Quantum Phase Transition in Quasi-two-dimensional Heisenberg Antiferromagnet with Single-Ion Ani

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第一届凝聚态物理会议

第一届凝聚态物理会议The 1st Conference on Condensed Matter Physics2015年7月15日- 17日清华大学目录01 会议概况02 组织委员会04 会议日程•总日程•大会报告•分会场报告•海报会场会议概况为了配合凝聚态物理在中国的迅速发展和国际地位的全面提升，进一步加强国内科研工作者在不同前沿领域的交流，推进国内和国际在凝聚态物理领域的相互交流和合作，为青年学生和研究人员学习和了解国际前沿进展创造更广泛的交流平台，拟定在过去已经成功举办了13届的“凝聚态理论与材料计算国际会议”系列会议的基础上，拓宽会议的主题，特别是加强凝聚态物理实验和理论的交流与融合，于2015年7月15日－17日在北京举办“第一届凝聚态物理会议”年会。

2015年第一届凝聚态物理会议是由清华大学物理系、中国科学院物理研究所、北京大学物理学院、量子物质科学协同创新中心联合主办。

这是国内首次在凝聚态物理方面举办的大型学术交流会。

本次会议是凝聚态理论与材料计算国际会议的延续和拓展，旨在增进国内外物理学者的学术交流，分享前沿科研成果，提高国内凝聚态物理的科研水平，扩大学术声誉。

第一届凝聚态物理会议将于2015年7月15日－17日在清华大学举行。

会议主题包括：拓扑量子态和多铁性、超导和多体物理、能源和低维物理、Quantum many-body theory and statistical physics、计算凝聚态物理、量子信息及其它与凝聚态物理的交叉领域等六个主题。

本次会议共设30个专题分会，将以大会特邀报告、分会特邀报告、口头报告和张贴海报等形式进行交流探讨。

组织委员会主办单位•清华大学物理系•中国科学院物理研究所•北京大学物理学院•量子物质科学协同创新中心顾问委员会：（按姓氏拼音序）崔田、杜瑞瑞、冯世平、龚新高、解士杰、李东海、李建新、林海青、李树深、陆卫、卢仲毅、吕力、沈保根、沈健、沈志勋、苏刚、王恩哥、王孝群、王玉鹏、向涛、薛其坤、张富春、张振宇组织委员会•清华大学物理系：陈曦、薛其坤•中科院物理研究所：胡江平、戴希、方忠、丁洪、周兴江、向涛•北京大学物理学院：谢心澄分会场负责人•拓扑量子态和多铁性：胡江平、陈曦、吕力、戴希、翁红明、寇谡鹏、吴从军•超导和多体物理：孙力玲、杨义峰、刘俊明、雒建林、袁辉球、李永庆、万歆、周毅•能源和低维物理：张振宇、李泓、陈弘、赵怀周、张远波•Quantum many-body theory and statistical physics：孟子扬、张广铭、郭文安、姚宏•计算凝聚态物理：姚裕贵、段文晖、龚新高、孟胜•量子信息及其它与凝聚态物理的交叉领域：范珩、田琳、翟荟、崔晓玲会议协调人•清华大学物理系：任俊（总协调人）•中国科学院物理研究所：齐建为、刘青梅•会务组：黄文艳、唐林、井小苏、周丹、骆洁、甘翠云、付德永、杨红、肖琳、胡文婷赞助单位•清华大学物理系•量子物质科学协同创新中心•中国科学院物理研究所•北京大学物理学院2015年第一届凝聚态物理会议分会场主题：A.拓扑量子态和多铁性A1拓扑半金属IA2拓扑半金属IIA3拓扑超导体和Majorana 费米子A4多铁性材料模拟与计算A5多铁性体系B.超导和多体物理B1铬基和锰基超导体B2极端条件下的超导行为B3铁基超导B4凝聚物质的激发态和动力学理论和实验B5重费米子物理C.能源和低维物理C1锂电池中的物理C2二维材料C3二维电子系统中的物理C4硅烯的最新进展C5热电中的新物理D.Quantum many-body theory and statistical physicsD1 Recent developments in strongly correlated quantum systems ID2 Recent developments in strongly correlated quantum systems IID3 Recent developments in strongly correlated quantum systems IIID4 Recent developments in strongly correlated quantum systems IVD5 Recent developments in strongly correlated quantum systems V注意事项：为了尊重外籍邀请报告人，如无特殊情况，D分会场报告请用英文。

Dissipative quantum phase transition in a quantum dot

a r X i v :c o n d -m a t /0602019v 2 [c o n d -m a t .m e s -h a l l ] 14 F eb 2006Dissipative quantum phase transition in a quantum dotL´a szl´o Borda 1,Gergely Zar´a nd 1,2,and D.Goldhaber-Gordon 31Department of Theoretical Physics and Research Group “Theory of Condensed Matter”of the Hungarian Academy of Sciences,Budapest University of Technology and Economics,Budafoki ´u t 8.H-1521Hungary2Institut f¨u r Theoretische Festk¨o rperphysik,Universit¨a t Karlsruhe,76128Karlsruhe,Germany3Physics Department and Geballe Laboratory for Advanced Materials,Stanford University,Stanford CA 94305,USA(Dated:February 5,2008)We study the transport properties of a quantum dot (QD)with highly resistive gate electrodes,and show that the QD displays a quantum phase transition analogous to the famous dissipative phase transition ﬁrst identiﬁed by S.Chakravarty [Phys.Rev.Lett.49,681-684(1982)];for a review see [A.J.Leggett et al.,Rev.Mod.Phys.59,1(1987)].At temperature T =0,the charge on the central island of a conventional QD changes smoothly as a function of gate voltage,due to quantum ﬂuctuations.However,for suﬃciently large gate resistance charge ﬂuctuations on the island can freeze out even at the degeneracy point,causing the charge on the island to change in sharp steps as a function of gate voltage.For R g <R C the steps remain smeared out by quantum ﬂuctuations.The Coulomb blockade peaks in conductance display anomalous scaling at intermediate temperatures,and at very low temperatures a sharp step develops in the QD conductance.The single electron transistor (SET)is one of the mostbasic mesoscopic devices:A conducting island or quan-tum dot is attached by tunnel barriers to two leads and a capacitively-coupled gate electrode sets the number of electrons on the dot.For low enough temperatures,T ≪E C ,charge ﬂuctuations of the dot are suppressed except when the gate is tuned to make two charge states nearly degenerate.At these “charge degeneracy points”the charge on the dot strongly ﬂuctuates.For typical metallic SETs with a very large number of tunneling modes quantum ﬂuctuations of the charge turn out to be suppressed at low temperatures [1,2,3].For semi-conducting SETs with single mode junctions ,however,quantum ﬂuctuations of the charge are important and broaden out the charging steps at low T :In the limit of vanishing level spacing,δǫ→0charge ﬂuctuations are described by the two-channel Kondo model [4],while for T ≪δǫone recovers the so-called “mixed valence”regime of the Anderson model [5].In the above discussion we neglected the eﬀect of Ohmic dissipation in the lead electrodes.While this has been extensively studied for SETs with a very large number of tunneling modes [2],there is much less known about the eﬀects of dissipation in the Kondo regime:In a recent paper Le Hur showed that,assuming a contin-uum of quantum levels on the SET and a single tunnel mode,coupling to a dissipative bath drastically modiﬁes the results of Ref.[4]:large enough dissipation drives a Kosterlitz-Thouless-type phase transition and leads to a complete suppression of charge ﬂuctuations even at the degeneracy point [6,7].However,for most semiconduct-ing devices the level spacing δǫcannot be neglected in comparison to temperature,and spin ﬂuctuations must also be considered.Here we shall therefore investigate the eﬀects of dissipation at temperatures far below the level spacing on the dot,T ≪δǫ,a more realistic low-temperature limit for typical semiconductor SETs.As weshow below,a dissipation-induced quantum phase tran-sition takes place for T ≪δǫas well,although with dif-ferent and more complicated properties due to the in-terplay of charge and spin ﬂuctuations,and at a larger dissipation strength (gate resistance)than that needed for δǫ→0[6,7,8].In this T ≪δǫregime,the coupling of the quantum dot to the gate voltage is usually described by the Hamil-tonian,H dot =E C σd †σd σ−n g 2,(1)where E C ≡e 2/2C Σdenotes the charging energy,withC Σthe total capacitance of the dot,and e the electron charge.We retain only one single-particle level d ,and we assume that it is empty or singly occupied,depend-ing on the dimensionless gate voltage,n g [9].Assuming weak coupling between the dot and the source and drain electrodes,charge transfer can be described within the tunneling approximation,H tun =V σdǫσd †σψσ(ǫ)+h .c . ,(2)were ψσ(ǫ)annihilates an appropriate linear combinationof left and right lead electrons of energy ǫthat hybridize with the dot state d σ,and satisﬁes the anticommutation relation {ψσ(ǫ),ψσ′(ǫ′)}=δσσ′δ(ǫ−ǫ′)[10].Throughout this paper we assume that the quantum dot is close to symmetrical but our analysis carries over easily to asym-metrical dots as well.Eqs.(1)and (2)are thought to provide a satisfactory description of the SET for T ≪δǫfor most experimen-tal situations studied so far,including the Kondo regime [5].However,Eq.(1)does not account for the relax-ation of electrostatic charges in the nearby electrodes:in reality,when an electron tunnels into the dot,an elec-trostatic charge δQ =eC g /C Σis also generated on thegate.Transferring this charge from the outside world to the gate electrode throughashunt resistorrequirestime,andcreatesdissipation [11].Consequently,tunnelingbe-tweendotandleadswill be suppressed by Anderson’s orthogonality catastrophe.The simplest way to account for this shunt resistance is to add a term [1]H diss=λ ˆn −24C 2ΣR g2i,α,βS i (ψ†ασiαβψβ),(6)where the spin operators denote S i =1dl=14v +...,(7)djdl =−31dl=˜∆−32πδǫ≈v 2=22−ln α(0)c +13v +v 2+...,and the transition isof Kosterlitz-Thouless type [19]:On the localized side,α>α(0)c (or Γ<Γ(0)c ),at the degeneracy point the height δG of Coulomb blockade peaks scales to zero as a power law [18],δG (T )δǫ 2α∞−1(12)with G Q the quantum conductance.On the metallicside,on the other hand,quantum ﬂuctuations always dominate and preserve conductance even at T =0,though near the transition the conductance shows a non-monotonic behavior:δG (T )ﬁrst slowly decays and then starts to increase below a temperature T ∗that vanishes exponentially as one approaches the phase transition,αFIG.1:Schematic phase diagram of the SET in the presence of dissipative coupling.αc denotes the critical value ofα, whileα(0)c is its value obtained by neglecting the generated exchange coupling j.Forα>αc there is a phase transition from n =0to n =1,while in the more familiar situation of weak dissipation there is a crossover.T∗≈δǫexp{−π/2(α(0)c2−α2)1/2},untilﬁnally a mixed valence state with a large conductance is formed at a temperature T∗∗∼T∗2/δǫ≪T∗.For the critical value ofα,δG decays to zero logarithmically,1δG(T,α=α(0)c)∼G Q4−∆/δε0.51n >FIG.2:Charging steps,computed using NRG for a relatively small hybridization.For these parameters T K /δǫ∼10−10at α≈αc .Inset:Temperature dependence of the occu-pation number ˆn at the critical dissipation,α≈αc ,for ∆/δǫ=−0.0028800,−0.0028300,−0.0028200,−0.0028198,−0.0028190,−0.0028140,−0.0028000(bottom to top).order of α≈1can be reached in this way.The SET can be then tuned through the quantum phase transition by either continuously changing the tunneling V ,or by depleting a second 2DEG positioned below the dot and thereby changing the total capacitance of the dot and hence the value of α.In summary,we have shown that suﬃciently strong dis-sipation in the gate electrodes can drive the SET through a quantum phase transition into a state where charge de-grees of freedom become localized while spin ﬂuctuations lead to a Kondo eﬀect.In this state both the conductance and the expectation value of the charge on the SET dis-play a jump at temperature T =0,while at higher tem-1010−510−310−1ω/δε10−210−110R e [G (ω)]/G 0−0.0042400−0.0042450−0.0042460−0.0042500∆/δε=FIG.3:T =0AC conductivity of the SET in the localized phase for α=0.75and Γ/δǫ=0.5(G 0∼G Q ).peratures an anomalous scaling of the Coulomb blockade peaks is predicted.We estimate that this quantum phase transition can be detected by coupling a highly resistive gate electrode to a SET in a shallow 2DEG.We are grateful to P.Simon,K.Le Hur,Q.Si,O.Sauret,A.Zaikin and Y.Nazarov for valuable discus-sions.This research has been supported by NSF-MTA-OTKA Grant No.INT-0130446,Hungarian Grants Nos.T046303,NF061726,D048665,and T048782,the Euro-pean ’Spintronics’RTN HPRN-CT-2002-00302,and at Stanford University by NSF CAREER Award DMR-0349354and a Packard Fellowship.L.B.is a grantee of the J´a nos Bolyai Scholarship.[1]For early reviews,see e.g.G.Sch¨o n and A.D.Zaikin,Phys.Rep.198,237(1990),or G.-L.Ingold and Y.V.Nazarov,in:Single Charge Tunneling,ed.by H.Grabert and M.Devoret,NATO ASI Series B,vol.294,pp.21-107(Plenum,1992).[2]See also:S.V.Panyukov and A.D.Zaikin,Phys.Rev.Lett.67,3168(1991);G.Falci,G.Sch¨o n,and G.T.Zi-manyi,Phys.Rev.Lett.74,3257(1995);M.Kindermann and Yu.V.Nazarov,Phys.Rev.Lett.91,136802(2003).[3]P.Joyez et al.,Phys.Rev.Lett.79,1349-1352(1997);D.Chouvaev et al.,Phys.Rev.B 59,10599(1999);C.Wallisser et al.,Phys.Rev.B 66,125314(2002).[4]K.A.Matveev,Phys.Rev.B 51,1743(1995).[5]T.A.Costi,Phys.Rev.B 64,241310(R)(2001).[6]K.Le Hur,Phys.Rev.Lett.92,196804(2004).[7]L.Borda,G.Zarand,and P.Simon,Phys.Rev.B 72,155311(2005);M.-R.Li,K.Le Hur,and W.Hofstetter,Phys.Rev.Lett.95,086406(2005).[8]It has been argued earlier based on calculations for a sim-ple spinless model that the dissipative transition should survive even in this limit:K.Le Hur and M.-R.Li Phys.Rev.B 72,073305(2005).[9]The analysis would be very similar for the transition be-tween a singly-and doubly-occupied state.[10]With this normalization V ∼̺1/20,with ̺0the density ofstates in the leads.[11]We shall neglect dissipation on source and drain elec-trodes which we assume not to be highly resistive.[12]The constant 2/3appears naturally along the calcula-tions and is related to the (classical)expectation value of the charge at the degeneracy point.[13]M.H.Devoret et al.,Phys.Rev.Lett.64,1824(1990);S.M.Girvin,et al.,Phys.Rev.Lett.64,3183-3186(1990).[14]J.von Delft and H.Schoeller,Annalen Phys.7,225(1998).[15]J.Cardy,Scaling and Renormalization in StatisticalPhysics (Cambridge University Press,Cambridge,1996).[16]Q.Si and G.Kotliar,Phys.Rev.Lett.70,3143(1993).[17]The scaling equation for ˜∆in Ref.16breaks SU(2)in-variance,and some care is needed.[18]G.Zar´a nd et al.,unpublished.[19]J.M.Kosterlitz,J.Phys.C 7,1046(1974).[20]H.R.Krishna-murthy et al.,Phys.Rev.B 21,1003(1980).[21]G.Kotliar and Q.Si,Phys.Rev.B 53,12373(1996).5[22]P.Nozi`e res,J.Low Temp.Phys.17,31(1974).[23]Slightly below the critical couplingα(0)c,the tunnelingv is suppressed so much that the Kondo scale becomes larger than the mixed valence scale T∗∗.At the Kondo ﬁxed point,however,the tunneling becomes marginal,and smaller values ofαare suﬃcient to localize charge ﬂuctuations.Note that Eq.(7)is inappropriate in this Kondo regime,and a strong coupling analysis is needed to obtain the above picture.。

