quantum simulation algorithm in duality quantum computer21日上午，地点：208，主持人：颜辉，华南师范大学 时 间 报告人 报告题目8:30-9:00张靖山西大学Experimental realization of a two-dimensionalsynthetic spin-orbit coupling in ultracoldFermi gases9：00-9：30周小计北京大学Quantum dynamical evolution of cold atoms in the high bands of an optical lattice9：30-10：00张熙博北京大学Studying many-body physics based on coldstrontium atoms休息21日上午，地点：208，主持人：龙桂鲁，清华大学10：20-10：50冯芒物数所Precise control and quantum gating with trappedions10：50-11：20颜波浙江大学Ultracold polar molecules in an 3D opticallattice11：20-11：50陈澍物理所Existence of critical phase in quasiperiodic optical lattices11：50-12：10周智超武汉大学Thermal valence-bond-solid transition andcooling of SU(2N) ultra-cold Dirac fermions inthe optical lattice休息与海报21日下午，地点：208，主持人：刘伍明，中科院物理所 时 间 报告人 报告题目13：30-14：00 龙桂鲁清华大学Duality Quantum Computing: A New Paradiam forEfficient Quantum Simulation14：00-14：30 王大军港中文Creation of an ultracold gas of ground-statedipolar 23Na87Rb molecules14：30-15：00 纪安春首师大Oscillations of Solitons in 1D Spin-Orb it Coupled Bose-Einstein Condensates休息21日下午，地点：208，主持人：陈澍，中科院物理所15：20-15：50 许志芳华中科大Interaction-driven topological edgeexcitations in a bosonic chiral p-wavesuperfluid15：50-16:20 刘伍明物理所光晶格中冷原子的拓扑量子相变16：20-16：50 江开军物数所TBA16：50-17：20 朱诗亮南京大学Simulation of PT-invariant topological nodal loop bands with ultracold atoms in an optical lattice。
大学写作 College English Writing 作者：萧立明
College WritingbyLiming XiaoUniversity of Central-South China2001作者简介萧立明，字萧颀，1941年10月20日出生于洪江市安江中山圆，祖籍湖南省洞口高沙镇。
1955年在省立黔阳一中初中毕业后考入长沙一中，偏爱英语，启蒙教师为应开石先生。
1961年在湖南师范大学外语系师从罗凯岚、廖六如、刘重德、赵甄陶、张文庭等教授。
1965-1975年在岳云中学任教，其间参加湖南英语人员统考，获全省第二名；1975-1979，由中共湖南省委组织部调往岳阳洞庭氮肥厂担任国家重点工程现场翻译。
1980-1984，出任衡阳师院外语系讲师、代理系主任。
1984年以后，先后在原长沙铁道学院和中南工业大学任教，1987年任副教授、硕士导师，担任一届副系主任。
1991年晋升为教授，担任一届系主任，并于1994年起享受国务院特殊津贴。
现任中南大学铁道校区外语学院教授、硕士导师、英汉语比较研究所所长。
萧立明教授从事从中学到英语专科、本科、硕士多层次英语教学工作，主要任课课程为：大学英语（英语专业）、大学英语（非英语专业）、高级英语、英语语法、高级英语写作、翻译理论与实践、英美文学选读、翻译学、英汉比较等。
他所创导的“功能-结构-输入”教学模式连续三次获得突出成果，荣获湖南省第二届教学成果二等奖；获校级教学成果一等奖2次，2等奖和3等奖数次。
萧立明教授现出版著作24部（含主审6部），发表学术论文40余篇。
最有影响的学术专著为：《英语结构要义》、《翻译新探》、《新译学论稿》和《英汉语比较研究与翻译》；最有代表性的学术论文为：“系统语言观与辩证论译”、“中国译学论”、“论科学的翻译与翻译的科学”、“语言变体与文学翻译”、“话语结构与翻译”、“试论修辞与翻译”、“语义纵横与翻译”、“输入强化与文化适应”等。
为此，荣获部级科研成果二等奖2次；湖南省社科优秀成果奖2次。
其教学与科研业绩先后载入《东方之子》、《当代湘籍著作家大词典》、《中国翻译家词典》等。
Empirical Determination of Bang-Bang Operations
Mark S. Byrd∗† and Daniel A. Lidar‡
Chemical Physics Theory Group, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H6, Canada (Dated: February 9, 2008) Strong and fast ”bang-bang” (BB) pulses have been recently proposed as a means for reducing decoherence in a quantum system. So far theoretical analysis of the BB technique relied on model Hamiltonians. Here we introduce a method for empirically determining the set of required BB pulses, that relies on quantum process tomography. In this manner an experimenter may tailor his or her BB pulses to the quantum system at hand, without having to assume a model Hamiltonian.
one particular model. It is often very difficult to identify and isolate the various sources. The result is that the model-dependent approach for overcoming decoherence breaks down when applied to realistic systems, since it inevitably fails to capture all sources. In addition, current methods tend to ignore the experimental constraints imposed by the finiteness of resources, such as the scarcity of qubits in present-day implementations of quantum computers (presently, fewer than 10 qubits). Of course, this criticism in no way diminishes the importance of the model-specific approach: it is through that approach that ground-breaking new results have been obtained which establish the in-principle possibility of overcoming decoherence. In particular, this work has led to the observation that fault tolerant quantum computation is possible in the independent errors model provided the fidelity of gate operations is above a certain threshold [30, 31, 32, 33, 34]. We focus here on the BB method and consider a paradigm that is the reverse of the model-dependent approach to decoherence-reduction: Instead of assuming a specific model of decoherence, designing a corresponding QECC, and then looking for a system that might be described to a good approximation by that model, we propose to tailor a set of BB pulses to a system, from experimentally measured decoherence data. We call this approach, which we introduced first in [26], “Empirical Bang-Bang”. Empirical BB is a phenomenological approach which forsakes a microscopic understanding of the underlying decoherence processes in favor of a direct attack on the combined effect of all sources of decoherence at once. The procedure can be iteratively optimized using a closed-loop learning algorithm [35, 36, 37, 38, 39, 40, 41]. In this manner one may take into account practical constraints imposed by the specific physical and experimental realization. That empirical BB is feasible in principle follows from two key facts: (i) It is possible to experimentally measure the superoperator (i.e., the map that propagates the density matrix) characterizing the noise in a particular system by using Quantum Process Tomography (QPT); (ii) As we show here, given knowledge of the superoperator it is possible to design a BB procedure. Thus an experiment can, in principle, provide all the information
subject matter of realisation
subject matter of realizationRealisation can refer to different things depending on the context, so the subject matter of realisation can vary. Here are some possible examples:1. Personal growth: Realisation can refer to a person's awareness or understanding of something about themselves, such as their strengths, weaknesses, values, or goals. The subject matter of realisation in personal growth could include self-awareness, self-improvement, and personal development.2. Spirituality: Realisation can also refer to a spiritual awakening or enlightenment, where a person gains a deeper understanding of the nature of reality, the self, and existence. The subject matter of realisation in spirituality could include哲学,冥想,宗教信仰, and灵性成长.3. Creativity: Realisation can refer to the process of bringing an idea or concept to fruition, such as creating a work of art, writing a book, or developing a new product. The subject matter of realisation in creativity could include创意产生,创新,和创造力的发展.4. Business: Realisation can refer to the achievement of a goal or objective, such as completing a project, meeting a sales target, or launching a new business. The subject matter of realisation in business could include目标设定,战略规划,和业务增长.These are just a few examples of the subject matter of realisation, and there are many other areas where realisation can play a role, such as education, relationships, and health. The specific subject matter of realisation will depend on the context and the individual's experiences and goals.。
量子计算
–可以验证:
0 10 1 1 0 1 01 0 0 1
NOT NOT
数学描述 量子比特 向量
物理实现
微观粒子 电磁脉冲，激光等
量子门
矩阵
量子电路示例
量子算法
量子算法基本步骤： 量子初态制备 量子算法处理（需要精心巧妙的设计） 量子测量
2014-2-16
52
决定论的 鼓吹者
拉 普 勒 斯
2014-2-16 53
2014-2-16
54
土星及其卫星
“旅行者1号”和“旅行者2号”探测器的合 成照片
目前出现的常用量子算法：
① Shor 大数质因子分解算法 (1994年)
② Grover量子搜索算法 (1996年）
③ 量子动力系统仿真算法 ④ 求解线性方程组的量子算法 (2009年)
Shor 大数分解算法
• 1994年，Peter Shor提出利用量子 计算机将大数的素 因子分解从NP问题 简化为P问题。 • Shor算法使双密钥 系统土崩瓦解（如 RSA算法），是量 子计算机理论的里 程碑。
2 2 2
概率幅 (复数)
{ x1 , x2 ,...., xn } Orthogonal Basis
(Specific State， 用列向量表示)
对叠加态的一次运算，相当于对n个 基态同时进行一次运算
Any observation will force qubit into a certain state. 观察前: superposition of 0 and 1, but not pure 0 or 1 观察后: must be 0 or 1.