量子点太阳能电池技术概况

量子点太阳能电池技术概况作者：孟庆波来源：《新材料产业》 2013年第3期文/ 孟庆波中国科学院物理研究所一、概述1．量子点太阳能电池概念近年来，量子点太阳能电池已成为国际上的研究热点。

此类电池的主要特点是以无机半导体纳米晶（量子点）作为吸光材料。

量子点（QuantumDots,QDs）是准零维(quasi-zerodimensional)纳米材料。

粗略地说，量子点3个维度的尺寸均小于块体材料激子的德布罗意波长。

从外观上看，量子点恰似一极小的点状物，其内部电子在各方向上的运动都受到局限，即量子局限效应(quantum confinementeffect)特别显著。

量子点有很多的优点：①吸光范围可以通过调节颗粒的组分和尺寸来获得，并且可以从可见光到红外光；②化学稳定性好；③合成过程简单，是低成本的吸光材料；④具有高消光系数和本征偶极矩，电池的吸光层可以制备得极薄，因此可进一步降低电池成本；⑤相对于体相半导体材料，采用量子点可以更容易实现电子给体和受体材料的能级匹配，这对于获得高效太阳能电池十分关键。

更重要的是，量子点可以吸收高能光子并且一个光子可以产生多个电子-空穴对（多激子效应），理论上预测的量子点电池效率可以达到44%。

因此，量子点太阳能电池常常被称作第3代太阳能电池，具有巨大的发展前景。

2．量子点太阳能电池分类目前，量子点太阳能电池主要分为肖特基太阳能电池、耗尽型异质结太阳能电池、极薄层太阳能电池、体相异质结太阳能电池、有机-无机异质结太阳能电池和量子点敏化太阳能电池等，具体说明如下：（1）肖特基量子点太阳能电池肖特基量子点太阳能电池的结构非常简单，在导电玻璃上涂覆量子点层，再在量子点层上加载金属阴极即可。

它的优点在于：第一，结构简单，量子点层可以通过喷雾涂覆或者喷墨打印的方式获得，有利于工业化生产；第二，量子点层的厚度仅为100nm左右，可以进一步降低电池成本。

但是，肖特基量子点太阳能电池有一些缺点：首先，少数载流子（这里为电子）必须在到达目标电极前穿过整个量子点层，易产生较严重的复合；其次，金属-半导体界面的缺陷态导致费米能级的钉扎现象，降低了电池的开路电压，所以肖特基量子点太阳能电池的开路电压一般较低。

激光专业英语

2011年技术物理学院08级（激光方向）专业英语翻译重点！！！作者：邵晨宇Electromagnetic电磁的principle原则principal主要的macroscopic宏观的microscopic微观的differential微分vector矢量scalar标量permittivity介电常数photons光子oscillation振动density of states态密度dimensionality维数transverse wave横波dipole moment偶极矩diode 二极管mono-chromatic单色temporal时间的spatial空间的velocity速度wave packet波包be perpendicular to线垂直be nomal to线面垂直isotropic各向同性的anistropic各向异性的vacuum真空assumption假设semiconductor半导体nonmagnetic非磁性的considerable大量的ultraviolet紫外的diamagnetic抗磁的paramagnetic顺磁的antiparamagnetic反铁磁的ferro-magnetic铁磁的negligible可忽略的conductivity电导率intrinsic本征的inequality不等式infrared红外的weakly doped弱掺杂heavily doped重掺杂a second derivative in time对时间二阶导数vanish消失tensor张量refractive index折射率crucial主要的quantum mechanics 量子力学transition probability跃迁几率delve研究infinite无限的relevant相关的thermodynamic equilibrium热力学平衡（动态热平衡）fermions费米子bosons波色子potential barrier势垒standing wave驻波travelling wave行波degeneracy简并converge收敛diverge发散phonons声子singularity奇点（奇异值）vector potential向量式partical-wave dualism波粒二象性homogeneous均匀的elliptic椭圆的reasonable公平的合理的reflector反射器characteristic特性prerequisite必要条件quadratic二次的predominantly最重要的gaussian beams高斯光束azimuth方位角evolve推到spot size光斑尺寸radius of curvature曲率半径convention管理hyperbole双曲线hyperboloid双曲面radii半径asymptote渐近线apex顶点rigorous精确地manifestation体现表明wave diffraction波衍射aperture孔径complex beam radius复光束半径lenslike medium类透镜介质be adjacent to与之相邻confocal beam共焦光束a unity determinant单位行列式waveguide波导illustration说明induction归纳symmetric 对称的steady-state稳态be consistent with与之一致solid curves实线dashed curves虚线be identical to相同eigenvalue本征值noteworthy关注的counteract抵消reinforce加强the modal dispersion模式色散the group velocity dispersion群速度色散channel波段repetition rate重复率overlap重叠intuition直觉material dispersion材料色散information capacity信息量feed into 注入derive from由之产生semi-intuitive半直觉intermode mixing模式混合pulse duration脉宽mechanism原理dissipate损耗designate by命名为to a large extent在很大程度上etalon 标准具archetype圆形interferometer干涉计be attributed to归因于roundtrip一个往返infinite geometric progression无穷几何级数conservation of energy能量守恒free spectral range自由光谱区reflection coefficient（fraction of the intensity reflected）反射系数transmission coefficient（fraction of the intensity transmitted）透射系数optical resonator光学谐振腔unity 归一optical spectrum analyzer光谱分析grequency separations频率间隔scanning interferometer扫描干涉仪sweep移动replica复制品ambiguity不确定simultaneous同步的longitudinal laser mode纵模denominator分母finesse精细度the limiting resolution极限分辨率the width of a transmission bandpass透射带宽collimated beam线性光束noncollimated beam非线性光束transient condition瞬态情况spherical mirror 球面镜locus（loci）轨迹exponential factor指数因子radian弧度configuration不举intercept截断back and forth反复spatical mode空间模式algebra代数in practice在实际中symmetrical对称的a symmetrical conforal resonator对称共焦谐振腔criteria准则concentric同心的biperiodic lens sequence双周期透镜组序列stable solution稳态解equivalent lens等效透镜verge 边缘self-consistent自洽reference plane参考平面off-axis离轴shaded area阴影区clear area空白区perturbation扰动evolution渐变decay减弱unimodual matrix单位矩阵discrepancy相位差longitudinal mode index纵模指数resonance共振quantum electronics量子电子学phenomenon现象exploit利用spontaneous emission自发辐射initial初始的thermodynamic热力学inphase同相位的population inversion粒子数反转transparent透明的threshold阈值predominate over占主导地位的monochromaticity单色性spatical and temporal coherence时空相干性by virtue of利用directionality方向性superposition叠加pump rate泵浦速率shunt分流corona breakdown电晕击穿audacity畅通无阻versatile用途广泛的photoelectric effect光电效应quantum detector 量子探测器quantum efficiency量子效率vacuum photodiode真空光电二极管photoelectric work function光电功函数cathode阴极anode阳极formidable苛刻的恶光的irrespective无关的impinge撞击in turn依次capacitance电容photomultiplier光电信增管photoconductor光敏电阻junction photodiode结型光电二极管avalanche photodiode雪崩二极管shot noise 散粒噪声thermal noise热噪声1.In this chapter we consider Maxwell’s equations and what they reveal about the propagation of light in vacuum and in matter. We introduce the concept of photons and present their density of states.Since the density of states is a rather important property，not only for photons，we approach this quantity in a rather general way. We will use the density of states later also for other(quasi-) particles including systems of reduced dimensionality.In addition,we introduce the occupation probability of these states for various groups of particles.在本章中，我们讨论麦克斯韦方程和他们显示的有关光在真空中传播的问题。

光学英语对照

Paraxial ray 近轴光线 interference 干涉image formation 成像 diffraction 衍射optical axis光轴 Polarization 偏振optical component 光学元件 electromagnetic wave 电磁波 homogenous medium均匀介质 monochromatic wave 单色波 Propagation传播 polychromatic wave 多色波 Fermat’s principle 费马原理plane wave 平面波Reflection反射 spherical wave 球面波Refraction折射 amplitude 振幅Transmission 透射 phase 相位refractive index折射率 Wavenumber 波数Normal法线，正交的 wavefront 波前Total reflection全反射 Wavevector 波矢Surface 表面 envelope 包络Interface界面 Wave envelope 波包critical angle临界角 Wave packet theory 波包理论 prism棱镜 quarter wave plate 四分之一波片 Splitter分束器 Grating 光栅convex lens 凸透镜 absorption 吸收Resolution分辨率 phase shift 相移concave boundary凹形边界 Spectrometer 分光计，光谱仪 focal length焦距 spectroscopy 光谱学 antireflection coating减反覆层，抗反射膜superposition principle 叠加原理 Fiber光纤 Optical intensity 光强Cladding 包层 interferometer 干涉仪Perfect image完善像 Scattering 散射Object(image) space物(像)空间 Free space 自由空间 magnification 放大率 spacial filter 空间滤波器 Parallel plate平行平板 fourier-transforming 傅立叶变换focal plane焦平面 inverse fourier-transforming 逆傅立叶变换stop光阑 transfer function 传递函数pupil光瞳 Magnitude 量值，值，大小ray tracing 光线追迹 Pinhole 针孔Incident beam入射光 Hologram 全息图Ultraviolet 紫外的 holography 全息术Visible 可见的 holographic reconstruction 全息再现Infrared 红外的 holographic recording 全息记录 scalar function 标量函数 volume holography 体全息术vector function 矢量函数 reference wave 参考波Wavelength 波长 object wave 物波frequency 频率 coherent light 相干光Angular frequency 角频率Radian 弧度bragg condition 布拉格（布喇格）条件Electric flux density 电通量密度 conjugate 共扼 Magnetic flux density 磁通量密度 rainbow hologram 彩虹全息图 electric displacement 电位移 Exposure 曝光 Free space 自由空间Emulsion 感光乳剂 Medium 介质slit 缝 Linear 线性的Orthogonal 正交的 Disperisive 色散的Monochromatic 单色的 Nondispersive 非色散的Vibrate 振动 Isotropic 各向同性的Apparatus 器械，仪器 Anisotropic 各向异性的Minimal 最小的 refractive index 折射率Fluctuation 波动，起伏 absorption coefficient 吸收系数 illuminate 照明 phase velocity 相速度Transparency 透明物 group velocity 群速度Planar 平面的 Attenuation 衰减Three-dimensinal 三维的 alumina 氧化铝Electric field 电场 Pulse 脉冲Magnetic field 磁场 Delay 延迟Electromagnetic field 电磁场 Integrated-optical device 集成光学器件Spectrum 光谱 Coherent 相干的Maxwell equation 麦克斯韦方程 incoherent 非相干的Permittivity 介电系数 Photon 光子Permeability 磁导率 amplifier 放大器transverse electromagnetic wave 横电磁波energy level 能级Polarization 偏振 atomic 原子的linearly polarized wave 线偏振波 Transition 跃迁circularly polarized light 圆偏振光elliptically polarized light 椭圆偏振光polarization-maintaining fiber 偏振保持光纤，保偏光纤Polarizer 偏光器 single-mode fiber 单模光纤Polarizing beamsplitter 偏振分束器 multimode fiber 多模光纤brewster angle 布儒斯特角 modal dispersion 模式色散Symmetry 对称 Dispersion-shifted fiber 色散位移光纤biaxial crystal 双轴晶体 step-index fiber 阶跃折射率光纤 Uniaxial crystal 单轴晶体 graded-index fiber 渐变折射率光纤 ordinary index 寻常折射率 numerical aperture（NA）数值孔径 extraordinary light 异常光 Speckle 散斑double refraction 双折射Birefringence 双折射Calcite 方解石Quartz 石英Dichroic 二向色的, 二色性的Linewidth 线宽 Threshold 阈值thermal equilibrium 热平衡 resonator 共振器，共振腔 Nonequlibrium 非平衡 pulse train 脉冲序列population inversion 粒子数反转 Period 周期Pump 泵浦，抽运 mode locking/mode locked 锁模 Feedback 反馈 Q-switch Q开关Loss 损耗 Modulate 调制Gain 增益 longitudinal mode 纵模saturated gain coefficient 饱和增益系数Free-running mode 自由振动模式spatial hole burning 空间烧孔 correlation 相关，关联 eigenfunction 本征函数 statistical distribution 统计分布 harmonic oscillator 谐振子 Random 随机的 quanta of energy 能量量子 probability 概率 Particle 粒子poisson distribution 泊松分布 Momentum 动量Orthonormal 标准正交的，规范正交的 uncertainty relation 不确定关系 orthogonal 正交的，垂直的 Heisenberg 海森堡quantum theory 量子理论 squeezed light 压缩光photon flux 光子通量 Coherent light 相干光entangle 纠缠 frequency conversion 频率转换 entangled photon pairs 纠缠光子对 Down conversion 下转换Bell inequality 贝尔不等式 Parametric process 参量过程 Teleportation 隐形传态、离物传态 Nonparametric process 非参量过程quantum cryptography 量子密码 Spontaneous Parametric Down conversion 自发参量下转换Second harmonic generation 二次谐波产生quasi-phase match 准相位匹配Sun-frequency generation 和频产生 Phase mismatch 相位失配 difference-frequency generation 差频产生Optical parametric amplification 光学参量放大Optical parametric oscillation 光学参量振荡Quality factor 品质因子nonlinear susceptibility 非线性极化率Polarization 极化强度。

Quantum_Dot

定义量子点(quantum dot)是准零维(quasi-zero-dimensional)的纳米材料，由少量的原子所构成。

粗略地说，量子点三个维度的尺寸都在100纳米(nm)以下，外观恰似一极小的点状物，其内部电子在各方向上的运动都受到局限，所以量子局限效应(quantum confinement effect)特别显著。

研究历史现代量子点技术要追溯到上世纪70年代中期，它是为了解决全球能源危机而发展起来的。

通过光电化学研究，开发出半导体与液体之间的结合面，以利用纳米晶体颗粒优良的体表面积比来产生能量。

初期研究始于上世体80年代早期2个实验室的科学家:贝尔实验室的Louis E.Brus博士和前苏联Yoffe研究所的AlexanderEfros和A.I.Ekimov博士。

Brus博士与同事发现不同大小的硫化镉颗粒可产生不同的颜色。

这个工作对了解量子限域效应很有帮助，该效应解释了量子点大小和颜色之间的相互关系，也同时也为量子点的应用铺平了道路。

1997年以来，随着量子点制备技术的不断提高，量子点己越来越可能应用于生物学研究。

1995年，AlivisatosI.Z.]和Nie两个研究小组首次将量子点作为生物荧光标记，并且应用于活细胞体系，他们解决了如何将量子点溶于水溶液，以及量子点如何通过表面的活性基团与生物大分子偶联的问题，由此掀起了量子点的研究热潮。

主要性质(1)量子点的荧光寿命长。

有机荧光染料的荧光寿命一般仅为几纳秒(这与很多生物样本的自发荧光衰减的时间相当）。

而量子点的荧光寿命可持续数十纳秒（20ns一50ns)，这使得当光激发后，大多数的自发荧光已经衰变子点荧光仍然存在，此时即可得到无背景干扰的荧光信号。

(2)生物相容性好。

量子点经过各种化学修饰之后，可以进行特异性连接，其细胞毒性低，对生物体危害小，可进行生物活体标记和检测。

(3)量子点具有很好的光稳定性。

量子点的荧光强度比最常用的有机荧光材料“罗丹明6G”高20倍，它的稳定性更是“罗丹明6G”的100倍以上。

利用多氟丙烯酸酯添加剂提升准二维钙钛矿发光二极管性能

物理化学学报Acta Phys. -Chim. Sin. 2023, 39 (12), 2301024 (1 of 8)Received: January 14, 2023; Revised: February 13, 2023; Accepted: February 14, 2023; Published online: February 28, 2023. *Correspondingauthors.Emails:****************.cn(P.C.);*******************.cn(Q.C.);*******************.cn(L.C.).The project was supported by the Ministry of Science and Technology of China (2021YFA1202802), the National Natural Science Foundation of China (21875280, 21991150, 21991153, 22022205), the CAS Project for Young Scientists in Basic Research (YSBR-054), the Special Foundation for Carbon Peak Neutralization Technology Innovation Program of Jiangsu Province (BE2022026) and the Natural Science Foundation Project of Chongqing (CSTB2022NSCQ-MSX0438). 科技部国家重点研发计划(2021YFA1202802), 国家自然科学基金(21875280, 21991150, 21991153, 22022205), 中国科学院稳定支持基础研究领域青年团队计划(YSBR-054), 江苏省碳达峰碳中和科技创新专项资金(BE2022026)和重庆市自然科学基金(CSTB2022NSCQ-MSX0438)资助项目© Editorial office of Acta Physico-Chimica Sinica[Article]doi: 10.3866/PKU.WHXB202301024Incorporation of a Polyfluorinated Acrylate Additive for High-Performance Quasi-2D Perovskite Light-Emitting DiodesTao Zhang 1,2, Simin Gong 3, Ping Chen 3,*, Qi Chen 1,2,*, Liwei Chen 2,4,*1 School of Nano-Tech and Nano-Bionics, University of Science and Technology of China, Hefei 230026, China.2 i -Lab, CAS Key Laboratory of Nanophotonic Materials and Devices, Suzhou Institute of Nano-Tech and Nano-Bionics,Chinese Academy of Sciences, Suzhou 215123, Jiangsu Province, China.3 Chongqing Key Laboratory of Micro&Nano Structure Optoelectronics, School of Physical Science and Technology, Southwest University, Chongqing 400715, China.4 In-situ Center for Physical Sciences, School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.Abstract: Quasi-two-dimensional (quasi-2D) perovskites are one of the most promising luminescent layer candidates for light-emitting diodes (LEDs) because of their excellent optoelectronic properties such as large exciton binding energy, efficient energy transfer, high photoluminescence quantum yield, and adjustable band gap. However, the formation of a large number of low-dimensional phases and surface/interface defects during solution processing of quasi-two-dimensionalperovskite films gives rise to an increase in non-radiative recombination, resulting in deteriorated light-emitting diode performance. It is highly desirable to simultaneously realize low-dimensional phase formation inhibition and surface/interface defect passivation during quasi-two-dimensional perovskite film formation. Herein, we report a multifunctional additive, 1,6-bis(acryloyloxy)-2,2,3,3,4,4,5,5-octafluorohexane (OFHDODA), which has strong physical and chemical interactions with the PEA 2Cs 2Pb 3Br 10 precursor that can effectively suppress non-radiative recombination in the perovskite films. The distinct C ＝C peak in the Fourier transform infrared spectroscopy (FTIR) spectra and the F 1s peak in the X-ray photoelectron spectroscopy (XPS) spectra showed that OFHDODA molecules were successfully incorporated into the perovskite films, and most OFHDODA molecules existed as monomers. With the addition of OFHDODA, the photoluminescence quantum yield (PLQY) of the perovskite film increased from 19.7% to 49.0%, and the PL emission wavelength red-shifted from 508 to 511 nm. It was demonstrated that hydrogen bond interactions between the polyfluorine structure and PEA + can tune perovskite crystallization dynamics, which inhibit the formation of low-dimensional phases, as shown by the reduced peak intensities at 403 nm (n = 1), 434 nm (n = 2), and 465 nm (n = 3) in the absorption spectra. The strong Lewis base moiety of the ester groups passivates the unsaturated Pb 2+ defects at the surface and grain boundaries of the perovskite films, as evidenced by the Pb 4f peak shift in the XPS spectra and the C ＝O shift in the FTIR spectra. The trap-filled limiting voltage (V TFL ) decreased in both hole-only and electron-only devices, which also proves the reduction of Pb 2+ defects. At the optimized OFHDODA concentration, the scanning electron microscopy (SEM) and atomic force microscopy (AFM) results from the perovskite films show lower roughness and smoother surface potential, which promotes superior interfacial contact. As a result, perovskite LEDs with a device structure of indium tin oxide glass/poly (9-vinylcarbazole)/perovskite/1,3,5-tris(1-phenyl-1H -benzimidazol-2-yl)benzene/8-hydroxyquinolinolato-lithium/Al exhibitedanimproved maximum external quantum efficiency (EQE) from 8.55% to 13.76%, improved maximum brightness from 16400 to 17620 cd∙m−2, and increased lifetime from 8 min to 12 min. This process provides an effective way to suppress non-radiative recombination in quasi-2D perovskites via additive molecular structure design, leading to superior electroluminescence performance.Key Words: Quasi-two-dimensional perovskite; Non-radiative recombination; Low-dimensional inhibition;Defect passivation; Polyfluorinated acrylate additive利用多氟丙烯酸酯添加剂提升准二维钙钛矿发光二极管性能张涛1,2，龚思敏3，陈平3*，陈琪1,2,*，陈立桅2,4,*1中国科学技术大学纳米技术与纳米仿生学院，合肥2300262中国科学院苏州纳米技术与纳米仿生研究所创新实验室，中科院纳米光子材料与器件重点实验室，江苏苏州215123 3西南大学物理科学与技术学院，微纳结构光电子学重庆市重点实验室，重庆4007154上海交通大学化学与化工学院物质科学原位中心，上海200240摘要：准二维钙钛矿由于具有较大的激子结合能和高效的能量转移等优势，在发光二极管(light-emitting diodes，LED)中的应用前景被广泛看好。

工程流体力学中英翻译

fluctuatingstress
脉动应力
fluid
流体
fluid dynamics
流体动力学
fluid field
流场
fluid machinery
流体机械
fluid mechanics
流体力学
fluid particle
流体质点
fluid statics
流体静力学
free surface
自由表面
比热比
real fluid
粘性流体
real gas
真实气体，实际气体
rectangular coordinate system
直角坐标系
reduced Navier-Stokes equation
简化纳维—斯托克斯方程
Reynoldsnumber
雷诺数
adiabatic flow
绝热流动
airfoil
翼型
angle of attack
冲角
angular velocity
角速度
apparent shear stresses
表面剪切应力
apparent stresses
表面应力
Archimedes law
阿基米德定律
atmospheric pressure
临界雷诺数
critical speed of sound
临界声速
critical state
临界状态
cross section
横截面
curvature radius
曲率半径
curved shock
曲面波
cylindrical coordinate system
柱坐标系