• Qubit( Quantum bit ): 0 and 1 （亦 0 亦 1）
光学专业英语50句翻译
光学专业英语50句翻译1.The group's activities in this area have concentrated on the mechanicaleffects of angular momentum on a dielectric and on the quantum properties of orbital angular momentum.在这个研究领域，这个研究组主要集中在电介质中的角动量的机械效应和轨道角动量的量子属性。
2. Experimental realization of entanglement have been restricted totwo-state quantum systems. In this experiment entanglement exploiting the orbital angular momentum of photons, which are states of the electromagnetic field with phase singularities (doughnut modes).纠缠的实验认识还只停留在二维量子系统。
在这实验中，利用了光子的轨道角动量的纠缠是具有相位奇点（暗中空模式）的电磁场的状态。
3. Laguerre Gaussian modes with an index l carry an orbital angular momentum of per photon for linearly polarized light that is distinct from the angular momentum of the photons associated with their polarization对线偏振光来说，具有因子l的LG模式的每个光子能携带的轨道角动量，这是与偏振态相关的光子的角动量是截然不同的。
经典英语影视赏析
《经典英语影视赏析》课程教学大纲课程名称（中文）：经典英语影视赏析课程名称（英文）：Appreciation of English Classic Films and Television Plays课程类型：历史与文化类适用范围：贵州大学各专业本科生学时数：32 其中：实验/实践学时：课外学时：无周学时：2 学分数： 2 考核方式：考查制订单位：外国语学院制订日期：2014-07-10 执笔者：张涛【课程性质】本课程是各专业本科阶段的一门选修课程。
【教学目的】本课程旨在提高学生对语言真实度的各类视听材料的理解能力和口头表达能力。
以经典英语影视为对象，通过“视”、“听”、“说”、“写”的结合，以直观画面和情节内容为基础开展有针对性的口语训练，运用复述、总结、对话、口头概述等活动形式，提高学生的听力理解和口头表达能力，同时通过论文写作的形式，加深他们对英语国家的政治、经济、社会、文化等方面的认识和了解，从文化层面上更好的把握语言这门艺术。
【教学任务】此课程教学旨在使学生在提高英语语言能力的同时对西方的电影和文化有更多的了解和认识。
【教学内容】1.阐述当代原版电影的一般知识，即通俗地介绍电影的文化特征和艺术特征，同时比较完整地介绍英美电影的历史和特点。
2.精心挑选了在世界上具有广泛影响的影片作为读解素材，其中大部分影片曾获得过奥斯卡奖。
在理解剧情的基础上，领略电影作品从独特的美学价值和文化性格所展现出不同民族的艺术风格。
3.介绍部分当代英美电影的著名导演和演员，了解各种电影手法和创作技巧。
【教学原则和方法】教学原则：英语影视课的教学既要注意结合各门课程所学内容，打好扎实的语言基本功，又要突出语言交际能力的培养，注重培养学生的跨文化交际能力。
在教学中，要正确引导学生学习中西文化的差异，处理好欣赏和批判的关系以及如何正确接受西方文化的方法。
教学方法：课堂教学采取学生为主体、教师为主导的教学模式。
在教学中，利用音像环境所提供生动的英语语境训练听力和口语，分析英语经典影片，长、短片结合。
新编英语教程第三版李观仪Unit课文及译文参考
新编英语教程第三版李观仪Unit课⽂及译⽂参考Unit 1 恰到好处Have you ever watched a clumsy man hammering a nail into a box? He hits it first to one side, then to another, perhaps knocking it over completely, so that in the end he only gets half of it into the wood. A skillful carpenter, on the other hand, will drive the nail with a few firm, deft blows, hitting it each time squarely on the head. So with language; the good craftsman will choose words that drive home his point firmly and exactly. A word that is more or less right, a loose phrase, an ambiguous expression, a vague adjective （模糊的形容词）, will not satisfy a writer who aims at clean English. He will try always to get the word that is completely right for his purpose.你见过⼀个笨⼿笨脚的男⼈往箱⼦上钉钉⼦吗？只见他左敲敲，右敲敲，说不准还会将整个钉⼦锤翻，结果敲来敲去到头来只敲进了半截。
⽽娴熟的⽊匠就不这么⼲。
他每敲⼀下都会坚实巧妙地正对着钉头落下去，⼀钉到底。
语⾔也是如此。
2017考研《英语》基础阶段模拟试题及答案详解（2）
相关推荐：新东⽅校推荐： 1.本试卷考试时间150分钟，满分100分。
2.试卷后⾯附有参考答案，供学员测试后核对。
Section I Structure and Vocabulary In each question, decide which of the four choices given will most suitably complete the sentence if inserted at the place marked. Put your choice on the answer sheet. (20 points) 1. A variety of small clubs can provide _____ opportunities for leadership, as well as for practice in successful group dynamics. [A] durable [B] excessive [C] surplus [D] multiple 2. By turning this knob to the right you can _____ the sound from this radio. [A] amplify [B] enlarge [C] magnify [D] reinforce 3. Under the _____ confronting them it was impossible to continue the strike any longer. [A] surroundings [B] settings [C] circumstances [D] environments 4. We have the system of exploitation of man by man. [A] cancelled [B] abolished [C] refused [D] rejected 5. We shall probably never be able to _____ the exact nature of these sub-atomic particles. [A] assert [B] impart [C] ascertain [D] notify 6. This diploma _____ that you have completed high school. [A] proves [B] certifies [C] secures [D] approves 7. Up until that time, his interest had focused almost _____ on fully mastering the skills and techniques of his craft. [A] restrictively [B] radically [C] inclusively [D] exclusively 8. That sound doesn’t _____ in his language so it’s difficult for him to pronounce. [A] happen [B] take place [C] occur [D] run 9. The security guard _____ two men who were yelling in the courtroom. [A] expelled [B] propelled [C] repelled [D] dispelled 10. In most cases politicians are _____ as they seldom tell the truth. [A] credible [B] credulous [C] incredulous [D] incredible 11. He soon received promotion, for his superiors realized that he was a man of considerable _____. [A] future [B] possibility [C] ability [D] opportunity 12. Britain has the highest _____ of road traffic in the world—over 60 cars for every mile of road. [A] density [B] intensity [C] popularity [D] prosperity 13. CCTV programs are _____ by satellite to the remotest areas in the country. [A] transferred [B] transported [C] transformed [D] transmitted 14. An energy tax would curb ordinary air pollution, limit oil imports and cut the budget _____. [A] disposition [B] deficit [C] defect [D] discrepancy 15. The government will _____ a reform in the educational system. [A] initiate [B] initial [C] initiative [D] intimate 16. Estimates _____ anywhere from 600 000 to 3 million. Although the figure may vary, analysts do agree on another mater: that the number of the homeless is increasing. One of the federal government’s studies predicts that the number of the homeless will reach nearly 19 million by the end of this decade. [A] cover [B] change [C] differ [D] range 17. As time went by, computers became smaller and more powerful, and they became “personal” too, as well as institutional, with display becoming sharper and storage _____ increasing. [A] ability [B] capability [C] capacity [D] faculty 18. It soon becomes clear that the interior designer’s most important basic _____ is the function of the particular space. For example, a theater with poor sight lines, poor sound-shaping qualities, and too few entries and exits will not work for its purpose, no matter how beautifully it might be decorated. [A] care [B] concern [C] attention [D] intention 19. The purpose of non-REM sleep is even more mysterious. The new experiments, such as those _____ for the first time at a recent meeting or the society for Sleep Research in Minneapolis, suggest fascinating explanations for the purpose of non-REM sleep. [A] maintained [B] described [C] settled [D] afforded 20. Changes in the social structure may indirectly _____ juvenile crime rates. For example, changes in the economy that lead to fewer job opportunities for youth and rising unemployment in general make gainful employment increasingly difficult to obtain. [A] affect [B] reduce [C] check [D] reflect Section II Use of English Read the following text. Choose the best word (s) for each numbered blank and mark [A], [B], [C] or [D] on ANSWER SHEET. (20 points) Health implies more than physical fitness. It also implies mental and emotional well-being. An angry, frustrated, emotionally 21 person in good physical condition is not 22 healthy. Mental health, therefore, has much to do 23 how a person copes with the world as s/he exists. Many of the factors that 24 physical health also affect mental and emotional well-being. Having a good self-image means that people have positive 25 pictures and good, positive feelings about themselves, about what they are capable 26 , and about the roles they play. People with good self-images like themselves, and they are 27 like others. Having a good self-image is based 28 a realistic, as well as positive, or optimistic 29 of one’s own worth and value and capabilities. Stress is an unavoidable, necessary, and potentially healthful 30 of our society. People of all ages 31 stress. Children begin to 32 stress during prenatal development and during childbirth. Examples of stress-inducing 33 in the life of a young person are death of a pet, pressure to 34 academically, the divorce of parents, or joining a new youth group. The different ways in which individuals 35 to stress may bring healthful or unhealthy results. One person experiencing a great deal of stress may function exceptionally well 36 another may be unable to function at all. If stressful situations are continually encountered, the individual’s physical, social, and mental health are eventually affected. Satisfying social relations are vital to 37 mental and emotional health. It is believed that in order to 38 , develop, and maintain effective and fulfilling social relationships people must 39 the ability to know and trust each other, understand each other, influence, and help each other. They must also be capable of 40 conflicts in a constructive way. 21. [A] unstable [B] unsure [C] imprecise [D] impractical 22. [A] normally [B] generally [C] virtually [D] necessarily 23. [A] on [B] at [C] to [D] with 24. [A] signify [B] influence [C] predict [D] mark 25. [A] intellectual [B] sensual [C] spiritual [D] mental 26. [A] to be doing [B] with doing [C] to do [D] of doing 27. [A] able better to [B] able to better [C] better to able [D] better able to 28. [A] on [B] from [C] at [D] about 29. [A] assessment [B] decision [C] determination [D] assistance 30. [A] ideality [B] realization [C] realism [D] reality 31. [A] occur [B] engage [C] confront [D] encounter 32. [A] tolerate [B] sustain [C] experience [D] undertake 33. [A] evidence [B] accidents [C] adventures [D] events 34. [A] acquire [B] achieve [C] obtain [D] fulfill 35. [A] respond [B] return [C] retort [D] reply 36. [A] why [B] when [C] while [D] where 37. [A] sound [B] all-round [C] entire [D] whole 38. [A] illuminate [B] enunciate [C] enumerate [D] initiate 39. [A] access [B] assess [C] process [D] possess 40. [A] resolving [B] saluting [C] dissolving [D] solving Section III Reading Comprehension Read the following four texts. Answer the questions below each text by choosing [A], [B], [C] or [D] Mark your answers on ANSWER SHEET (40 points) Text 1 The period of adolescence, i.e., the period between childhood and adulthood, may be long or short, depending on social expectations and on society’s definition as to what constitutes maturity and adulthood. In primitive societies adolescence is frequently a relatively short period of time, while in industrial societies with patterns of prolonged education coupled with laws against child labor, the period of adolescence is much longer and may include most of the second decade of one’s life. Furthermore, the length of the adolescent period and the definition of adulthood status may change in a given society as social and economic conditions change. Examples of this type of change are the disappearance of the frontier in the latter part of the nineteenth century in the United States, and more universally, the industrialization of an agricultural society. In modern society, ceremonies for adolescence have lost their formal recognition and symbolic significance and there no longer is agreement as to what constitutes initiation ceremonies. Social ones have been replaced by a sequence of steps that lead to increased recognition and social status. For example, grade school graduation, high school graduation and college graduation constitute such a sequence, and while each step implies certain behavioral changes and social recognition, the significance of each depends on the socio-economic status and the educational ambition of the individual. Ceremonies for adolescence have also been replaced by legal definitions of status roles, right, privileges and responsibilities. It is during the nine years from the twelfth birthday to the twenty-first that the protective and restrictive aspects of childhood and minor status are removed and adult privileges and responsibilities are granted. The twelve-year-old is no longer considered a child and has to pay full fare for train, airplane, theater and movie tickets. Basically, the individual at this age loses childhood privileges without gaining significant adult rights. At the age of sixteen the adolescent is granted certain adult rights which increases his social status by providing him with more freedom and choices. He now can obtain a driver’s license; he can leave public schools; and he can work without the restrictions of child labor laws. At the age of eighteen the law provides adult responsibilities as well as rights; the young man can now be a soldier, but he also can marry without parental permission. At the age of twenty-one the individual obtains his full legal rights as an adult. He now can vote, he can buy liquor, he can enter into financial contracts, and he is entitled to run for public office. No additional basic rights are acquired as a function of age after majority status has been attained. None of these legal provisions determine at what point adulthood has been reached but they do point to the prolonged period of adolescence. 41. The period of adolescence is much longer in industrial societies because ________. [A] the definition of maturity has changed [B] the industrialized society is more developed [C] more education is provided and laws against child labor are made(C) [D] ceremonies for adolescence have lost their formal recognition and symbolic significance 42. Former social ceremonies that used to mark adolescence have given place to ________. [A] graduations from schools and colleges [B] social recognition [C] socio-economic status(A) [D] certain behavioral changes 43. No one can expect to fully enjoy the adulthood privileges until he is ________. [A] eleven years old [B] sixteen years old [C] twenty-one years old(C) [D] between twelve and twenty-one years old 44. Starting from 22, ________. [A] one will obtain more basic rights [B] the older one becomes, the more basic rights he will have [C] one won’t get more basic rights than when he is 21(C) [D] one will enjoy more rights granted by society 45. According to the passage, it is true that ________. [A] in the late 19th century in the United States the dividing line between adolescence and adulthood no longer existed [B] no one can marry without the permission of his parents until the age of twenty-one [C] one is considered to have reached adulthood when he has a driver’s license(A) [D] one is not free from the restrictions of child labor laws until he can join the arm Text 2 Well, no gain without pain, they say. But what about pain without gain? Everywhere you go in America, you hear tales of corporate revival. What is harder to establish is whether the productivity revolution that businessmen assume they are presiding over is for real. The official statistics are mildly discouraging. They show that, if you lump manufacturing and services together, productivity has grown on average by 1.2% since 1987. That is somewhat faster than the average during the previous decade. And since 1991, product i v i t y h a s i n c r e a s e d b y a b o u t 2 % a y e a r , w h i c h i s m o r e t h a n t w i c e t h e 1 9 7 8 - 1 9 8 7 a v e r a g e . T h e t r o u b l e i s t h a t p a r t o f t h e r e c e n t a c c e l e r a t i o n i s d u e t o t h e u s u a l r e b o u n d t h a t o c c u r s a t t h i s p o i n t i n a b u s i n e s s c y c l e , a n d s o i s n o t c o n c l u s i v e e v i d e n c e o f a r e v i v a l i n t h e u n d e r l y i n g t r e n d . T h e r e i s , a s R o b e r t R u b i n , t h e t r e a s u r y s e c r e t a r y , s a y s , a d i s j u n c t i o n b e t w e e n t h e m a s s o f b u s i n e s s a n e c d o t e t h a t p o i n t s t o a l e a p i n p r o d u c t i v i t y a n d t h e p i c t u r e r e f l e c t e d b y t h e s t a t i s t i c s . / p > p > 0 0 S o m e o f t h i s c a n b e e a s i l y e x p l a i n e d . N e w w a y s o f o r g a n i z i n g t h e w o r k p l a c e a l l t h a t r e - e n g i n e e r i n g a n d d o w n s i z i n g a r e o n l y o n e c o n t r i b u t i o n t o t h e o v e r a l l p r o d u c t i v i t y o f a n e c o n o m y , w h i c h i s d r i v e n b y m a n y o t h e r f a c t o r s s u c h a s j o i n t i n v e s t m e n t i n e q u i p m e n t a n d m a c h i n e r y , n e w t e c h n o l o g y , a n d i n v e s t m e n t i n e d u c a t i o n a n d t r a i n i n g . M o r e o v e r , m o s t o f t h e c h a n g e s t h a t c o m p a n i e s m a k e a r e i n t e n d e d t o k e e p t h e m p r o f i t a b l e , a n d t h i s n e e d n o t a l w a y s m e a n i n c r e a s i n g p r o d u c t i v i t y : s w i t c h i n g t o n e w m a r k e t s o r i m p r o v i n g q u a l i t y c a n m a t t e r j u s t a s m u c h . / p > p > 0 0 T w o o t h e r e x p l a n a t i o n s a r e m o r e s p e c u l a t i v e . F i r s t , s o m e o f t h e b u s i n e s s r e s t r u c t u r i n g o f r e c e n t y e a r s m a y h a v e b e e n i n e p t l y d o n e . S e c o n d , e v e n i f i t w a s w e l l d o n e , i t m a y h a v e s p r e a d m u c h l e s s w i d e l y t h a n p e o p l e s u p p o s e . / p > p > 0 0 L e o n a r d S c h l e s i n g e r , a H a r v a r d a c a d e m i c a n d f o r m e