拓扑绝缘体二维纳米结构与器件

doi:10.3866/PKU.WHXB 201208312[Review]物理化学学报(Wuli Huaxue Xuebao )Acta Phys.-Chim.Sin.2012,28(10),2423-2435October Received:July 27,2012;Revised:August 31,2012;Published on Web:August 31,2012.∗Corresponding authors.PENG Hai-Lin,Email:hlpeng@.LIU Zhong-Fan,Email:zfliu@.The project was supported by the National Natural Science Foundation of China (51121091,21173004,11104003)and National Basic Research Program of China (2011CB921904).国家自然科学基金(51121091,21173004,11104003)和国家重大科学研究计划(2011CB921904)资助项目ⒸEditorial office of Acta Physico-Chimica Sinica拓扑绝缘体二维纳米结构与器件李辉1,2彭海琳1,*刘忠范1,*(1北京大学化学与分子工程学院,北京大学纳米化学研究中心,北京100871;2中国科学院电工研究所,中国科学院太阳能热利用及光伏系统重点实验室,北京100190)摘要:拓扑绝缘体是一种全新的量子功能材料,具有绝缘性体能带结构和受时间反演对称性保护的自旋分辨的金属表面态,属于Dirac 粒子系统,将在新原理纳电子器件、自旋器件、量子计算、表面催化和清洁能源等方面有广泛的应用前景.理论和实验相继证实Sb 2Te 3,Bi 2Se 3和Bi 2Te 3单晶具有较大的体能隙和单一Dirac 锥表面态,已经迅速成为了拓扑绝缘体研究中的热点材料.然而,利用传统的高温烧结法所制成的拓扑绝缘体单晶块体样品常存在大量本征缺陷并被严重掺杂,拓扑表面态的新奇性质很容易被体载流子掩盖.拓扑绝缘体二维纳米结构具有超高比表面积和能带结构的可调控性,能显著降低体态载流子的比例和凸显拓扑表面态,并易于制备高结晶质量的单晶样品,各种低维异质结构以及平面器件.近年来,我们一直致力于发展拓扑绝缘体二维纳米结构的控制生长方法和物性研究.我们发展了拓扑绝缘体二维纳米结构的范德华外延方法,实现了高质量大比表面积的拓扑绝缘体二维纳米结构的可控制备,并实现了定点与定向的表面生长.开展拓扑绝缘体二维纳米结构的谱学研究,利用角分辨光电子能谱直接观察到拓扑绝缘体狄拉克锥形的表面电子能带结构,发现了拉曼强度与位移随层数的依赖关系.设计并构建拓扑绝缘体纳米结构器件,系统研究其新奇物性,观测到拓扑绝缘体Bi 2Se 3表面态的Aharonov-Bohm (AB)量子干涉效应等新奇量子现象,通过栅电压实现了拓扑绝缘体纳米薄片化学势的调控,并将拓扑绝缘体纳米结构应用于柔性透明导电薄膜.本文首先简单介绍拓扑绝缘体的发展现状,然后系统介绍我们开展的拓扑绝缘体二维纳米结构的范德华外延生长、谱学、电学输运特性以及透明柔性导电薄膜应用的研究,最后对该领域所面临的机遇和挑战进行简要的展望.关键词:拓扑绝缘体;狄拉克费米子;纳米结构;范德华外延;柔性透明导电薄膜中图分类号:O641Two-Dimensional Nanostructures of Topological Insulators andTheir DevicesLI Hui 1,2PENG Hai-Lin 1,*LIU Zhong-Fan 1,*(1Centre for Nanochemistry (CNC),College of Chemistry and Molecular Engineering,Peking University,Beijing 100871,P .R.China ;2Key Laboratory of Solar Thermal Energy and Photovoltaic System of Chinese Academy of Sciences,Institute of Electrical Engineering,Chinese Academy of Sciences,Beijing 100190,P .R.China )Abstract:Three-dimensional (3D)topological insulators are a new state of quantum matter that are insulating in the bulk but have current-carrying massless Dirac surface states.Nanostructured topological insulators,such as quasi-two-dimensional (2D)nanoribbons,nanoplates,and ultrathin films with extremely large surface-to-volume ratios,distinct edge/surface effects,and unique physicochemical properties,can have a large impact on fundamental research as well as in applications such as electronics,spintronics,photonics,and the energy sciences.Few-layer topological insulator nanostructures have very large2423Acta Phys.⁃Chim.Sin.2012V ol.28surface-to-volume ratios that can significantly enhance the contribution of exotic surface states,and their unique quasi-2D geometry also facilitates their integration into functional devices for manipulation and manufacturing.Here,we present our recent results on the controlled growth of quasi-2D nanostructures of topological insulators,as well as their novel functional devices.High quality quasi-2D nanostructures ofBi2Se3and Bi2Te3topological insulators have been synthesized by vapor-phase growth.Ultra-thin nanoplates of the topological insulators with uniform thickness down to a single layer have been grown on various substrates,including conductive graphene.A facile,high-yield method has been developed for growing single-crystal nanoplate arrays of Bi2Se3and Bi2Te3with well-aligned orientations,controlled thickness,and specific placement on mica substrates by van der Waals epitaxy.A systematic spectroscopic study,including angle-resolved photoemission spectroscopy(ARPES),micro-Raman spectroscopy,and micro-infrared spectroscopy,was carried out to investigate the quasi-2D nanostructuresof topological insulators.Pronounced Aharonov-Bohm(AB)interference effects were observed in the topological insulator nanoribbons,providing direct transport evidence of the robust,conducting surface states.Transport measurements of a single nanoplate device,with a high-k dielectric top gate,showed a significant decrease in the carrier concentration and a large tuning of the chemical potential with electrical gating.We also present the first experimental demonstration of near-infrared transparent flexible electrodes based on few-layer topological insulator Bi2Se3nanostructures that was epitaxially grown on amica substrate by van der Waals epitaxy.Topological insulator nanostructures show promise as transparent flexible electrodes because of their good near-infrared transparency and excellent conductivity,which is robust against surface contamination and bending.Our studies suggest that quasi-2D nanostructures of topological insulators show promise for future electronic and optoelectronic applications.Key Words:Topological insulator;Dirac fermion;Nanostructure;van der Waals epitaxy;Transparent flexible electrode1引言拓扑绝缘体是一类正在凝聚态物理、固体化学与材料领域掀起科学风暴的“明星”材料.1-3作为一种全新的量子物质,拓扑绝缘体不同于传统意义上的绝缘体和金属,其体材料是有能隙的绝缘体,而其表面是无能隙的金属态.4-10因内禀的自旋轨道相互作用,拓扑绝缘体的金属性表面态与因表面未饱和键或者是表面重构导致的表面态不同,具有线性色散关系且自旋与动量满足特定的手性关系.拓扑表面态形成一种无有效质量的二维电子气,受到很严格的拓扑保护,不会因为外来的扰动而失去金属性,具有独特的自旋和输运性质,载流子可在表面无散射、无能量损耗地传导.在基础物理研究上,拓扑绝缘体可以用来探索和发现新奇的量子效应,如量子化的反常霍尔效应、马拉约那(Majorana)费米子等.4,5此外,拓扑绝缘体可以用来发展未来新型量子功能材料,将在新原理纳电子器件、自旋电子器件、自容错的拓扑量子计算、表面催化及清洁能源等方面有着巨大的应用前景.1-5因此,在短短几年内,拓扑绝缘体的研究正在世界范围内蓬勃兴起.量子自旋霍尔相和狄拉克费米子这两个奇异的量子相在拓扑绝缘体中是高度耦合的.4-6通过对具有自旋-轨道耦合作用的样品施加纵向电场,会产生横向自旋流,即自旋向上和向下的电子分别沿横向相反的方向运动,从而在横向边界产生自旋积累,这种自旋也会产生量子霍尔效应,这就是量子自旋霍尔效应.6,10,11拓扑绝缘体内禀的自旋轨道相互作用起到了类似外场的作用,导致自旋流在表面无散射的传导(图1A和1B).2006年,斯坦福大学的Zhang等6首先提出在二维拓扑绝缘体HgTe/CdTe 量子阱体系可以实现量子自旋霍尔效应的理论预言.2007年,量子自旋霍尔效应在HgTe/CdTe量子阱器件上得到实验证实,10这一科研成果被Science 杂志评为2007年十大科学进展之一.随后,研究人员用电压探针证明自旋电流可在HgTe/CdTe量子阱样品的边界出现,而且无需外界施加的磁场.12继二维拓扑绝缘体之后,Kane,7Moore8和Zhang9等小组分别独立地理论预言了兼具绝缘体态和金属表面态的三维拓扑绝缘体的存在.其中Kane等13预测了Bi1-x Sb x合金是三维拓扑绝缘体.2008-2009年,普林斯顿大学的Hasan小组14,15率先从实验上证实了Bi1-x Sb x合金具有三维拓扑绝缘体的性质.他们利用角分辨光电子能谱研究了Bi1-x Sb x合金的体能带和表面能带结构,发现Bi1-x Sb x合金具有复杂的表面态2424李辉等:拓扑绝缘体二维纳米结构与器件No.10结构,表面具有奇数个狄拉克点.寻找体能隙大、表面态结构简单、组成为化学计量比、存在非常稳定、且容易合成的晶态拓扑绝缘体材料成为了物理学家、材料学家及化学家关注的焦点.2009年,Zhang 等16理论预言了三方相的V 2VI 3化合物(Sb 2Te 3,Bi 2Se 3,Bi 2Te 3)是三维拓扑绝缘体,其表面布里渊区k=0的Γ点具有单一的无能隙的狄拉克锥.这些理论预测被同时进行的实验所证实.普林斯顿大学的Hasan 小组17和斯坦福大学的Shen 小组18分别利用角分辨光电子能谱在Bi 2Se 3和Bi 2Te 3单晶中观察到了单个狄拉克锥型表面态的存在.此外,该类材料的体态存在能隙,比如Bi 2Se 3的体能隙约为0.3eV (等价于3600K),远远超出室温能量尺度,这说明有可能实现室温低能耗的自旋电子器件.尽管不断有理论预言新的拓扑绝缘体的存在,比如half-Heusler 和chalcopyrite 三元化合物等家族中被预测存在着大量拓扑绝缘体材料,19-23V 2VI 3晶体材料(Sb 2Te 3,Bi 2Se 3,Bi 2Te 3)仍然是目前的研究热点.然而,相对于常规绝缘体而言,拓扑绝缘体V 2VI 3的体能隙并不大,目前体能隙最大的拓扑绝缘体Bi 2Se 3也才0.3eV .事实上,通常利用高温烧结方法制备的单晶块体样品具有很大的本征缺陷密度并被严重掺杂,样品的费米能级往往位于体相的导带或者价带中,很难实现其体态的本征绝缘.由于单晶块体样品中的体相原子远多于其表面态原子,样品的电学特性将完全由大量的体态载流子所支配,这将制约深入研究拓扑绝缘体这种新的量子态及其器件物理.24拓扑绝缘体表面态本征物性的研究备受关注,是决定拓扑绝缘体未来的研究和应用潜力的关键问题之一.科学工作者正通过外场调控和化学掺杂等方法来调控拓扑绝缘体的费米能级位置,使费米能级只与表面态相交,以降低体态载流子的影响,凸显表面态相关的新奇物理现象.对于常用的拓扑绝缘体单晶块体样品,因样品的厚度远远大于电场的穿透深度,难以利用外场来调控单晶块体样品的费米能级.人们主要采取掺杂与化学改性对单晶块体样品的费米能级进行调控,比如在Bi 2Te 3中掺入Sn 和在Bi 2Se 3中掺入Ca 、Sb 、Mg 、Pb 等元素可以实现费米能级的调控.18,25-31虽然单晶块体样品的掺杂可改变其能带结构,但往往同时也降低了晶体的质量和载流子的迁移率,32导致掺杂的块体材料的电学测量结果并不乐观.比如,Ong 等33对体态绝缘的拓扑绝缘体Ca x Bi 2-x Se 3单晶进行了低温电磁测量,在毫米级大小的单晶样品中的电磁测量中发现一种反常的电磁涨落,其振幅远远大于普适电导涨落.分析结果表明这种涨落现象仍然来源于体相杂质载流子,而不是拓扑表面态.考虑到Ran 等34最近的理论计算预言——拓扑绝缘体晶体中存在的线位错将形成一维拓扑态,Ong 等33推测他们测得的这种电磁涨落可能与体材料的晶格位错等缺陷有关.由以上的分析可知,高质量材料的可控制备依然是拓扑绝缘体研究领域亟待解决的关键科学问题.发展新颖的材料制备方法制备高质量的拓扑绝缘体材料尤为重要.相比块体单晶材料,拓扑绝缘体的纳米材料尤其是二维纳米结构(如纳米带、纳米薄片、薄膜等)更具优势:24(1)纳米材料具有大的比表面积,其比表面积随样品尺寸的变小而显著增大;(2)少量的掺杂或化学改性可能显著调控拓扑绝缘体纳米材料的电学性质;(3)高质量的拓扑绝缘体低维纳米材料具有明确的晶体结构和组分,是构筑复杂纳米结构与纳米器件的理想基元,借助现代表征和测量技术,可以方便地研究器件中存在的材料和界面问题;(4)拓扑绝缘体材料的载流子浓度可利用纳米薄片或薄膜场效应管的场效应来调控,并可以制备成低维异质结构以及各种平面器件,有助图1(A,B)三维拓扑绝缘体的绝缘性体态和金属表面态的示意图;(C)三维拓扑绝缘体层状Bi 2X 3(X=Se,Te)的晶体结构图Fig.1(A,B)Schematic explanation for the reason why the surface of the insulating bulk exhibits metallic state due to polarized spins in three-dimensional topological insulator;(C)layered crystal structure of three-dimensional topological insulator Bi 2X 3(X=Se,Te)2425Acta Phys.⁃Chim.Sin.2012V ol.28于器件加工和集成.迄今为止,人们已经发展了“自上而下”(Top-Down)和“自下而上”(Bottom-Up)两大类方法来制备拓扑绝缘体二维纳米材料.3,35“自上而下”是从单晶块体样品中通过机械剥离或者化学剥离的方法获得单层或少层二维纳米材料,包括:显微机械剥离方法、36,37化学插层方法、38,39通过原子力显微镜(AFM)针尖进行剥离的方法40等.“自下而上”是通过化学反应从原子或者分子尺度上合成单层或少层二维纳米材料,包括分子束外延(MBE)、41-45化学气相沉积(CVD)、24,46,58物理气相沉积(PVD)、47-49湿化学合成50,51等.2009年开始,清华大学薛其坤教授的研究团队首次建立了在不同单晶基底上高质量拓扑绝缘体薄膜的MBE生长动力学,52实现了体相绝缘的拓扑绝缘体Bi2Se3薄膜的外延生长,并利用STM观察到MBE薄膜表面电子在原子台阶和杂质附近散射形成的驻波以及表面金属态的朗道量子化现象.53北京大学的彭海琳与斯坦福大学Cui等人合作,通过气-液-固(VLS)生长机制,利用简单易得的CVD装置制备了高质量的拓扑绝缘体纳米带,发现构筑具有大的比表面积的纳米结构可以有效降低体态载流子的贡献,并通过电学输运测量,首次观测到与拓扑绝缘体Bi2Se3表面电子态相关的Aharonov-Bohm(AB)量子干涉效应,证实了拓扑绝缘体中能产生AB效应的表面态电子波的存在.24这一工作给拓扑绝缘体在电学测量实验上的研究带来了新的转机,推动了拓扑绝缘体的实验进展.54随后,科研工作者迅速展开了拓扑绝缘体Bi2Se3、Bi2Te3和Sb2Te3纳米结构的制备和电学输运研究.2010年,Jarillo-Herrero等55通过微机械剥离的方法得到了厚度为17nm的砷掺杂的Bi2Se3纳米薄片,构建了场效应晶体管,通过在晶体管上构造高k值的顶栅,实现了对Bi2Se3准二维纳米材料表面电子态的外场调控,并观察到了类似石墨烯的双极化效应.2011年,Wang等31通过液相反应合成了Bi2Te3纳米带,通过场效应晶体管的顶栅实现了Bi2Te3纳米带费米能级的调控.通过顶栅电压把费米能级调节到了体态的带隙中,进而在Bi2Te3纳米带中直接观测到了表面电子态的AB干涉和SdH振荡.2011年,Cui等56在(Bi x Sb1-x)2Te3本征拓扑绝缘体二维纳米薄片中,发现了与石墨烯场效应晶体管类似的双极化场效应现象.围绕拓扑绝缘体二维纳米结构的可控生长方法与器件研究,根据Bi2Se3和Bi2Te3的层状各向异性晶体结构特点,我们提出和发展了拓扑绝缘体二维纳米结构的范德华外延(van der Waals epitaxy)生长方法,35,47,48,57通过对生长基底种类、基底温度、载气流量、粉源温度、压强等生长条件进行设计和优化,在不同基底(石墨烯、云母)上外延生长了高质量的少层拓扑绝缘体二维纳米结构,35,48,57实现层数、尺寸、定点与定向的控制,47并对少层拓扑绝缘体纳米结构进行系统的谱学与电学测量,24,35,48,49还对其在柔性透明导电薄膜上的应用进行了初步探索.57本文将对我们在拓扑绝缘体二维纳米结构的生长与器件等方面的成果进行归纳和总结,并对拓扑绝缘体未来的研究方向、实际应用前景进行展望.2拓扑绝缘体二维纳米材料的范德华外延层状的Bi2X3(X=Se,Te)是典型的三维拓扑绝缘体,其晶体结构属于D53d(R3m)为斜方晶系,沿着c 轴方向可视为层状六面体结构(图1C),59每层包括X-Bi-X-Bi-X(X=Se,Te)五个原子层(quintuple layer, QL),每QL的层厚约1nm.层内为强的共价键合,而层间为相对较弱的范德华相互作用.每层的上下表面为饱和键合的Se或Te,而层的边侧存在大量悬挂键.作为一种独特的气相沉积技术,范德华外延利用外延层和基底之间范德华力或静电力弱相互作用,生长高质量层状材料的外延技术(图2A).60,61范德华外延无需外延层与基底成键,外延层的应变能快速和有效的驰豫可有效减少外延层和基底晶格失配的影响,尤其适用于与基底晶格失配度大的层状结构的生长.许多二维层状晶体材料具有各向异性结构,层内是很强的共价结合,而层间为较弱的范德华相互作用;表面不含悬挂键,呈化学惰性,而边侧存在大量化学活性的悬挂键.62-65因此,这种各向异性成键特性决定了层内的生长速度远大于层间生长速度,理论上可以通过范德华外延的方法逐层生长高质量、层数可控的二维晶体材料.范德华外延基底的表面物理化学性质对二维外延层的生长有重要影响.我们在非晶态SiO2基底上的生长结果表明,49基底上表面悬挂键的存在制约着大面积超薄的拓扑绝缘体二维纳米材料的生长.在SiO2基底上只能得到3层以上、取向不一致的Bi2X3(X=Se,Te)二维纳米薄片,横向尺寸最大约为20µm.表面化学惰性的层状单晶基底有助于制备2426李辉等:拓扑绝缘体二维纳米结构与器件No.10取向一致、大面积、高结晶质量、厚度达单层的拓扑绝缘体二维纳米材料.我们发现表面原子级平整、化学惰性的层状石墨烯和云母是理想的范德华外延基底,47,48,57可实现厚度可控、尺寸可控的高结晶质量的少层至单层拓扑绝缘体二维纳米结构和大面积薄膜的范德华外延,并首次实现了拓扑绝缘体二维纳米结构均匀阵列的定向与定点生长.47如图2B所示,在导电基底石墨烯上生长的三角形或六边形Bi 2Se 3纳米薄片定向排列.由于石墨烯表面的褶皱或缺陷等影响,少数纳米薄片的取向有一定的角度偏移.纳米薄片具有高的结晶质量,厚度均一、可达单层,可覆盖石墨烯整个畴区.在绝缘的云母基底上,范德华外延法制备的三角形或六边形Bi 2Se 3二维纳米薄片的取向完全一致(图2C),厚度均一,横向尺寸在几个到几十微米之间.通过精确控制生长条件,降低Bi 2X 3在基底上的成核密度和体系蒸气分压,可进一步增加纳米薄片的侧向尺寸.目前,单一厚度的Bi 2Te 3二维纳米单晶薄片的最大尺寸可达0.1mm (图2(E,F)),远大于用机械剥离、液相剥离及化学合成等方法制备的样品尺寸.进一步控制生长条件,可以在云母基底上外延得到Bi 2X 3的二维纳米薄膜.图2D 为约10nm 厚的Bi 2Se 3纳米薄膜的典型光学照片,表明整个纳米薄膜的厚度较为均一,而其表面上有取向一致的三角形或者六方形纳米岛状结构.拓扑绝缘体二维纳米阵列单晶的定向与定点控制生长有助于生长机理的探索和纳米器件的批量构建.在新鲜剥离、平整的云母表面上,拓扑绝缘体Bi 2X 3的成核具有随机性;而通过人为控制云母基底上的成核位点,将促使Bi 2X 3纳米结构的定点生长.因此,我们巧妙地利用“掩模版”和“等离子体刻蚀”选择性处理云母基底,控制成核位点,实现了拓扑绝缘体Bi 2X 3单晶纳米结构的定点控制生长.47我们首先设计各种形状的光刻模板,通过标准光刻方法,把光刻模板上的图形复制到事先在云母表面旋涂的聚甲基丙烯酸甲酯(PMMA)掩膜上,或者把铜网直接覆盖在云母表面,用氧等离子体对暴露的云母基底刻蚀,除去PMMA 或铜网掩膜版,进行Bi 2X 3二维纳米材料的生长.氧等离子体刻蚀后的云母表面形貌和化学组成发生一定的变化,66破坏了范德华外延生长的条件,而没有被刻蚀处理的云母表面区域仍然可以进行范德华外延生长,从而实现定点生长.图3A 和3B 分别显示了5×7和3×3Bi 2Se 3纳米薄片阵列定点生长的光学照片.图3C 和3D 显示了云母基底上Bi 2Te 3纳米薄片大面积阵列的光学照片和相应的AFM 高度成像.在绝缘透明的云母基底上大面积、高质量的拓扑绝缘体二维纳米结构生长的实现将为光谱测量、器件加工与电学测量提供很好的材料基础,而定点定向与层数的精确控制生长的实现将为速度更快、能耗更低的拓扑绝缘体纳电子图2(A)范德华外延示意图;(B)石墨烯上范德华外延生长的Bi 2Se 3纳米薄片的SEM 照片;(C)云母基底上范德华外延生长的Bi 2Se 3纳米薄片阵列的透过模式光学照片;(D)云母基底上外延生长的Bi 2Se 3纳米薄膜的透过模式光学照片,圆圈中的白色部分为云母基底;(E,F)云母基底上外延生长得到的厚度为6QL 、大尺寸单晶Bi 2Te 3纳米薄片的透过模式光学照片和AFM 像Fig.2(A)Scheme diagram of van der Waals epitaxy;(B)SEM image of Bi 2Se 3epitaxy on grapheme;(C)typical transmission-mode optical microscopy image of nanoplate arrays of Bi 2Se 3on transparent mica substrates;(D)typical transmission-mode optical microscopy image of large-area,few-layer Bi 2Se 3nanosheets grown on a mica substrate,the blank mica substrate is indicated by the black circle;(E,F)optical image and the corresponding AFM image of large-size Bi 2Te 3nanoplate single crystal with 6QL inthickness grown on micaSEM:scanning electron microscopy,OM:optical microscopy,AFM:atomic force microscopy,QL:quintuple layer.Reproduced from Refs.47,48,57.Copyright ©2012Nature Publishing Group,2010and 2012American Chemical Society.2427Acta Phys.⁃Chim.Sin.2012V ol.28器件的批量构建提供契机.3拓扑绝缘体二维纳米材料的谱学研究3.1角分辨光电子能谱拓扑绝缘体表面态的检测是研究拓扑绝缘体的新奇物性和制备拓扑绝缘体电子学器件的前提.角分辨光电子能谱(ARPES)是利用光电效应研究固体的电子结构的表面分析技术,即通过高能光子对材料的电子进行激发,测量激发电子的能量和动量,得到电子的能带结构,并同时测量费米能级附近电子的能量、运动方向和散射性质.目前,ARPES 是研究晶体表面电子结构,如能带、费米面以及多体相互作用的重要工具,也是探测拓扑绝缘体的表面态最直接最有效的实验手段之一.67拓扑绝缘体Bi 2Se 3、Bi 2Te 3和Sb 2Te 3的狄拉克锥形的表面电子结构已经相继被ARPES 直接观察到.我们与斯坦福大学的沈志勋教授小组、牛津大学的陈宇林博士合作,利用基于同步辐射光源的ARPES,研究了在管式炉CVD 系统中制备的Bi 2Se 3、Bi 2Te 3等二维纳米薄片的电子能带结构.47,57ARPES 结果表明,在室温大气下放置相当一段时间后,厚度约为10nm 的Bi 2Se 3和Bi 2Te 3二维纳米薄片仍然具有拓扑绝缘体的狄拉克表面电子能带结构的鲜明特征(图4(A,B)),这说明拓扑表面态具有很好稳定性.二维纳米薄片的费米能级与体态导带能级相交,表现为明显的电子掺杂.在体态导带区域,分布着与表面态共存的额外的量子阱态,可能是生长时存在缺陷或者暴露空气掺杂引起的.我们分析约10nm 厚的Bi 2Se 3二维纳米薄片的ARPES 数据,发现表面态与体态的载流子数目已基本一致.这一结果表明,由于纳米薄片具有大的比表面积,其体态载流子对样品整体导电性的贡献减少,而表面态载流子的贡献增大;随着厚度的减小,表面态的贡献将占主导作用.3.2拉曼光谱在研究固体样品的能带结构和准粒子动力学方面,光谱检测与ARPES 有一定互补性.光谱响应能探测带间跃迁,还能探测其它任何能够和光耦合的集体激发如声子的响应.其中,振动光谱法作为微细结构变化的灵敏探针,是揭示新型低维量子材图4(A)ARPES 测量的云母基底上Bi 2Se 3纳米薄片在Κ-Γ-Κ方向的能带结构图,Bi 2Se 3能带结构由导带(CB)和价带(VB)之间直接带隙的体态和具有Dirac 锥结构的表面电子态(SS)组成;(B)在特定结合能下,以k x 和k y 为函数的能带结构等能量图Fig.4(A)Electronic band dispersion along the Κ-Γ-Κdirection of large-scale Bi 2Se 3nanoplate aggregates grown on a mica substrate measured by ARPES.A direct band gap between the conduction band (CB)and valence band (VB)and Dirac-cone-typed surface state (SS)were identified;(B)constant-energy contour images of the band structure as functions of k x and k y at certainbinding energiesReproduced from Ref.47,Copyright ©2012AmericanChemicalSociety.图3(A)云母基底上定点生长的5×7圆形Bi 2Se 3纳米薄片阵列光学照片;(B)云母基底上定点生长的3×3三角形Bi 2Se 3纳米薄片阵列光学照片;(C)云母基底上定点生长的11×14Bi 2Te 3纳米薄片阵列的光学照片;(D)图C 虚线方形框中2×2Bi 2Te 3纳米薄片相应的AFM 像及其高度像Fig.3Optical microscopy images of (A)the 5×7round and (B)3×3triangular Bi 2Se 3nanoplate arrays on mica;(C)optical microscopy image of 11×14Bi 2Te 3nanoplate array on mica;(D)corresponding AFM image and high profile of the 2×2Bi 2Te 3nanoplate array shown in thedashed black box of (C)Reproduced from Ref.47,Copyright ©2012AmericanChemical Society.2428。