r c h i e f e x e c u t i v e o f A u B o n g P a i n , a r a p i d l y g r o w i n g c h a i n o f b a k e r y c a f e s , s a y s t h a t m u c h r e - e n g i ne e r i n g h a s b e e n c r u d e . I n m a n y c a s e s , h e b e l i e v e s , t h e l o s s of r e v e n u e h a s b e e ng r e a t e r th a n t h e r e d u c ti o n s i n c o s t . H i s c o l l e a g u e , M i c h a e l B e e r , s a y s t h a t f a r t o o m a n y c o m p a n i e s h a v e a p p l i e d r e - e n g i n e e r i n g i n a m e c h a n i s t i c f a s h i o n , c h o p p i n g o u t c o s t s w i t h o u t g i v i n g s u f f i c i e n t t h o u g h t t o l o n g t e r m p r o f i t a b i l i t y . B B D O s A l R o s e n s h i n e i s b l u n t e r . H e d i s m i s s e s a l o t o f t h e w o r k o f r e - e n g i n e e r i n g c o n s u l t a n t s a s m e r e r u b b i s h t h e w o r s t s o r t o f a m b u l a n c e c a s h i n g . / p > p > 0 0 4 6 . A c c o r d i n g t o t h e a u t h o r , t h e A m e r i c a n e c o n o m i c s i t u a t i o n i s _ _ _ _ _ _ _ _ . / p > p > 0 0 [ A ] n o t a s g o o d a s i t s e e m s / p > p > 0 0 [ B ] a t i t s t u r n i n g p o i n t / p > p > 0 0 [ C ] m u c h b e t t e r t h a n i t s e e m s ( A ) / p > p > 0 0 [ D ] n e a r t o c o m p l e t e r e c o v e r y / p > p > 0 0 4 7 . T h e o f f i c i a l s t a t i s t i c s o n p r o d u c t i v i t y g r o w t h _ _ _ _ _ _ _ _ . / p > p > 0 0 [ A ] e x c l u d e t h e u s u a l r e b o u n d i n a b u s i n e s s c y c l e / p > p > 0 0 [ B ] f a l l s h o r t o f b u s i n e s s m e n s a n t i c i p a t i o n / p > p > 0 0 [ C ] m e e t t h e e x p e c t a t i o n o f b u s i n e s s p e o p l e ( B ) / p > p > 0 0 [ D ] f a i l t o r e f l e c t t h e t r u e s t a t e o f e c o n o m y / p > p > 0 0 4 8 . T h e a u t h o r r a i s e s t h e q u e s t i o n w h a t a b o u t p a i n w i t h o u t g a i n ? b e c a u s e _ _ _ _ _ _ _ _ . / p > p > 0 0 [ A ] h e q u e s t i o n s t h e t r u t h o f n o g a i n w i t h o u t p a i n / p > p > 0 0 [ B ] h e d o e s n o t t h i n k t h e p r o d u c t i v i t y r e v o l u t i o n w o r k s / p > p > 0 0 [ C ] h e w o n d e r s i f t h e o f f i c i a l s t a t i s t i c s a r e m i s l e a d i n g ( B ) / p > p > 0 0 [ D ] h e h a s c o n c l u s i v e e v i d e n c e f o r t h e r e v i v a l o f b u s i n e s s e s / p > p > 0 0 4 9 . W h i c h o f t h e f o l l o w i n g s t a t e m e n t s i s N O T m e n t i o n e d i n t h e p a s s a g e ? / p > p > 0 0 [ A ] R a d i c a l r e f o r m s a r e e s s e n t i a l f o r t h e i n c r e a s e o f p r o d u c t i v i t y . / p > p > 0 0 [ B ] N e w w a y s o f o r g a n i z i n g w o r k p l a c e s m a y h e l p t o i n c r e a s e p r o d u c t i v i t y . / p > p > 0 0 [ C ] T h e r e d u c t i o n o f c o s t s i s n o t a s u r e w a y t o g a i n l o n g t e r m p r o f i t a b i l i t y . ( A ) / p > p > 0 0 [ D ] T h e c o n s u l t a n t s a r e a b u n c h o f g o o d - f o r - n o t h i n g s . / p > p > 0 0 5 0 . A c c o r d i n g t o t h e p a s s a g e , t h e a u t h o r s a t t i t u d e t o w a r d s t h e p r o d u c t i v i t y r e v o l u t i o n i n t h e U . S . A i s _ _ _ _ . / p > p > 0 0 [ A ] b i a s e d / p > p > 0 0 [ B ] o p t i m i s t i c / p > p > 0 0 [ C ] a m b i g u o u s / p >。
生命打印机英语作文500字 代复制的另一个我
全文分为作者个人简介和正文两个部分：作者个人简介：Hello everyone, I am an author dedicated to creating and sharing high-quality document templates. In this era of information overload, accurate and efficient communication has become especially important. I firmly believe that good communication can build bridges between people, playing an indispensable role in academia, career, and daily life. Therefore, I decided to invest my knowledge and skills into creating valuable documents to help people find inspiration and direction when needed.正文：生命打印机英语作文500字代复制的另一个我全文共3篇示例，供读者参考篇1The Printer of Life - Another MeAs I sit here staring at the blank computer screen, I can't help but feel a sense of unease. The essay prompt seems simple enough - write about a time when technology had a significantimpact on your life. But for me, this topic hits a little too close to home. You see, I'm not like most kids my age. I'm what some might call a "clone" - a genetic replica of another human being. And the technology that made me possible? A highly advanced 3D bio-printer, capable of creating living, breathing organisms from a mere sample of DNA.It all started about 18 years ago, when my parents found out that they were unable to conceive a child naturally. They had always dreamed of starting a family, and the news hit them hard. But they refused to give up hope. After exploring various options, they stumbled upon a cutting-edge fertility clinic that offered a revolutionary solution: cloning.At first, the idea seemed straight out of a science fiction movie. Creating a genetically identical copy of a person? It sounded like something from the realm of mad scientists and secret laboratories. But as they learned more about the process, their apprehension began to fade. The technology, while still in its infancy, had already shown promising results in animal trials. And with the guidance of experienced geneticists and ethicists, they felt assured that the procedure was safe and morally sound.The process itself was nothing short of miraculous. Using a small sample of my father's DNA, the scientists were able tocreate an embryo that was an exact genetic replica of him. This embryo was then nurtured and developed inside an artificial womb, a highly advanced incubator that simulated the conditions of a human uterus. Nine months later, I was "born" –not in the traditional sense, but rather, printed into existence by a machine that could only be described as a "life printer."As I grew older, my parents were always transparent about my origins. They never tried to hide the fact that I was a clone, and they instilled in me a deep appreciation for the technology that had made my existence possible. I remember being fascinated by the concept, poring over books and articles that explained the intricate science behind cloning and bio-printing.Of course, not everyone was as accepting of my unique circumstances. There were those who viewed cloning as unnatural, a violation of the sanctity of life. Some even went so far as to call me a "soulless copy" or a "lab experiment gone wrong." But my parents, bless their hearts, always stood by me, reminding me that I was a human being deserving of love and respect, regardless of how I came into this world.As I entered my teenage years, I began to grapple with questions of identity and self-worth. Was I truly my own person, or was I just a carbon copy of my genetic donor? Did I have asoul, or was I merely a biological machine, a product of advanced technology? These existential crises weighed heavily on my mind, and there were times when I felt lost and alone, like a stranger in my own skin.But then, something remarkable happened. During a routine medical checkup, my doctor made a startling discovery: despite being a genetic clone, my DNA had begun to diverge from that of my donor. Tiny mutations, likely caused by environmental factors and random chance, had crept in, making me ever so slightly different on a molecular level.This realization was a turning point for me. It meant that, while I may have started out as an identical copy, I was slowly but surely becoming my own unique individual. The fact that my DNA was changing, evolving, was proof that I was more than just a mindless replica. I was a living, breathing entity, capable of growth and adaptation, just like any other human being.From that moment on, I embraced my identity as a clone with newfound confidence and pride. I was no longer ashamed or apologetic about my origins. Instead, I saw them as a testament to the incredible power of human ingenuity and the boundless potential of technology.As I prepare to graduate from high school and embark on the next chapter of my life, I can't help but feel a sense of wonder and excitement. The world is rapidly advancing, and who knows what other technological marvels lie just over the horizon? Perhaps one day, cloning and bio-printing will become commonplace, giving countless individuals the opportunity to experience the miracle of life.And as for me? Well, I plan to live my life to the fullest, constantly striving to grow and evolve, to become the best version of myself that I can be. Because at the end of the day, whether I was born in the traditional sense or printed into existence by a machine, I am my own person – a unique and irreplaceable individual, with a story that is mine and mine alone to write.篇2The Life Printer: A Copied Version of MyselfAs I sit here pondering the rapid advancements in technology, a particular innovation has captured my imagination – the Life Printer. This groundbreaking device has the potential to revolutionize our understanding of life itself, and it raisesprofound questions about identity, ethics, and the boundaries of human existence.Imagine a world where you could create an exact replica of yourself, a living, breathing copy that shares your thoughts, memories, and experiences. This is the promise of the Life Printer, a technology that can scan and map every cell, every molecule, every intricate detail of your being, and then recreate it with precise accuracy. It's like having a backup copy of yourself, a contingency plan for the unpredictable twists and turns of life.At first, the idea seems almost too surreal to comprehend. How could a machine possibly replicate the complexities of a human being, with all our intricacies and idiosyncrasies? Yet, as I delve deeper into the science behind it, I'm amazed by the ingenuity and the sheer audacity of this endeavor.The process begins with a full-body scan, capturing every minute detail of your physical form, down to the molecular level. This data is then fed into the Life Printer, which uses a combination of advanced 3D printing techniques and synthetic biology to construct a replica of your body, cell by cell, tissue by tissue. It's like having a biological blueprint that can be brought to life with remarkable precision.But what truly fascinates me is the concept of transferring consciousness, of imbuing this replica with the essence of who you are. Through a process known as "mind uploading," your thoughts, memories, and experiences are encoded into a digital format and integrated into the replica's neural pathways. In theory, this would create a virtually indistinguishable copy of your consciousness, your very sense of self.As I contemplate the implications of this technology, a myriad of questions arise. Would this replica truly be "me," or merely a simulacrum, a convincing facsimile that lacks the depth and nuance of the original? If it were to diverge from my path, making different choices and accumulating unique experiences, would it still be considered a part of me, or would it become a separate entity altogether?Moreover, the ethical considerations are staggering. Should we have the power to create replicas of ourselves, essentially playing God with the very fabric of life? What safeguards would need to be in place to prevent misuse or exploitation of this technology? And what would it mean for the concept of individuality if multiple versions of ourselves were to coexist?Despite these concerns, I can't help but be drawn to the potential benefits of the Life Printer. Imagine the possibilities formedical research, where replicas could be used to test treatments and therapies without putting human lives at risk. Or consider the implications for space exploration, where a copy of an astronaut could be sent on perilous missions, ensuring the continuity of their consciousness even in the face of catastrophic events.Beyond practical applications, the Life Printer also holds profound philosophical implications. It challenges our very understanding of what it means to be human, to have a unique identity and a sense of self. If we can create replicas of ourselves, does it diminish the inherent value of our existence, or does it enhance it, offering a chance at virtual immortality?As I grapple with these questions, I realize that the Life Printer is not merely a technological marvel; it is a mirror reflecting the depths of our humanity. It forces us to confront our deepest fears and desires, our quest for understanding and our yearning for transcendence.In the end, perhaps the true value of the Life Printer lies not in the creation of physical replicas, but in the profound contemplation it inspires within us. It is a catalyst forself-reflection, a reminder that we are more than just molecules and atoms, but beings imbued with a spark of something greater– a consciousness that defies replication, a spirit that transcends the boundaries of flesh and bone.And so, as I consider the possibility of a copied version of myself, I am reminded of the inherent value of my own existence, the uniqueness of my experiences, and the profound journey that has shaped my identity. For even if a replica were to be created, it could never truly capture the essence of who I am, the ever-evolving tapestry of my life woven by the choices I make and the paths I choose to walk.The Life Printer may offer a glimpse into the future, but it is my life, my choices, and my journey that will ultimately define who I am – a singular, irreplaceable being forging their own path through the vast expanse of existence.篇3Life's Printing Machine: The Copy of MeHave you ever imagined being copied or cloned? Like a photocopy machine spitting out an exact replica of you. At first, the idea sounds crazy and maybe even a little creepy. But think about it - what if there was another version of yourself out there? Not just someone who looks like you, but a precise genetic duplicate with the same experiences, memories, and personality.Would it be like looking in a mirror or more like meeting along-lost twin?I can't stop pondering these mind-bending questions ever since our biology teacher, Mr. Jameson, introduced the concept of cloning in class last week. He explained how scientists have already successfully cloned simple organisms like bacteria and even some mammals like Dolly the sheep back in 1996. But cloning complex lifeforms like humans is still banned pretty much everywhere due to ethical concerns.At first, I thought "well duh, of course cloning humans is unethical and shouldn't be allowed." Creating duplicate copies of people just seems...unnatural. Like something out of a freaky science fiction movie. There are so many issues - religious and moral objections, the loss of human individuality and uniqueness, not to mention all the crazy legal and rights issues a clone would face. Whose child is it? Can you claim dual citizenship if your clone is from another country? Do you get double the inheritance money? My brain was spinning.But then Mr. Jameson said something that made me see the idea of human cloning in a new light. He asked us to consider the potential medical applications, like creating cloned stem cells that could cure diseases or regrow organs and limbs. Or beingable to replace tragic losses by cloning those who have passed away. Suddenly the idea didn't seem so crazy afterall.I started wondering what it would actually be like to have a clone of myself. Maybe not an exact clone, but more of a delayed twin that lags behind by X number of years developmentally. It would be like getting a preview of my future self - a genetic crystal ball. I could see the man I'll become and the life that may be in store. Or maybe the opposite and I'd get a second childhood through my clone.Imagine having a clone that was basically your younger self. Like a biological hard drive backup of your childhood that you could reload at any time. No more lost memories or forgotten experiences - your clone would have a complete record. You could re-live your glory days through their eyes. Or maybe give your clone a chance at a childhood re-do, avoiding the mistakes and struggles you went through. Implement software updates to optimize their code.Then again, would being able to shape and mold another version of yourself create unrealistic expectations or a constant temptation to try and edit your clone into the ideal person you wish you could be? To live vicariously by pushing them towards goals and achievements you failed to reach yourself? Thatsounds like it could breed resentment, rebellion, or even corrupt the uniqueness that makes each of us who we are.And what if it was the opposite - if your clone ended up more successful, happier, or more actualized than you? How would you feel having to watch a better version of yourself achieve the dreams you failed