Disorder-induced rounding of certain quantum phase transitions

a r X i v :c o n d -m a t /0212305v 1 [c o n d -m a t .s t r -e l ] 12 D e c 2002Disorder-induced rounding of certain quantum phase transitionsThomas VojtaDepartment of Physics,University of Missouri-Rolla,Rolla,MO 65409(Dated:February 1,2008)We study the inﬂuence of quenched disorder on quantum phase transitions in systems with over-damped dynamics.For Ising order parameter symmetry disorder destroys the sharp phase transition by rounding because a static order parameter can develop on rare spatial regions.This leads to an exponential dependence of the order parameter on the coupling constant.At ﬁnite temperatures the static order on the rare regions is destroyed.This restores the phase transition and leads to a double-exponential relation between critical temperature and coupling strength.We discuss the behavior based on Lifshitz-tail arguments and illustrate the results by simulations of a model system.The inﬂuence of quenched disorder on phase tran-sitions is an important problem in condensed matter physics.Initially it was suspected that disorder destroys any critical point [1].However,it was soon found that classical continuous phase transitions generically remain sharp in the presence of weak disorder.If a clean critical ﬁxed point (FP)fulﬁlls the Harris criterion [2]ν≥2/d ,where νis the correlation length exponent and d is the spatial dimensionality,weak disorder is renormalization group irrelevant.The system becomes asymptotically ho-mogeneous at large length scales.Even if the Harris cri-terion is violated,the transition will generically be sharp.In this case the inhomogeneities either remain ﬁnite at all length scales,leading to a ﬁnite disorder FP,or the relative magnitude of the disorder diverges under coarse graining corresponding to an inﬁnite-randomness FP.A prominent example of the latter occurs in the McCoy-Wu model [3],a disordered 2D Ising-model in which the disorder is perfectly correlated in one dimension.These correlations increase the eﬀects of the disorder.An important aspect of phase transitions in disordered systems are the Griﬃths phenomena [4].They are caused by large spatial regions that are devoid of any impurities and can be locally in the ordered phase even if the bulk system is in the disordered phase.Since these regions are of ﬁnite size,no true static order develops.The ﬂuctua-tions of these regions are very slow because they require changing the order parameter in a large volume.Griﬃths [4]showed that this leads to a singular free energy.In generic classical systems this is a weak eﬀect,since the singularity is only an essential one.An exception is the McCoy-Wu model [3].Here,the disorder correlations lead to stronger eﬀects,with the average susceptibility diverging in a ﬁnite region of the phase diagram.Recently disorder eﬀects have gained a lot of atten-tion in the context of quantum phase transitions [5].At these transitions order-parameter ﬂuctuations in space and time have to be considered.Quenched disorder is time-independent,it is thus always correlated in one of the relevant dimensions making disorder eﬀects at quan-tum phase transitions generically stronger than at clas-sical transitions.A prototypical model is the random quantum Ising ferromagnet.Its quantum phase tran-sition in 1D [6,7,8]and 2D [9,10]is controlled by an inﬁnite-randomness FP with activated rather than power-law dynamical scaling.The Griﬃths singularities are enhanced,too:Several observables including the av-erage susceptibility display power-law singularities with continuously varying exponents over a ﬁnite region of the disordered phase.Similar phenomena have also been found in quantum Ising spin glasses [11,12,13].The systems in which inﬁnite-randomness FPs and quantum Griﬃths phenomena have been shown unam-biguously all have undamped dynamics (a dynamical ex-ponent z =1in the corresponding clean system).How-ever,in itinerant electronic systems the order parame-ter couples to fermionic modes leading to overdamped dynamics (clean dynamical exponent z >1).A proto-type example is the itinerant quantum antiferromagnetic phase transition.The conventional perturbative renor-malization group for this transition [14]yields a ﬁnite-disorder FP.However,by taking into account the eﬀects of rare regions it was shown [15]that this FP is unsta-ble,and the renormalization group ﬂow is towards large disorder.The meaning of this runaway ﬂow is presently not fully understood.In addition to the transition itself,quantum Griﬃths phenomena in itinerant systems have also attracted much attention since they are of potential importance for a variety of heavy-fermion systems.It has been suggested [16]that overdamped systems show quantum Griﬃths phenomena very similar to that of un-damped systems.However,recently it has been argued [17]that for Ising symmetry the overdamping prevents the rare regions from tunneling leading to superpara-magnetic rather than quantum Griﬃths behavior.In this Letter we reconsider the important question of disorder and rare regions at quantum phase transi-tions.We show that for Ising order parameter symmetry and Landau overdamped dynamics,the sharp quantum phase transition is destroyed by rounding,because static order can develop on isolated rare regions.Our results can be summarized as follows:The relation between the order parameter m and the distance t from the clean critical point is exponential for small m .The precise form depends on the disorder distribution.For a Gaus-sian coupling constant distribution,m is ﬁnite for all t .2Asymptotically it behaves aslog(m)∼−t2−d/φfor t→∞.(1a)Hereφis theﬁnite-size scaling shift exponent of the clean system.If the disorder is of dilution type aﬁnite order parameter starts to develop at the clean transition,i.e., for t<0[18].For small|t|it behaves aslog(m)∼−|t|−d/φfor t→0−.(1b)Atﬁnite temperatures the static order on the rare re-gions is destroyed,and aﬁnite interaction between them is required for long-range order.This restores a sharp phase transition.The dependence of the critical temper-ature on t is double-exponential.For small T c we obtain log(−a log T c)∼t2−d/φGaussian,(2a)log(−a log T c)∼|t|−d/φdilution,(2b)Moreover,inﬁnite-size samples strong sample-to-sample ﬂuctuations occur if the number of rare regions displaying static order becomes of order one.Asymptotically for large linear system size L,the coupling strength t L at which theseﬂuctuations start behaves liket L∼(log L)1/(2−d/φ)Gaussian,(3a)|t L|∼(log L)−φ/d dilution.(3b)Thus,ﬁnite size eﬀects are suppressed only logarith-mically.In the remainder of this Letter,we sketch the derivation of these results,illustrate them by numerical results from a model system and discuss their relevance for experiments as well as simulations.For deﬁniteness we consider the antiferromagnetic quantum phase transition of itinerant electrons with Ising spin symmetry.The Landau-Ginzburg-Wilson free en-ergy functional of the clean transition reads[14,19] S= dx dy m(x)Γ(x,y)m(y)+u dx m4(x)(4) Here x≡(x,τ)comprises position x and imaginary timeτ,and dx≡ d x 1/T0dτ.Γ(x,y)is the bare two-point vertex,whose Fourier transform isΓ(q,ωn)= (t+q2+|ωn|).Here t=(g−g c)/g c is the distance of the coupling constant g from the critical point.The dynam-ical part ofΓis proportional to|ωn|reﬂecting the over-damping of the dynamics(undamped dynamics leads to ω2n).Quenched disorder is introduced by making t a ran-dom function of position,t→t+δt(x).We consider two diﬀerent disorder distributions.Theﬁrst is a Gaussian distribution with zero mean and a correlation function δt(x)δt(y) =∆2δ(x−y).The second disorder distri-bution is of dilution type,δt(x)=0everywhere except on randomly distributedﬁnite-size islands(impurities)of spatial density c whereδt(x)=W>0.In the presence of disorder there are rare large spatial regions which are locally in the ordered phase while the bulk system is not.For the Gaussian disorder distribu-tion which is unbounded,these regions exist for all t.For the dilution case they appear below the transition of the clean system,i.e.for t<0.At zero temperature a sin-gle such region is equivalent to a classical Ising model in a rod-like geometry.It isﬁnite in the d space dimen-sions but inﬁnite in imaginary time.If the interaction in the time direction is short-ranged,as is the case for un-damped dynamics,true static order cannot develop on such a rare region.Instead,the order parameter displays slowﬂuctuations leading to quantum Griﬃths phenom-ena.This is drastically diﬀerent in a system with over-damped dynamics.The linear frequency dependence in Γis equivalent to a long-range interaction in time of the form(τ−τ′)−2.1D Ising models with1/r2interaction are known to develop long-range order atﬁnite temper-atures[20].Thus,in our quantum system,true static order develops on those rare regions which are locally in the ordered phase.In agreement with Ref.[17]we therefore do notﬁnd the usual quantum Griﬃths phe-nomena.Once static order has developed on a few iso-lated rare regions,an inﬁnitesimally small interaction or an inﬁnitesimally small symmetry-breakingﬁeld are suf-ﬁcient to align them.Consequently,a macroscopic order parameter arises.We now use Lifshitz tail arguments[21]to derive the leading thermodynamic behavior for small order param-eter m.In the dilution case,the probability w toﬁnd a region of linear size L R devoid of any impurities(δt=0) is given by w∼exp(−cL d R)(up to pre-exponential fac-tors).Such a rare region develops static order at a some t c(L R)<0.Finite size scaling yields|t c(L R)|∼L−φR whereφis theﬁnite-size scaling shift exponent of the clean system[22].Thus,the probability forﬁnding a rare region which becomes critical at t c is given byw(t c)∼exp(−B|t c|−d/φ)for t→0−.(5a)For a Gaussian distribution similar arguments[23]givew(t c)∼exp(−¯B t2−d/φc)for t→∞.(5b)Here B and¯B are constants.The total order parameter m is obtained by integrating over all rare regions which are ordered at t,i.e.,all rare regions having t c>t.This leads to eqs.(1).Note that the functional dependence on t of the order parameter on a given island is of power-law type and thus only inﬂuences the pre-exponential factors. Atﬁnite temperatures the static order on the rare re-gions is destroyed,and aﬁnite interaction of the order of the temperature is necessary to align them.This means a sharp phase transition is recovered.To estimate the transition temperature we note that the interaction be-tween two rare regions depends exponentially on their spatial distance r,E int∼exp(−r/ξ0),whereξ0is the3bulk correlation length.The typical distance r itself de-pends exponentially on t via r ∼w −1/d .The leading dependence of the critical temperature T c on t is thusT c ∼exp(−r/ξ0)∼exp(−a w −1/d /ξ0),(6)where a is a constant.Inserting eqs.(5)for w leads to eqs.(2).Above this exponentially small critical temperature the rare regions essentially behave classically.We now turn to ﬁnite-size eﬀects at zero temperature.Since the total order parameter is the sum of contribu-tions of many independent islands,ﬁnite size-eﬀects in a macroscopic sample are governed by the central limit theorem.However,for t →∞(Gaussian distribution)or t →0−(dilution)very large and thus very rare regions are responsible for the order parameter.The number N of rare regions which start to order at t c in a sample of size L behaves like N ∼L d w (t c ).When N becomes of order one,strong sample-to-sample ﬂuctuations ing eqs.(5)for w (t c ),this leads to eqs.(3).To illustrate the rounding of the phase transition we now present numerical data for a model system,viz.,a disordered classical Ising model with two space dimen-sions and one time-like dimension.The disorder is of di-lution type and completely correlated in time direction.The interaction is short-ranged in the space directions but inﬁnite-ranged in the time-like direction.This sim-pliﬁcation retains the crucial property of static order on the rare regions but allows us to treat system sizes large enough for the investigation of exponentially rare events.The Hamiltonian of the model readsH =−1L τ x ,τ,τ′J x S x ,τS x ,τ′(7)Here x and τare the space and time coordinates,respec-tively.L τis the system size in time direction and x ,y denotes pairs of nearest neighbors.J x is a quenched binary random variable with the distribution P (J )=(1−c )δ(J −1)+c δ(J ).In this classical model L τtakes the role of the inverse temperature in the corresponding quantum system and the classical temperature takes the role of the coupling constant g .Because the interaction is inﬁnite-ranged in time,the time-like dimension can be treated in mean-ﬁeld theory.For L τ→∞,this leads to a set of coupled mean-ﬁeld equations (one for each x )m x =tanh β[J x m x +y (x )′m y +h ],(8)where we have added a very small symmetry-breaking magnetic ﬁeld,h =10−8.These equations are solved numerically in a self-consistency cycle.Fig.1shows the total magnetization and the suscepti-bility (which corresponds to the inverse energy gap of the quantum system)as functions of temperature for linear size L =100and impurity concentration c =0.2.TheTχm FIG.1:Magnetization and susceptibility (L =100,c =0.2).TmFIG.2:Magnetization and susceptibility close to the seemingtransition for diﬀerent system sizes.data are averages over 200disorder realizations [24].At a ﬁrst glance these data suggest a sharp phase transition close to T =4.88.However,a closer investigation,Fig.2,shows that the singularities are rounded.If this round-ing was a conventional ﬁnite-size eﬀect the magnetization curve should become sharper with increasing L and the susceptibility peak should diverge.This is not the case here,instead the transition remains rounded for L →∞.For comparison with the analytical results,Fig.3shows the logarithm of the average magnetization as afunction of 1/(T 0c −T )where T 0c =5is the critical tem-perature of the clean system (c =0).The data follow eq.(1b)over almost four orders of magnitude in m with the expected shift exponent of φ=2.This ﬁgure also shows ”typical”,i.e.,logarithmically averaged magneti-zation data for diﬀerent system sizes.Deviations between the typical and the average values (which are essentially size-independent)reﬂect strong sample-to-sample ﬂuctu-ations.The data show that the onset T L of these ﬂuctua-tions shifts to larger temperatures with increasing systemsize.A more detailed analysis shows that t L =(T L −T 0c)follows eq.(3b)in good approximation.In the remaining paragraphs we discuss the general-ity of the results and their consequences for experiments and simulations.The rounding of the transition is due to the fact that at zero temperature static order can de-velop on a ﬁnite spatial region in a Landau-damped sys-41/(T c0 - T)1010101010mFIG.3:Log(m )as a function of distance from the clean crit-ical point.The solid line is a ﬁt of the average magnetization to eq.(1b)with φ=2.The logarithmically averaged data show the onset of the sample-to-sample ﬂuctuations.tem.We thus expect all quantum phase transitions with discrete order parameter symmetry and overdamped dy-namics (i.e.,a low frequency dependence ∼|ω|or slower in the Gaussian propagator)to be rounded by disorder.Systems with continuous symmetry behave diﬀerently.It is known [25]that classical 1D XY and Heisenberg sys-tems develop long-range order at ﬁnite T only if the in-teraction falls oﬀmore slowly than 1/r 2.Consequently,in a quantum system at zero temperature static order on a rare region only develops if the frequency dependence in the Gaussian propagator is slower than |ω|.The itin-erant ferromagnetic or antiferromagnetic quantum phase transitions with XY or Heisenberg symmetries will thus remain sharp in the presence of disorder [26].The rounding of the quantum phase transition leads to an unusual phenomenology in experiments.Data taken at larger order parameter and not too low temperature do not resolve the exponentially small order parameter tail but probe the rounded transition.However,with increasing precision and decreasing temperature the ap-parent critical point shifts further and further towards the disordered phase,accompanied by the onset of strong sample-sample ﬂuctuations.Similar eﬀects will also oc-cur in simulations.In a recent Monte-Carlo simulation of a related model [27]a sharp transition was found con-trolled by an inﬁnite randomness ﬁxed point.However,in this simulation the linear system sizes are below L =30,therefore it likely probes the rounded transition rather than the exponentially small magnetization tail.In this Letter we have concentrated on the behavior of the system for very small order parameter values,i.e.,in the ”tail region”of the rounded transition.The above ar-guments suggest that the properties of the rounded tran-sition itself are experimentally also very important be-cause they control the behavior in a wide pre-asymptotic region.However,these properties are likely to be non-universal,so far they are not very well understood.We thank D.Belitz,D.Huse,T.R.Kirkpatrick,J.Schmalian and R.Sknepnek for helpful discussions,and we acknowledge support from the University of MissouriResearch Board.Part of this work has been performed at the Aspen Center for Physics.[1]For a pedagogical discussion,see,G.Grinstein in Fun-damental Problems in Statistical Mechanics VI ,E.G.D.Cohen (ed.),Elsevier (New York 19850),p.147.[2]A.B.Harris,J.Phys.C 7,1671(1974).[3]B.M.McCoy and T.T.Wu,Phys.Rev.176,631(1968);188,982(1969).[4]R.B.Griﬃths,Phys.Rev.Lett.23,17(1969).[5]S.L.Sondhi,S.M.Girvin,J.P.Carini,and D.Shahar,Rev.Mod.Phys.69,315(1997);S.Sachdev,Quantum Phase Transitions ,Cambridge University Press (Cam-bridge,1999);T.R.Kirkpatrick and D.Belitz,in N.H.March (Ed.),Electron Correlation in the Solid State ,Im-perial College Press (London 1999),pp.297.[6]B.M.McCoy,Phys.Rev.Lett.23,383(1969).[7]D.S.Fisher,Phys.Rev.69,534(1992);Phys.Rev.B 51,6411(1995).[8]A.P.Young and H.Rieger,Phys.Rev.B 53,8486(1996).[9]C.Pich,A.P.Young,H.Rieger,and N.Kawashima,Phys.Rev.Lett.81,5916(1998).[10]O.Motrunich,S.-C.Mau,D.A.Huse,and D.S.Fisher,Phys.Rev.B 61,1160(2000).[11]M.Thill and D.Huse,Physica A 214,321(1995).[12]M.Guo,R.Bhatt and D.Huse,Phys.Rev.B 54,3336(1996).[13]H.Rieger and A.P.Young,Phys.Rev.B 54,3328(1996).[14]T.R.Kirkpatrick and D.Belitz,Phys.Rev.Lett.76,2571(1996);78,1197(1997).[15]R.Narayanan,T.Vojta,D.Belitz,and T.R.Kirkpatrick,Phys.Rev.Lett.82,5132(1999);Phys.Rev.B 60,10150(1999).[16]A.H.Castro Neto,G.Castilla,and B.A.Jones,Phys.Rev.Lett.81,3531(1998);A.H.Castro Neto and B.A.Jones,Phys.Rev.B 62,14975(2000).[17]lis,D.K.Morr,and J.Schmalian,Phys.Rev.Lett.87,167202(2001);cond-mat/0208396.[18]D.Huse (private communication).[19]J.Hertz,Phys.Rev.B 14,1165(1976).[20]D.J.Thouless,Phys.Rev.187,732(1969);J.Cardy,J.Phys.A 14,1407(1981).[21]I.M.Lifshitz,Usp.Fiz.Nauk.83,617(1964)[Sov.Phys.–Usp.7,549(1965)].[22]The upper critical dimension of the clean itinerant anti-ferromagnetic quantum phase transition is d +c =2.Thus,hyperscaling is not valid in 3D and φ=1/ν.For our pur-pose the exact value of φis not important.[23]B.I.Halperin and x,Phys.Rev.148,722(1966).[24]Thermodynamic quantities involve averaging over thewhole system.Thus ensemble averages rather than typi-cal values give the correct inﬁnite system approximation.[25]P.Bruno,Phys.Rev.Lett.87,137203(2001).[26]A.Abanov and A.V.Chubukov,Phys.Rev.Lett.84,5608(2000)argued that in the 2D itinerant antiferro-magnet mode coupling leads to a frequency dependence |ω|αwith α<1.If this is so,the transition would be rounded even for continuous order parameter symmetry.[27]R.Sknepnek and T.Vojta,cond-mat/0206161.。