at? It could just as easily breed unhappiness, jealousy, and feelings of inadequacy. There are so many unpredictable psychological implications to being faced with an alternate reality iteration of your own identity.Despite my roller coaster of changing perspectives, I keep coming back to the same truth - we are each miracles of chance, a once-in-a-universe occurrence. Clones can never truly replace or recreate the precise genetic lottery that made each of us unique. We may share the same raw materials, but it's the tiny variations, mutations, and inexplicable combinations that make us who we are. Like a clone is a cover band, playing all the same songs, while we are the original artists.No copy, no matter how precise, can authentically replicate the original version's magic. There is only one version of you that has lived your exact life, with your precise formative experiences and indefinable personal essence. Cloning may be able to reproduce your bio-facts, but it can never recreate the grande-arof your soul's journey or life story's narrative arc. You are the Official Deluxe Edition of yourself - the clones are justRe-Releases.So while the science of cloning is fascinating and I respect its potential benefits, I don't think I'll be lining up for my own copy anytime soon. I'm still wrapping my head around being the only original edition of me that will ever exist in this universe. For better or worse, these are the cards I was dealt in life's game, and I'm strapped in to see where this crazy ride takes me. No need for a clone sitting rode-along when the REAL thing is still going full steam ahead.。
the practical reality indicates that
the practical reality indicatesthat“the practical reality indicates that”是一个英语短语，意思是“实际情况表明”。
它通常用于表达根据实际经验或观察得出的结论。
以下是一个例子，展示了如何使用这个短语来表达一个超过 400 字的观点：The practical reality indicates that climate change is a serious threat to our planet. Despite the existence of some skeptics, the scientific community has reached a consensus that human activities, particularly the emission of greenhouse gases, are the primary cause of climate change. We are witnessing the increasing occurrence of extreme weather events, rising sea levels, and the melting of glaciers. These phenomena have direct and tangible impacts on ecosystems, human societies, and economies around the world.The evidence is compelling. Numerous scientific studies have shown that the Earth's temperature is rising at an alarming rate. Ice caps are shrinking, leading to a rise in sea levels that threatens coastal cities and low-lying areas. Weather patterns are becoming more unpredictable, resulting in more frequent droughts, floods, and heatwaves. These changes have already had profound effects on agriculture, water availability, and human health.In addition to the scientific evidence, the practical reality of climate change is visible in our daily lives. We see it in the news, as communities struggle to cope with natural disasters. We feel it when heatwaves make it uncomfortable to go outside or when air pollution reaches unhealthy levels. Governments, businesses, and individuals are beginning to take action as they recognize the urgency of the situation. However, more needs to be done to address this global challenge.In conclusion, the practical reality indicates that climate change is a pressing issue that requires immediate action. We cannot afford to忽视 the scientific evidence or the visible impacts on our planet. By working together and takingdecisive steps, we can strive to mitigate the effects of climate change and create a more sustainable future for generations to come.。
感悟的英语名词
感悟的英语名词Epiphany is a profound moment of sudden and striking realization, a transformative experience that can alter one's perspective and understanding of the world. It is a powerful phenomenon that has captivated philosophers, artists, and thinkers throughout history, inspiring countless works of literature, art, and personal reflection.At its core, epiphany is a deeply personal and subjective experience, a moment of clarity that transcends the mundane and reveals a deeper truth about the nature of existence. It can come in many forms, from a sudden flash of insight that solves a longstanding problem, to a profound emotional or spiritual awakening that shifts one's fundamental beliefs and values.For some, epiphany may manifest as a moment of profound awe and wonder, a deep connection with the natural world or the cosmos that leaves them feeling small and humbled, yet infinitely connected to the greater tapestry of life. Others may experience epiphany as a moment of profound self-discovery, a sudden realization about their own identity, purpose, or place in the world.Regardless of its specific form, epiphany is characterized by a sense of clarity, a feeling of certainty and conviction that transcends the everyday. It is a moment of pure, unfiltered understanding, a glimpse into the true nature of reality that can be both exhilarating and unsettling.One of the most famous examples of epiphany in literature is the story of the ancient Greek philosopher Archimedes, who is said to have had a sudden realization while taking a bath that the volume of an irregularly shaped object could be measured by the amount of water it displaced. This "Eureka!" moment, as it has come to be known, led to a breakthrough in the field of hydrostatics and is considered a landmark moment in the history of science.Similarly, the Irish writer James Joyce, known for his innovative and experimental approach to literature, often explored the theme of epiphany in his work. In his short story "The Dead," for example, the protagonist, Gabriel Conroy, experiences a profound moment of self-awareness and emotional awakening as he reflects on the transience of life and the nature of his own existence.In the realm of art, epiphany has also played a significant role, inspiring countless works that seek to capture the essence of this transformative experience. Impressionist painters, such as ClaudeMonet and Vincent van Gogh, are known for their ability to convey a sense of fleeting, ephemeral beauty that evokes a sense of wonder and awe in the viewer.Similarly, in the field of music, composers such as Ludwig van Beethoven and Gustav Mahler have been praised for their ability to create works that elicit a profound emotional response, a sense of transcendence that can be likened to a spiritual or metaphysical experience.But epiphany is not limited to the realm of the arts and sciences; it is a universal human experience that can occur in the most ordinary of moments. A chance encounter with a stranger, a sudden connection with nature, or a moment of profound self-reflection can all trigger a transformative moment of insight and understanding.Indeed, many spiritual and religious traditions have long recognized the power of epiphany, and have developed practices and rituals aimed at cultivating this state of heightened awareness and insight. In the Christian tradition, for example, the Feast of the Epiphany commemorates the moment when the Three Wise Men recognized the divinity of the infant Jesus, a profound moment of spiritual awakening that has inspired countless works of art and literature.Similarly, in the Buddhist tradition, the concept of satori, or suddenenlightenment, is a central tenet of the religion, with practitioners seeking to achieve a state of pure, unmediated awareness that transcends the limitations of the ego and the material world.Ultimately, the power of epiphany lies in its ability to challenge and transform our understanding of the world and our place within it. It is a moment of pure, unfiltered insight that can shatter our preconceptions and open us up to new ways of seeing and understanding the world around us.Whether it manifests as a sudden flash of inspiration, a profound emotional or spiritual awakening, or a moment of deep connection with the natural world, epiphany is a powerful and transformative experience that has the potential to shape and define our lives in profound and lasting ways.。
被证实的真相英语作文
被证实的真相英语作文Title: The Confirmed Truth: Exploring the Nature of Verified Facts。
In today's interconnected world, the pursuit of truth is both essential and complex. As information flows rapidly through various channels, discerning what is genuine from what is not has become a significant challenge. However, amidst this sea of uncertainty, there are instances where truths are verified and established beyond doubt. In this essay, we delve into the significance of verified truths and their implications.Verified truths hold a unique position in human understanding. Unlike conjectures or opinions, they are backed by concrete evidence and rigorous analysis. When a truth is confirmed, it serves as a cornerstone upon which further knowledge can be built. Whether in scientific discoveries, historical events, or societal phenomena, these truths shape our collective understanding of theworld.One realm where verified truths play a crucial role isin science. Scientific inquiry relies on the meticulous process of observation, experimentation, and peer review to establish facts. When a hypothesis withstands rigorous testing and scrutiny, it graduates into a verified truth. For example, the theory of evolution by natural selection, proposed by Charles Darwin, has been corroborated by extensive evidence from various fields such as paleontology, genetics, and comparative anatomy. It stands as a confirmed truth in the scientific community, guiding ourunderstanding of the diversity of life on Earth.Similarly, in historical studies, the confirmation of truths is vital for unraveling the complexities of the past. Historians meticulously sift through primary sources, artifacts, and eyewitness accounts to piece together an accurate narrative. When historical events are verified through multiple credible sources, they become accepted truths. Take, for instance, the moon landing in 1969. Through photographs, video recordings, and testimony fromastronauts and engineers involved, the event has beenfirmly established as a historical truth, marking a significant milestone in human achievement.Moreover, in the realm of societal issues, verified truths serve as a foundation for informed decision-making and policy formulation. For instance, in public health, epidemiological studies and clinical trials provide evidence for the effectiveness of vaccines in preventing the spread of infectious diseases. When these findings are verified through peer review and replicated in diverse populations, they form the basis for vaccination programs that save millions of lives globally.However, the journey to establishing verified truths is not without challenges. In an era of misinformation and fake news, discerning fact from fiction has become increasingly arduous. The proliferation of social media platforms and the rapid dissemination of unverified information have led to widespread confusion and distrust. Consequently, it is imperative to cultivate critical thinking skills and promote media literacy to navigate thislandscape effectively.Furthermore, the process of verifying truths itself can be subject to bias and manipulation. Confirmation bias, where individuals seek out information that confirms their preconceived beliefs, can hinder impartial analysis. Additionally, external pressures from vested interests may influence the dissemination of information, leading to the distortion or suppression of verified truths. Hence, maintaining the integrity of the verification process is paramount to upholding the credibility of established facts.In conclusion, verified truths occupy a pivotal role in human knowledge and understanding. Whether in science, history, or societal issues, they provide a solidfoundation upon which progress and innovation thrive. However, in an age marked by information overload and misinformation, the quest for truth requires vigilance, critical inquiry, and a commitment to intellectualintegrity. By upholding the principles of evidence-based reasoning and peer review, we can navigate the complexitiesof the modern world and uncover the enduring truths that shape our collective consciousness.。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
a r X i v :0705.3056v 1 [p h y s i c s .p l a sm-p h ] 21 M a y 2007Experimental Realization of an Exact Solution to the Vlasov Equations for anExpanding Plasmaha 1,P.Gupta 1,C.E.Simien 1,H.Gao 1,J.Castro 1,T.Pohl 2,and T.C.Killian 11Rice University,Department of Physics and Astronomy,Houston,TX,USA 770052ITAMP,Harvard-Smithsonian Center for Astrophysics,60Garden Street,Cambridge,MA,USA 02138(Dated:February 1,2008)We study the expansion of ultracold neutral plasmas in the regime in which inelastic collisions are negligible.The plasma expands due to the thermal pressure of the electrons,and for an initial spherically symmetric Gaussian density profile,the expansion is self-similar.Measurements of the plasma size and ion kinetic energy using fluorescence imaging and spectroscopy show that the expansion follows an analytic solution of the Vlasov equations for an adiabatically expanding plasma.Exactly solvable problems are rare in physics and serve as ideal models that provide a starting point for under-standing more complex systems.Here,we report the ex-perimental realization of a laser-produced plasma whose dynamics can be described by an exact analytic solution to the Vlasov equations [1,2],which are central equations in the kinetic theory of plasmas.Expansion into a sur-rounding vacuum is fundamentally important and typ-ically dominates the dynamics of plasmas created with pulsed lasers [3],such as in experiments pursuing inertial confinement fusion [4],x-ray lasers [5],or the production of energetic (>MeV)ions through irradiation of solids [6,7],thin foils [8,9,10,11,12,13,14,15],clusters [16].We study plasma expansion with ultracold neutral plasmas (UNPs)[17,18],which are created by pho-toioinizing laser-cooled strontium atoms [19]just above the ionization threshold.These systems occupy a new regime of neutral plasma physics,and their well-controlled initial conditions and relatively slow dynamics have enabled precise studies of strongly coupled plasma properties [20,21].Here we use fluorescence imaging and spectroscopy for the first time on these systems.These powerful diagnostics allows us to apply the advantages of UNPs to a new class of important problems.The investigation of plasma expansion dates back many decades [22,23].Recently,exact solutions for spa-tially finite plasmas expanding into vacuum were identi-fied for a 1-dimensional plasmas [1]and later extended to 3-dimensions [2,24].This work was motivated by plas-mas produced with short-pulse lasers.The Vlasov equations,along with Poisson’s equation,describe the evolution of the electron (α=e )and ion (α=i )distribution functions,f α(r ,v ).The Vlasov equations neglect radiative processes and collisional phe-nomena such as electron-ion thermalization and three-body recombination [25],but this formalism describes many types plasmas and is part of the foundation of ki-netic theory.Among broad classes of general analytic solutions to the Vlasov equations [24],UNPs realize a particular so-lution,that even describes collisional systems and is valid for a quasi-neutral plasma with spherical Gaussian dis-tribution functionsf α∝exp−r 22k B T α.(1)Quasi-neutrality is defined by n e ≈n i ,where the elec-tron and ion densities are n α(r )= d v f α(r ,v ).T αare the electron and ion temperatures,and the local average velocity varies in space according to u (r ,t )=γ(t )r .The temperatures must scale as σ2T α=constant [1],which is expected for adiabatic cooling in a spherically symmetric UNP [26,28].Under these conditions,the plasma dynamics is givenby T α(t )=T α(0)/(1+t 2/τ2exp ),where the char-acteristic expansion time τexp is given by τexp =k Bτ2exp[T e (t )+T i (t )]+T i (t )(3)describe the evolution of the characteristic plasma size and ion velocity,which are important experimental ob-servables.We define the rms 1-dimensional ion velocitym i∇n (r,t )m i σ(t )2r .