非线性混沌现象及其在激光原子相互作用和玻色爱因斯坦凝聚中的表

•Laser beam
•What happens if we replace the ultra-cold atom with the BEC?
非线性混沌现象及其在激光原子相互作用和玻色爱因斯坦凝聚中的表
2021/1/4
非线性混沌现象及其在激光原子相互作用和玻色爱因斯坦凝聚中的表
•概要 •1、非线性动力学混沌现象简介 • 保守系统的混沌 • 耗散系统的混沌 • 量子混沌 •2、应用于强激光的原子电离 •3、应用于波色---爱因斯坦凝聚体 •4、应用于纳米材料（如有时间）
非线性混沌现象及其在激光原子相互作用和玻色爱因斯坦凝聚中的表
一、非线性系统的混沌现象
• 保守系统与耗散系统区别点
相体积收缩与否
相同点
•混沌轨道有李雅谱诺夫指数描述
非线性混沌现象及其在激光原子相互作用和玻色爱因斯坦凝聚中的表
•保守系统的标准映象
非线性混沌现象及其在激光原子相互作用和玻色爱因斯坦凝聚中的表
hing
•Chirped pulse amplification
非线性混沌现象及其在激光原子相互作用和玻色爱因斯坦凝聚中的表
强激光场中的原子----引言
• 近些年来，强场与原子相互作用问题引起人们的广泛关注。这主要由于在过去几十年里激光技术和实验技术的飞速发展使得①电磁场强度与库仑场(原子玻尔半径处)在同．一量级(甚至超过)；②可以非常精确地测量光电子的能量及角分布等物理量。
作用和玻色爱因斯坦凝聚中的表
What is BECs good for
• Too new and we know too little • Potential application: Sensitive
measurement, tiny instrument, atom laser, quantum information, etc.

二次量子化英文文献

二次量子化英文文献An Introduction to Second Quantization in Quantum Mechanics.Abstract: This article delves into the concept of second quantization, a fundamental tool in quantum field theory and many-body physics. We discuss its historical development, mathematical formalism, and applications in modern physics.1. Introduction.Quantum mechanics, since its inception in the early20th century, has revolutionized our understanding of matter and energy at the atomic and subatomic scales. One of the key concepts in quantum theory is quantization, the process of assigning discrete values to physical observables such as energy and momentum. While first quantization focuses on the quantization of individual particles, second quantization extends this principle tosystems of particles, allowing for a more comprehensive description of quantum phenomena.2. Historical Development.The concept of second quantization emerged in the late 1920s and early 1930s, primarily through the works of Paul Dirac, Werner Heisenberg, and others. It was a natural extension of the first quantization formalism, which had been successful in explaining the behavior of individual atoms and molecules. Second quantization provided a unified framework for describing both bosons and fermions, two distinct types of particles that exhibit different quantum statistical behaviors.3. Mathematical Formalism.In second quantization, particles are treated as excitations of an underlying quantum field. This approach introduces a new set of mathematical objects called field operators, which act on a Fock space – a generalization of the Hilbert space used in first quantization. Fock spaceaccounts for the possibility of having multiple particles in the same quantum state.The field operators, such as the creation and annihilation operators, allow us to represent particle creation and destruction processes quantum mechanically. These operators satisfy certain commutation or anticommutation relations depending on whether the particles are bosons or fermions.4. Applications of Second Quantization.Second quantization is particularly useful in studying systems with many particles, such as solids, gases, and quantum fields. It provides a convenient way to describe interactions between particles and the emergence of collective phenomena like superconductivity and superfluidity.In quantum field theory, second quantization serves as the starting point for perturbative expansions, allowing physicists to calculate the probabilities of particleinteractions and scattering processes. The theory has also found applications in particle physics, cosmology, and condensed matter physics.5. Conclusion.Second quantization represents a significant milestone in the development of quantum theory. It not only extends the principles of quantization to systems of particles but also provides a unified mathematical framework for describing a wide range of quantum phenomena. The impact of second quantization on modern physics is profound, and its applications continue to expand as we delve deeper into the quantum realm.This article has provided an overview of second quantization, its historical development, mathematical formalism, and applications in modern physics. The readeris encouraged to explore further the rich and fascinating world of quantum mechanics and quantum field theory.。

mott-insu-transition-MI相变

articles Quantum phase transition from a super¯uid to a Mott insulator ina gas of ultracold atomsMarkus Greiner*,Olaf Mandel*,Tilman Esslinger²,Theodor W.HaÈnsch*&Immanuel Bloch**Sektion Physik,Ludwig-Maximilians-UniversitaÈt,Schellingstrasse4/III,D-80799Munich,Germany,and Max-Planck-Institut fuÈr Quantenoptik,D-85748Garching, Germany²Quantenelektronik,ETH ZuÈrich,8093Zurich,Switzerland ............................................................................................................................................................................................................................................................................ For a system at a temperature of absolute zero,all thermal¯uctuations are frozen out,while quantum¯uctuations prevail.These microscopic quantum¯uctuations can induce a macroscopic phase transition in the ground state of a many-body system when the relative strength of two competing energy terms is varied across a critical value.Here we observe such a quantum phase transition in a Bose±Einstein condensate with repulsive interactions,held in a three-dimensional optical lattice potential.As the potential depth of the lattice is increased,a transition is observed from a super¯uid to a Mott insulator phase.In the super¯uid phase,each atom is spread out over the entire lattice,with long-range phase coherence.But in the insulating phase,exact numbers of atoms are localized at individual lattice sites,with no phase coherence across the lattice;this phase is characterized by a gap in the excitation spectrum.We can induce reversible changes between the two ground states of the system.A physical system that crosses the boundary between two phases changes its properties in a fundamental way.It may,for example, melt or freeze.This macroscopic change is driven by microscopic ¯uctuations.When the temperature of the system approaches zero, all thermal¯uctuations die out.This prohibits phase transitions in classical systems at zero temperature,as their opportunity to change has vanished.However,their quantum mechanical counterparts can show fundamentally different behaviour.In a quantum system,¯uctuations are present even at zero temperature,due to Heisen-berg's uncertainty relation.These quantum¯uctuations may be strong enough to drive a transition from one phase to another, bringing about a macroscopic change.A prominent example of such a quantum phase transition is the change from the super¯uid phase to the Mott insulator phase in a system consisting of bosonic particles with repulsive interactions hopping through a lattice potential.This system was®rst studied theoretically in the context of super¯uid-to-insulator transitions in liquid helium1.Recently,Jaksch et al.2have proposed that such a transition might be observable when an ultracold gas of atoms with repulsive interactions is trapped in a periodic potential.To illustrate this idea,we consider an atomic gas of bosons at low enough temperatures that a Bose±Einstein condensate is formed.The condensate is a super¯uid,and is described by a wavefunction that exhibits long-range phase coherence3.An intriguing situation appears when the condensate is subjected to a lattice potential in which the bosons can move from one lattice site to the next only by tunnel coupling.If the lattice potential is turned on smoothly,the system remains in the super¯uid phase as long as the atom±atom interactions are small compared to the tunnel coupling.In this regime a delocalized wavefunction minimizes the dominant kinetic energy,and therefore also minimizes the total energy of the many-body system.In the opposite limit,when the repulsive atom±atom interactions are large compared to the tunnel coupling,the total energy is minimized when each lattice site is®lled with the same number of atoms.The reduction of¯uctuations in the atom number on each site leads to increased¯uctuations in the phase. Thus in the state with a®xed atom number per site phase coherence is lost.In addition,a gap in the excitation spectrum appears.The competition between two terms in the underlying hamiltonian (here between kinetic and interaction energy)is fundamental to quantum phase transitions4and inherently different from normal phase transitions,which are usually driven by the competition between inner energy and entropy.The physics of the above-described system is captured by the Bose±Hubbard model1,which describes an interacting boson gas in a lattice potential.The hamiltonian in second quantized form reads:H 2J^h i;j iÃa²iÃa j ^ie iÃn i12U^iÃn i Ãn i21 1HereÃa i andÃa²i correspond to the bosonic annihilation and creation operators of atoms on the i th lattice site,Ãn i Ãa²iÃa i is the atomic number operator counting the number of atoms on the i th lattice site,and e i denotes the energy offset of the i th lattice site due to an external harmonic con®nement of the atoms2.The strength of the tunnelling term in the hamiltonian is characterized by the hopping matrix element between adja-cent sites i,j J 2e d3x w x2x i 2~2=2=2m V lat x w x2x j , where w x2x i is a single particle Wannier function localized to the i th lattice site(as long as n i<O 1 ),V lat(x)indicates the optical lattice potential and m is the mass of a single atom.The repulsion between two atoms on a single lattice site is quanti®ed by the on-site interaction matrix element U 4p~2a=m e j w x j4d3x,with a being the scattering length of an atom.In our case the interaction energy is very well described by the single parameter U,due to the short range of the interactions,which is much smaller than the lattice spacing.In the limit where the tunnelling term dominates the hamilto-nian,the ground-state energy is minimized if the single-particle wavefunctions of N atoms are spread out over the entire lattice with M lattice sites.The many-body ground state for a homogeneous system(e i const:)is then given by:jªSF i U 0~^Mi 1Ãa²i23Nj0i 2Here all atoms occupy the identical extended Bloch state.An important feature of this state is that the probability distributionfor the local occupation n i of atoms on a single lattice site is poissonian,that is,its variance is given by Var n i hÃn i i.Further-more,this state is well described by a macroscopic wavefunction with long-range phase coherence throughout the lattice.If interactions dominate the hamiltonian,the¯uctuations in atom number of a Poisson distribution become energetically very costly and the ground state of the system will instead consist of localized atomic wavefunctions with a®xed number of atoms per site that minimize the interaction energy.The many-body ground state is then a product of local Fock states for each lattice site.In this limit,the ground state of the many-body system for a commensu-rate®lling of n atoms per lattice site in the homogeneous case is given by:jªMI i J 0~&Mi 1Ãa²i n j0i 3This Mott insulator state cannot be described by a macroscopic wavefunction like in a Bose condensed phase,and thus is not amenable to a treatment via the Gross-Pitaevskii equation or Bogoliubov's theory of weakly interacting bosons.In this state no phase coherence is prevalent in the system,but perfect correlations in the atom number exist between lattice sites.As the strength of the interaction term relative to the tunnelling term in the Bose±Hubbard hamiltonian is changed,the system reaches a quantum critical point in the ratio of U/J,for which the system will undergo a quantum phase transition from the super¯uid state to the Mott insulator state.In three dimensions,the phase transition for an average number of one atom per lattice site is expected to occur at U=J z35:8(see refs1,5,6,7),with z being the number of next neighbours of a lattice site.The qualitative change in the ground-state con®guration below and above the quantum critical point is also accompanied by a marked change in the excitation spectrum of the system.In the super¯uid regime, the excitation spectrum is gapless whereas the Mott insulator phase exhibits a gap in the excitation spectrum5±8.An essential feature of a quantum phase transition is that this energy gap¢opens up as the quantum critical point is crossed.Studies of the Bose±Hubbard hamiltonian have so far included granular superconductors9,10and one-and two-dimensional Josephson junction arrays11±16.In the context of ultracold atoms, atom number squeezing has very recently been demonstrated with a Bose±Einstein condensate in a one-dimensional optical lattice17. The above experiments were mainly carried out in the limit of large boson occupancies n i per lattice site,for which the problem can be well described by a chain of Josephson junctions.In our present experiment we load87Rb atoms from a Bose±Einstein condensate into a three-dimensional optical lattice poten-tial.This system is characterized by a low atom occupancy per lattice site of the order of h n i i<123,and thus provides a unique testing ground for the Bose±Hubbard model.As we increase the lattice potential depth,the hopping matrix element J decreases exponentially but the on-site interaction matrix element U increases.We are thereby able to bring the system across the critical ratio in U/J,such that the transition to the Mott insulator state is induced.Experimental techniqueThe experimental set-up and procedure to create87Rb Bose±Einstein condensates are similar to those in our previous experi-mental work18,19.In brief,spin-polarized samples of laser-cooled atoms in the(F 2,m F 2)state are transferred into a cigar-shaped magnetic trapping potential with trapping frequencies of n radial 240Hz and n axial 24Hz.Here F denotes the total angular momentum and m F the magnetic quantum number of the state. Forced radio-frequency evaporation is used to create Bose±Einstein condensates with up to23105atoms and no discernible thermal component.The radial trapping frequencies are then relaxed over a period of500ms to n rad 24Hz such that a spherically symmetric Bose±Einstein condensate with a Thomas±Fermi diameter of 26m m is present in the magnetic trapping potential.In order to form the three-dimensional lattice potential,three optical standing waves are aligned orthogonal to each other,with their crossing point positioned at the centre of the Bose±Einstein condensate.Each standing wave laser®eld is created by focusing a laser beam to a waist of125m m at the position of the condensate.A second lens and a mirror are then used to re¯ect the laser beam back onto itself,creating the standing wave interference pattern.The lattice beams are derived from an injection seeded tapered ampli®er and a laser diode operating at a wavelength of l 852nm.All beams are spatially®ltered and guided to the experiment using optical®bres.Acousto-optical modulators are used to control the intensity of the lattice beams and introduce a frequency difference of about30MHz between different standing wave laser®elds.The polarization of a standing wave laser®eld is chosen to be linear and orthogonal polarized to all other standing waves.Due to the different frequencies in each standing wave,any residual interfer-ence between beams propagating along orthogonal directions is time-averaged to zero and therefore not seen by the atoms.The resulting three-dimensional optical potential(see ref.20and references therein)for the atoms is then proportional to the sum of the intensities of the three standing waves,which leads to a simple cubic type geometry of the lattice:V x;y;z V0 sin2 kx sin2 ky sin2 kz 4 Here k 2p=l denotes the wavevector of the laser light and V0is the maximum potential depth of a single standing wave laser®eld. This depth V0is conveniently measured in units of the recoil energy E r ~2k2=2m.The con®ning potential for an atom on a single lattice site due to the optical lattice can be approximated by a harmonic potential with trapping frequencies n r on the order of n r< ~k2=2p mV0=E rp.In our set-up potential depths of up to 22E r can be reached,resulting in trapping frequencies of approxi-mately n r<30kHz.The gaussian intensity pro®le of the laser beams at the position of the condensate creates an additional weak isotropic harmonic con®nement over the lattice,with trap-ping frequencies of65Hz for a potential depth of22E r.The magnetically trapped condensate is transferred into the optical lattice potential by slowly increasing the intensity of the lattice laser beams to their®nal value over a period of80ms using an exponential ramp with a time constant of t 20ms.The slow ramp speed ensures that the condensate always remains in the many-body ground state of the combined magnetic and optical trapping potential.After raising the lattice potential the condensate has been distributed over more than150,000lattice sites(,65lattice sites in a single direction)with an average atom number of up to 2.5atoms per lattice site in the centre.In order to test whether there is still phase coherence between different lattice sites after ramping up the lattice potential,we suddenly turn off the combined trapping potential.The atomic wavefunctions are then allowed to expand freely and interfere with each other.In the super¯uid regime,where all atoms are delocalized over the entire lattice with equal relative phases between different lattice sites,we obtain a high-contrast three-dimensional interfer-ence pattern as expected for a periodic array of phase coherent matter wave sources(see Fig.1).It is important to note that the sharp interference maxima directly re¯ect the high degree of phase coherence in the system for these experimental values. Entering the Mott insulator phaseAs we increase the lattice potential depth,the resulting interference pattern changes markedly(see Fig.2).Initially the strength of higher-order interference maxima increases as we raise the potential height,due to the tighter localization of the atomic wavefunctions at a single lattice site.Quite unexpectedly,however,at a potentialarticlesdepth of around 13E r the interference maxima no longer increase in strength (see Fig.2e):instead,an incoherent background of atoms gains more and more strength until at a potential depth of 22E r no interference pattern is visible at all.Phase coherence has obviously been completely lost at this lattice potential depth.A remarkable feature during the evolution from the coherent to the incoherent state is that when the interference pattern is still visible no broad-ening of the interference peaks can be detected until they completely vanish in the incoherent background.This behaviour can be explained on the basis of the super¯uid±Mott insulator phase diagram.After the system has crossed the quantum critical point U =J z 35:8,it will evolve in the inhomogeneous case into alternating regions of incoherent Mott insulator phases and coher-ent super¯uid phases 2,where the super¯uid fraction continuously decreases for increasing ratios U/J .Restoring coherenceA notable property of the Mott insulator state is that phase coherence can be restored very rapidly when the optical potential is lowered again to a value where the ground state of the many-body system is completely super¯uid.This is shown in Fig.3.After only 4ms of ramp-down time,the interference pattern is fully visible again,and after 14ms of ramp-down time the interference peaks have narrowed to their steady-state value,proving that phase coherence has been restored over the entire lattice.The timescale for the restoration of coherence is comparable to the tunnelling time t tunnel ~=J between two neighbouring lattice sites in the system,articles2 ᐜkxyzFigure 1Schematic three-dimensional interference pattern with measured absorption images taken along two orthogonal directions.The absorption images were obtained after ballistic expansion from a lattice with a potential depth of V 0 10E r and a time of ¯ight of 15ms.a b 1c de f g hFigure 2Absorption images of multiple matter wave interference patterns.These were obtained after suddenly releasing the atoms from an optical lattice potential with different potential depths V 0after a time of ¯ight of 15ms.Values of V 0were:a ,0E r ;b ,3E r ;c ,7E r ;d ,10E r ;e ,13E r ;f ,14E r ;g ,16E r ;and h ,20E r .the three-dimensional lattice.This homogeneous populationthat all atoms are in the vibrational ground state of the lattice,the relative phase between lattice sites is random.Figure 3b that no phase coherence is restored at all for such a system over period of 14ms.Even for evolution times t of up to 400ms,reappearance of an interference pattern could be detected.demonstrates that the observed loss of coherence with potential depth is not simply due to a dephasing of the wavefunction.Probing the excitation spectrumIn the Mott insulator state,the excitation spectrum is modi®ed compared to that of the super¯uid state.The spectrum has now acquired an energy gap ¢,which in the J p U is equal to the on-site interaction matrix element ¢ U refs 5±8).This can be understood within a simpli®ed picture in following way.We consider a Mott insulator state with n 1atom per lattice site.The lowest lying excitation for such state is the creation of a particle±hole pair,where an atom removed from a lattice site and added to a neighbouring site (see Fig.4a).Due to the on-site repulsion between two the energy of the state describing two atoms in a single lattice site raised by an amount U in energy above the state with only a atom in this lattice site.Therefore in order to create an excitation ®nite amount of energy U is required.It can be shown that this also true for number states with exactly n atoms per lattice site.the energy required to make a particle±hole excitation is also Hopping of particles throughout the lattice is therefore in the Mott insulator phase,as this energy is only available in processes.If now the lattice potential is tilted by application of potential gradient,tunnelling is allowed again if the difference between neighbouring lattice sites due to the gradient equals the on-site interaction energy U (see Fig.4b).thus expect a resonant excitation probability versus the articlesFigure 4per site.a ,The lowest lying excitations in the Mott insulator phase consist of removing an atom from a lattice site and adding it to neighbouring lattice sites.Owing to the repulsion between the atoms,this requires a ®nite amount U in energy and hopping of atoms is therefore suppressed.b ,If a potential gradient is applied to the system along z -direction,such that the energy difference between neighbouring lattice sites equals on-site interaction energy U ,atoms are allowed to tunnel again.Particle±hole are then created in the Mott insulator phase.barticles14.van der Zant,H.S.J.,Fritschy,F.C.,Elion,W.J.,Geerligs,L.J.&Mooij,J.E.Field-inducedsuperconductor-to-insulator transitions in Josephson-junction arrays.Phys.Rev.Lett.69,2971±2974 (1992).15.van Oudenaarden,A.&Mooij,J.E.One-dimensional Mott insulator formed by quantum vortices inJosephson junction arrays.Phys.Rev.Lett.76,4947±4950(1996).16.Chow,E.,Delsing,P.&Haviland,D.B.Length-scale dependence of the superconductor-to-insulatorquantum phase transition in one dimension.Phys.Rev.Lett.81,204±207(1998).17.Orzel,C.,Tuchman,A.K.,Fenselau,M.L.,Yasuda,M.&Kasevich,M.A.Squeezed states in a Bose-Einstein condensate.Science291,2386±2389(2001).18.Greiner,M.,Bloch,I.,HaÈnsch,T.W.&Esslinger,T.Magnetic transport of trapped cold atoms over alarge distance.Phys.Rev.A63,031401-1±031401-4(2001).19.Greiner,M.,Bloch,I.,Mandel,O.,HaÈnsch,T.W.&Esslinger,T.Exploring phase coherence in a2Dlattice of Bose-Einstein condensates.Phys.Rev.Lett.87,160405-1±160405-4(2001).20.Grimm,R.,WeidemuÈller,M.&Ovchinnikov,Yu.B.Optical dipole traps for neutral atoms.Adv.At.Mol.Opt.Phys.42,95±170(2000).21.Kastberg,A.,Phillips,W.D.,Rolston,S.L.,Spreeuw,R.J.C.&Jessen,P.S.Adiabatic cooling of cesiumto700nK in an optical lattice.Phys.Rev.Lett.74,1542±1545(1995).22.Dalfovo,F.D.,Giorgini,S.,Pitaevskii,L.P.&Stringari,S.Theory of Bose-Einstein condensation intrapped gases.Rev.Mod.Phys.71,463±512(1999).23.Inouye,S.et al.Observation of Feshbach resonances in a Bose±Einstein condensate.Nature392,151±154(1998).24.Donley,E.A.et al.Dynamics of collapsing and exploding Bose±Einstein condensates.Nature412,295±299(2001).25.Bouyer,P.&Kasevich,M.Heisenberg-limited spectroscopy with degenerate Bose-Einstein gases.Phys.Rev.A56,R1083±R1086(1997).26.Jaksch,D.,Briegel,H.-J.,Cirac,J.I.,Gardiner,C.W.&Zoller,P.Entanglement of atoms via coldcontrolled collisions.Phys.Rev.Lett.82,1975±1978(1999).AcknowledgementsWe thank W.Zwerger,H.Monien,I.Cirac,K.Burnett and Yu.Kagan for discussions.This work was supported by the DFG,and by the EU under the QUEST programme.Competing interests statementThe authors declare that they have no competing®nancial interests. Correspondence and requests for materials should be addressed to I.B.(e-mail:imb@mpq.mpg.de).articles。

二维双量子魔角旋转核磁共振技术在功能材料研究中的应用

位置的峰则对应的是物种Ａ和Ｂ之间的空间相关（近）称之为对角峰．因为同核偶极相互常数与核邻，
旋磁比成正比，与核与核之间距离的三次方成反比，通常同核二维Ｄ — Ｓ相关谱可以提供距离在ＱＭＡ
０５ｎ．ｍ以内自旋对的相关信息，即只有当２个核自旋的空间距离小于０５ｎ．ｍ时，才会在二维相关谱
３４个９。，…）０脉冲，各脉冲之间相隔／（为转速的倒数）相邻的９。２，０脉冲的相位相差９。通常使０．用ＢＢＡＡ脉冲序列的双量子激发脉冲大多以４个或者８个９。冲为主．由于只需要满足与转速同步，０脉而脉冲强度与转速并没直接关系，所以ＢＢＡＡ方法可以在高转速（０～０ｋｚ下获得同核相关的信２４Ｈ）息．图１Ｃ为ＰＳ．７脉冲序列，（）ＯＴＣ主要包含７个重复单元，在每个重复板块中主要由３个组合脉冲组成，分别为２０，０以及３０脉冲，３个脉冲的相位相差分别为０，。１０，７。９。６。而。０和８。每个单元之间的相位相差为５．３．在ＰＳ —７脉冲序列中，常将脉冲强度设置为转速的７倍，１４。ＯＴＣ通这样所满足的旋转共
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ＭＡＳ技术可以部分消除以上相互作用以来，固体ＮＲ的谱图分辨率得到了极大的改善．近年来，随Ｍ

量子自旋霍尔效应的边缘态

量子自旋霍尔效应的边缘态量子自旋霍尔效应（Quantum Spin Hall Effect）是一种在拓扑量子物理中非常重要的现象，它是在二维电子系统中出现的一种量子态。