(4)The simplification implied by the last equality is only valid for a spherical Gaussian plasma,and the linearity in r preserves the shape of the distribution functions.Plasmas produced with solid targets,foils,and clus-ters are often quasi-neutral and well-described by theVlasov equations,and electrons cool adiabatically dur-ing much of their evolution,but experimental condi-tions studied are typically very complicated and evolve extremely rapidly,which frustrates detailed comparison between experiment and theory.Final ion kinetic en-ergy distributions have been shown to agree with simple models[15,16],but in general,these systems lack the Gaussian distribution functions necessary to realize the analytically describable self-similar expansion.For appropriate initial conditions,UNPs[17]fulfill the requirements for the analytic solution.UNPs have ion temperatures of about1K determined by disorder-induced heating[20,27].Electron temperatures ranging from1to1000K are set by the detuning,E e,of the ionization laser above threshold.The peak densities are on the order of1015m−3,and the profile follows that of the laser-cooled atom cloud,which we adjust to have a spherically symmetric Gaussian.The photoionization pulse length(∼10ns)is much less than the expansion time scale(∼10µs).The electron distribution equilibrates locally within 100ns and globally within1µs after photoionization [26,28].This ensures a Gaussian electron distribution function at the start of the expansion.Despite these very rapid electron-electron collisions the corresponding collision integral vanishes for the spherically symmetric, Gaussian velocity distribution eq.(1).Hence the highlycollisional UNP consideredhere provides an ideal modelsystem for truly collisionless plasmas behavior.Ions reach local thermal equilibrium within a few 100ns[20].They do not equilibrate globally on the time scale of the expansion[21],but the ions are so cold com-pared to the electrons,that the lack of a global ion tem-perature does not cause any significant deviation from the exact solution.The low ion temperature also implies that the ions form a strongly coupledfluid[20,29],which, however,negligibly affects the plasma expansion[26]. The analytic expansion solution has been discussed previously for UNPs[26,28,30],and it has been checked against average terminal ion expansion velocities[31]and measured electron temperatures[32]that qualitatively affirm the importance of adiabatic cooling for appropri-ate initial conditions.The lack of spatial and temporal resolution,available here,however prevented conclusive tests of the analytic predictions.Cummings et al.[33,34] adapted the formalism of[26,28,30]and used light-scattering from a small region of the plasma to study the expansion of ultracold plasmas with an elongated as-pect ratio,but they found significant deviations from the predictions of the model that perhaps arose because the condition of spherical symmetry was not fulfilled.To demonstrate that ultracold neutral plasmas can re-alize the analytic expansion solution,we willfirst de-scribe our diagnostic and show that the plasma remains Gaussian during its expansion.Then we will show the size variation and ion velocity are given by Eqs.2and3plasmazyimaging opticsUNPs.The correlation be-tween position and expansion velocity(red arrows)produces a striped image when the Doppler-shift due to expansion ex-ceeds the Doppler shift associated with thermal ion velocity.Figure1shows a schematic of thefluorescence imag-ing experiment.A laser beam that is near resonance with the2S1/2−2P1/2transition in Sr+atλ=422nm prop-agates alongˆy and illuminates the plasma.Fluorescence in a perpendicular direction(ˆz)is imaged with a1:1re-lay telescope onto an image-intensified CCD camera.The 422nm light is typically applied in a1µs pulse to pro-vide temporal resolution,and the intensity is only a few mW/cm2,which is low enough to avoid optical pumping to the metastable2D3/2state.A general expression for thefluorescence isF(ν,x,y)∝ ds1γeff/2π 2×dz n(r)2πσD[T i,therm(r)]exp − s−(ν0+νy exp(r)) 23FIG.2:Evolution of the areal density for a plasma with 1.6±0.1×108ions,2E e/3k B=48±3K,andσ(0)= 1.3±0.1mm.The arial density(arbitrary units)is found by summing together50images taken at equally spaced fre-quencies that fully cover the ion resonance.The Gaussian fits(solid line)to linear cuts show that the expansion is self-similar.The time indicated is the evolution time since plasma creation.The right-hand axes show that the differences be-tween data andfit are small. proportional to the areal plasma density, n(x,y,z)dz, which for a Gaussian density distribution should take theform n areal(x,y)=√4FIG.4:(A)Sample spectrum and(B)evolution of the rms ion velocity(v i,rms).(A)Spectrum for2E e/3k B=105±3K, peak ion density of3×1015m−3,and plasma evolution time of 3µs.Fits to a Voigt profile provide v i,rms.(B)The velocity evolution isfit well by Eq.3with T e(0)as afit parameter,σ(0)determined from the cloud size measurements(Fig.3), and T i(0)taken from the theoretical expression for disorder-induced heating[20,27].tron pressure drives the plasma expansion and electron thermal energy is converted into directed radial ion veloc-ity.Asσincreases and the electrons cool adiabatically, the acceleration decreases(Eq.4)and the ions eventu-ally reach terminal velocity when essentially all electron kinetic energy is transferred to the ions.Our measured density profiles(Fig.3)confirm the va-lidity of Eq.3,which shows that the ion acceleration is sensitive at all times to the instantaneous electron tem-perature and width of the plasma.Agreement between experiment and theory for both the size evolution and the ion velocity dynamics hence demonstrates that T e(t)also follows the dynamics predicted by the analytical solution to the Vlasov equations.We have demonstrated a plasma in which the expan-sion matches an analytic solution to the Vlasov equa-tions[2]proposed as a basic model for the dynamics of quasineutral laser-produced plasmas.To realize this situation experimentally,it is necessary to create UNPs with a spherical Gaussian density distribution.Rela-tively high initial electron temperature and low density are also required to avoid collisional and radiative pro-cesses[28,31,38,39]that would heat electrons or lead to electron-ion equilibration.In future studies,devia-tions from the model can be used to study these colli-sional processes when they become important.The ex-pansion dynamics shown here provide a general tool for developing a greater understanding and intuition for the expansion of plasmas.This work was supported by the National Science Foundation(Grant PHY-0355069and a grant for the Institute of Theoretical Atomic,Molecular and Optical Physics(ITAMP)at Harvard University and Smithso-nian Astrophysical Observatory)and the David and Lu-cille Packard Foundation.[1]A.V.Baitin and K.M.Kuzanyan,J.Plasma Phys.59,83(1998).[2]D.S.Dorozhkina and V.E.Semenov,Phys.Rev.Lett.81,2691(1998).[3]M.D.Perry and G.Mourou,Science264,917(1994).[4]J.Lindl,Phys.Plasmas2,3933(1995).[5]H.Daido,Rep.Prog.Phys.65,1513(2002).[6]E.L.Clark et al.,Phys.Rev.Lett.85,1654(2000).[7]R.A.Snavely et al.,Phys.Rev.Lett.85,2945(2000).[8]A.Maksimchuk et al.,Phys.Rev.Lett.84,4108(2000).[9]J.Badziak et al.,Phys.Rev.Lett.87,215001(2001).[10]A.J.Mackinnon et al.,Phys.Rev.Lett.88,215006(2002).[11]M.Hegelich,et al.,Phys.Rev.Lett.89,085002(2002).[12]M.Kaluza et al.,Phys.Rev.Lett.93,045003(2004).[13]J.Fuchs et al.,Phys.Rev.Lett.94,045004(2005).[14]L.Romagnani et al.,Phys.Rev.Lett.95,195001(2005).[15]M.Murakami et al.,Phys.Plasmas12,062706(2005).[16]D.R.Symes,M.Hohenberger,A.Henig,and T.Ditmire,Phys.Rev.Lett.98,123401(2007).[17]T.C.Killian,S.Kulin,S.D.Bergeson,L.A.Orozco,C.Orzel,and S.L.Rolston,Phys.Rev.Lett.83,4776(1999).[18]T.C.Killian,Science316,705(2007).[19]S.B.Nagel et al.,Phys.Rev.A67,011401(2003).[20]C.E.Simien et al.,Phys.Rev.Lett.92,143001(2004).[21]Y.C.Chen et al.,Phys.Rev.Lett.93,265003(2004).[22]A.V.Gurevich,L.V.Pariskaya,and L.P.Pitaievskii,Sov.Phys.JETP22,449(1966).[23]C.Sack and H.Schamel,Phys.Rep.156,311(1987).[24]V.F.Kovalev and V.Y.Bychenkov,Phys.Rev.Lett.90,185004(2003).[25]P.Mansbach and J.Keck,Phys.Rev.181,275(1969).[26]T.Pohl,T.Pattard,and J.M.Rost,Phys.Rev.A70,033416(2004).[27]M.S.Murillo,Phys.Rev.Lett.87,115003(2001).[28]F.Robicheaux and J.D.Hanson,Phys.Plasmas10,2217(2003).[29]S.Ichimuru,Rev.Mod.Phys.54,1017(1982).[30]F.Robicheaux and J.D.Hanson,Phys.Rev.Lett.88,55002(2002).[31]S.Kulin,T.C.Killian,S.D.Bergeson,and S.L.Rolston,Phys.Rev.Lett.85,318(2000).[32]J.L.Roberts,C.D.Fertig,M.J.Lim,and S.L.Rolston,Phys.Rev.Lett.92,253003(2004).[33]E.A.Cummings,J.E.Daily,D.S.Durfee,and S.D.Bergeson,Phys.Rev.Lett95,235001(2005).[34]E.A.Cummings,J.E.Daily,D.S.Durfee,and S.D.Bergeson,Phys.Plasmas12,123501(2005).[35]T.Grismayer and P.Mora,Phys.Plasmas13,032103(2006).[36]P.Mora,Phys.Plasmas12,112102(2005).[37]A.E.Kaplan,B.Y.Dubetsky,and P.Shkolnikow,Phys.Rev.Lett.91,143401(2003).[38]S.G.Kuzmin and T.M.O’Neil,Phys.Plasmas9,3743(2002).[39]S.Mazevet,L.A.Collins,and J.D.Kress,Phys.Rev.Lett.88,55001(2002).。