自旋霍尔效应的边缘态是指在一个自旋-轨道耦合存在的二维系统中，当外加磁场为零时，在系统的边界上会出现一种特殊的电子输运现象。

自旋霍尔效应最早由物理学家Kane和Mele在2005年提出，并且在2007年由Bernevig等人和Konig等人分别通过实验证实。

这一发现引起了广泛的关注，并且为拓扑绝缘体的研究奠定了基础。

在自旋霍尔效应中，电子的自旋和轨道运动耦合在一起，形成了一种新的量子态。

这种量子态具有特殊的拓扑性质，即边界上的电子态被分为两个相互独立的自旋态，一个自旋向上，一个自旋向下。

这两个自旋态之间的转换需要翻越一个能隙，因此在零温下，边界上的电子态是无法相互转换的，从而形成了一种稳定的边缘态。

自旋霍尔效应的边缘态具有很多有趣的性质。

首先，边缘态中的电子是无散射的，即它们在边界上运动时不会与杂质或者缺陷发生散射。

这一性质使得边缘态具有非常低的电阻，从而可以用于制造低功耗的电子器件。

其次，边缘态中的电子具有特殊的自旋-动量锁定性质。

这意味着电子的自旋方向与其运动方向是锁定在一起的，这种锁定使得边缘态中的电子可以用来进行自旋操控和存储信息。

这对于量子计算和量子通信等领域具有重要意义。

另外，边缘态还具有零能量模式。

这些零能量模式是由于拓扑保护而存在的，在没有外界扰动的情况下是稳定存在的。

这些零能量模式可以用来进行量子比特的编码和传输，从而实现量子计算和量子通信。

自旋霍尔效应不仅在理论上具有重要意义，在实际应用中也具有很大潜力。

目前已经有很多材料和结构被发现可以实现自旋霍尔效应，例如HgTe/CdTe量子阱和InAs/GaSb异质结构等。

这些材料和结构可以通过控制外界磁场或者施加压力来调节自旋霍尔效应，从而实现对边缘态的控制。

总之，自旋霍尔效应的边缘态是一种非常有趣和重要的量子态。

量子点

量子点（quantum dot），是准零维(quasi-zero-dimensional)的纳米材料，由少量的原子所构成。

由于量子局限效应会导致类似原子的不连续电子能阶结构，因此量子点又被称为“人造原子”(artificial atom)。

科学家已经发明许多不同的方法来制造量子点，并预期这种纳米材料在二十一世纪的纳米电子学(nanoelectronics)上有极大的应用潜力。

量子点-概述量子点量子点，电子运动在三维空间都受到了限制，因此有时被称为“人造原子”、“超晶格”、“超原子”或“量子点原子”，是20世纪90年代提出来的一个新概念。

量子点是在把导带电子、价带空穴及激子在三个空间方向上束缚住的半导体纳米结构。

这种约束可以归结于静电势（由外部的电极，掺杂，应变，杂质产生），两种不同半导体材料的界面（例如：在自组量子点中），半导体的表面（例如：半导体纳米晶体），或者以上三者的结合。

量子点具有分离的量子化的能谱。

所对应的波函数在空间上位于量子点中，但延伸于数个晶格周期中。

一个量子点具有少量的（1-100个）整数个的电子、空穴或空穴电子对，即其所带的电量是元电荷的整数倍。

小的量子点,例如胶状半导体纳米晶,可以小到只有2到10个纳米,这相当于10到50个原子的直径的尺寸,在一个量子点体积中可以包含100到100,000个这样的原子。

自组装量子点的典型尺寸在10到50纳米之间。

通过光刻成型的门电极或者刻蚀半导体异质结中的二维电子气形成的量子点横向尺寸可以超过100纳米。

将10纳米尺寸的三百万个量子点首尾相接排列起来可以达到人类拇指的宽度。

量子点，又可称为纳米晶，是一种由II－VI族或III－V族元素组成的纳米颗粒。

PhysRevLett.96.210403

Tuning the Mott Transition in a Bose-Einstein Condensate by Multiple Photon AbsorptionC.E.Crefﬁeld and T.S.MonteiroDepartment of Physics and Astronomy,University College London,Gower Street,London WC1E6BT,United Kingdom(Received4April2006;published1June2006)We study the time-dependent dynamics of a Bose-Einstein condensate trapped in an optical lattice.Modeling the system as a Bose-Hubbard model,we show how applying a periodic drivingﬁeld can inducecoherent destruction of tunneling.In the low-frequency regime,we obtain the novel result that thedestruction of tunneling displays extremely sharp peaks when the driving frequency is resonant with thedepth of the trapping potential(‘‘multi-photon resonances’’),which allows the quantum phase transitionbetween the Mott insulator and the superﬂuid state to be controlled with high precision.We further showhow the waveform of theﬁeld can be chosen to maximize this effect.DOI:10.1103/PhysRevLett.96.210403PACS numbers:05.30.Jp,03.65.Xp,03.75.Lm,73.43.NqRecent spectacular progress in trapping cold atomicgases[1]has provided a new arena for studying quantummany-body physics.In particular,ultracold bosons held inoptical potentials provide an almost ideal realization of theBose-Hubbard(BH)model[2],in which the model pa-rameters can be controlled to high precision.As well astheir purely theoretical interest,these systems attract at-tention because of their possible application to quantuminformation processing[3].The BH model is described by the HamiltonianH BH ÿJXh i;j i a yia j H:c:U2Xin i n iÿ1 ;(1)where a i(a y i)are the standard annihilation(creation) operators for a boson on site i,n i a y i a i is the number operator,J is the tunneling amplitude between neighboring sites,and U is the repulsion between a pair of bosons occupying the same site.Its physics is governed by the competition between the kinetic energy and the Hubbard interaction,and thus by the ratio U=J.When U=J 1the tunneling dominates,and the ground state of the system is a superﬂuid.As U=J is increased the system passes through a quantum phase transition,and evolves into a Mott-insulator(MI)state in which the bosons localize on the lattice sites.This phase transition was observed experimentally in Ref.[4]by varying the depth of the optical potential.In this Letter we propose an alternative method:applying an addi-tional oscillatory potential induces coherent destruction of tunneling(CDT),and thus suppresses the effect of J.CDT is a quantum interference effect,discovered in the pioneer-ing work of Ref.[5],in which the period for tunneling between states diverges as their associated quasienergies [6]approach degeneracy.Here we show how CDT can be used to control the dynamics of a boson condensate,by means of a novel resonance effect between U and the frequency of the drivingﬁeld.We consider a one-dimensional BH model, driven by a time-periodic potential which varies linearly with site number.The Hamiltonian is given byH t H BH Kf tX Njjn j;(2)where K is the amplitude of the drivingﬁeld,and f t is a T-periodic function of unit amplitude that describes its waveform.Such time-periodic linear potentials—gener-ated by an accelerated lattice for example—have already been used in cold-atom experiments[7].A similar form of driving potential was also recently investigated theoreti-cally[8]in the high-frequency regime(!>U),and was found to suppress the transition to the superﬂuid regime. Here,for theﬁrst time,the multiphoton(low-frequency) regime is investigated.An unexpected newﬁnding is that CDT is now modulated by a set of extremely sharp‘‘reso-nances’’[the contrast between the high-frequency behavior and the multiphoton regime investigated here is illustrated in Fig.1(a)].This means that the Mott transition can be induced by minute changes in experimental parameters. Henceforth we put@ 1and measure all energies in units of J,and set the number of bosons equal to the number of lattice sites N.Although the dimension of the Hilbert space increases exponentially with N,in a Fock basis H is extremely sparse,with at most 2Nÿ1)nonzero entries per row.Thus despite the rapid increase in the dimension of the Hilbert space,this sparsity allows us to treat relatively large systems of up to11sites,and so assess if the effects we observe survive in the thermodynamic limit.Our numerical investigation consists of initializing the system in the‘‘ideal’’MI state,j MI iQ a yjj0i,and evolving the many-particle Schro¨dinger equation over time(typically ten periods of the drivingﬁeld)using a Runge-Kutta method.To study the system’s time-evolution quantitatively,we measure the overlap of the wave func-tion with the initial state P t jh MI j t ij2.For conve-nience we term the minimum value of P t attained during the time evolution to be the localization.When CDT occurs,the system will remain frozen in the MI state,and consequently the localization will be close to 1.Conversely,if the bosons are able to tunnel freely from site to site,the value of the localization will be reduced.We begin by considering the case of sinusoidal driving,f t sin !t .The MI transition is quite soft in 1D,starting at U ’4and developing fully for U >20.Throughout this work we use an intermediate value of U 8.Figure 1(a)shows how the localization in a 7-site system varies as the amplitude of the driving ﬁeld is increased,while its fre-quency is held constant at ! 20.For K 0the local-ization has a value of 0:3,demonstrating that in the absence of a driving ﬁeld this value of U is indeed insufﬁ-cient to maintain the MI state.Applying the driving ﬁeld causes the localization to steadily rise from this value as K is increased from zero,indicating that the effective tunnel-ing between lattice sites is increasingly suppressed,until it peaks at a value close to 1at K=! 2:4.As K is increased further,the localization goes through a shallow local mini-mum,before again peaking at K=! 5:5.It was observed [8]that these values of K=!are close to the ﬁrst two zeros of J 0,the zeroth Bessel function.Reducing the driving frequency to a lower value,! 8,produces a radically different behavior—the value of the localization rapidly drops as K=!is increased from zero,indicating that the ﬁeld destroys the MI state.As K=!is increased further the value of the localization remains extremely low except at a series of very sharp peaks.Figure 1(b)emphasizes the narrowness of these peaks by showing the time evolution of the system for two values ofK .For the ﬁrst,K 3:5!,P t rapidly falls from its initial value,reaching a level near zero within ﬁve driving peri-ods.There is a small dependence on the system size,with the decay occurring more quickly as N is increased.At the localization peak,K 3:8!,P t decays far more slowly with time,so that after 20periods of driving it only falls to a value of 0:9,and only minor dependence on N is evident.Thus for this value of !,altering the amplitude of the ﬁeld by just 10%produces enormous differences in the localization.Although the Hamiltonian (2)is explicitly time depen-dent,the fact that it is periodic allows us to use the Floquettheorem to write solutions of the Schro¨dinger equation as t exp ÿi j t j t ,where j is the quasienergy,and j t is a T -periodic function called the Floquet state [6].As the quasienergies are only deﬁned up to an arbitrary multiple of !,the quasienergy spectrum possesses a Brillouin zone structure,in precise analogy to the quasi-momentum in spatially periodic crystals.For the Floquet analysis,we work in an extended Hilbert space of T -periodic functions [9].In this approach,the Floquet states and quasienergies satisfyH t j j t i j j j t i ;(3)where H t H t ÿi @@=@t .Working in this extended Hilbert space thus reduces the task of calculating the time-dependent,driven dynamics of the system to a time-inde-pendent eigenvalue problem.To study the behavior of the quasienergies,we make use of a perturbative scheme developed in Ref.[10]to treat noninteracting systems,and later generalized in Ref.[11]to include interactions.Our procedure is to ﬁrst ﬁnd the eigensystem of the operator H 0 t H 0 t ÿi @@=@t ,where H 0contains terms diagonal in a Fock basis (i.e.,the driving term and the Hubbard interaction).We are thenable to use standard Rayleigh-Schro¨dinger perturbation theory to evaluate the corrections to this result,using the remaining terms of H BH as the perturbation.For the two-site system,a natural basis is given by the Fock states fj 1;1i ;j 2;0i ;j 0;2ig ,where j n;m i denotes the state with n bosons on the ﬁrst site and m on the second.Finding the eigensystem of H 0then amounts to solving three ﬁrst-order differential equations,yielding the resultj t i0;exp ÿi U ÿ t i K!cos !t ;0j 0 t i0;0;exp ÿi U ÿ 0 t ÿi K!cos !tj ÿ t i exp i ÿt ;0;0 :(4)Imposing the T -periodic boundary condition on these states requires setting ÿ 0and U ÿ =0 m!,where m is an integer.Thus in general it is not possible to include the full Hubbard-interaction term within H 0,depending on its commensurability with !.To deal with this it is necessary to decompose U into a form which0246800.51L o c a l i z a t i o n Time / TP (t )ω=20ω=8(a)FIG.1(color online).(a)The minimum overlap with the MI state,or localization ,reached in a 7-site system with U 8,during 10periods of driving.For ! 20(dashed line)the localization peaks at K=! 2:4;5:5—the zeros of J 0 K=! .When !is reduced to ! 8(the ﬁrst photon resonance,solid line),the peaks become extremely narrow and are centered on the zeros of J 1 K=! .The diamonds mark the points K=! 3:5and 3.8(see below).(b)Time evolution of the ! 8case for three system sizes,7,9,and 11sites.For K=! 3:5,away from the resonance,the overlap with the initial state,P t ,rapidly drops to zero.For K=! 3:8,at the peak of the resonance,the decay is much slower,indicating that the driving ﬁeld preserves the MI state.duplicates the Brillouin zone structure of the quasienergiesU n! u;n 0;1;2...(5)where u is the ‘‘reduced interaction,’’j u j !=2.This decomposition reveals that only the reduced interaction needs to be included in the perturbation,while the remain-der of U (an integer multiple of !)can be retained in H 0.To ﬁrst order it is easily shown that the three quasiener-gies are given by0 u and u u 2 16J 2eff q =2;(6)where the intersite tunneling has been reduced to an effec-tive value J eff J J n K=! ,and n and u are deﬁned in Eq.(5).Thus in the high-frequency limit (! U ),when n 0and u U ,it is clear that the quasienergies 0and are degenerate when J 0 K=! 0.In Fig.2(a)we show the excellent agreement between the perturbative result and the exact quasienergies for a driving ﬁeld of frequency ! 20.In Fig.2(b)we plot the corresponding value of the localization,and it can be clearly seen that the peaks in this quantity are indeed centered on the points of closest approach of the quasienergies.It may be seen from Eq.(6)that for large values of u ,the quasienergy separa-tion ÿ 0 ’4J 2eff =u .The effect of u is thus to reduce the amplitude of oscillations in this quantity,and so to smear out the avoided crossings of the quasienergies.As a result,the peaks in the localization are rather broad andoverlap each other,and thus the localization cannot reach particularly low values.Equation (5)reveals the particular importance of photon resonances ,when U is an integer multiple of the frequency of the driving ﬁeld,U n!.When this condition is sat-isﬁed the reduced interaction is zero,and the crossings between the quasienergies are well-deﬁned.This is the origin of the extremely sharp peaks in localization seen in Fig.1(a)for ! U 8.Away from these peaks,the photon absorption compensates for the energy cost of doubly occupying a lattice site,in analogy to the photon-assisted tunneling studied in Ref.[12],thereby producing low values of localization.In Fig.2(c)we plot the quasie-nergies for the ﬁrst photon resonance (n 1)for the two-site system.For weak ﬁelds (K=!<2)small deviations of the exact quasienergies from the perturbative result are visible,but for higher ﬁeld strengths the agreement is again excellent.In Fig.2(d)we plot the localization produced in this system,and we can note that,as seen previously in the 7-site system,the localization takes extremely low values except at a set of very narrow peaks.These peaks are precisely aligned with the quasienergy crossings at the zeros of J 1 K=! .As we reduce !still further,we can expect to encounter a sequence of higher resonances with similar behavior.In Fig.3(a)we compare the values of localization produced in a 7-site system for the n 1and n 2resonances.The second photon resonance,however,produces a worse re-sult than for n 1.Although sharp peaks are still present in the localization,and in agreement with the perturbation theory they are indeed centered on the zeros of J 2 K=! ,the maximum value of localization produced is consider-ablylower.Q u a s i e n e r gyK/ω0.80.91L o c a l i z a t i o n K/ω01(b)(d)FIG.2(color online).(a)Quasienergy spectrum of a 2-site system,with U 8and ! 20.Only two of the three quasie-nergies are plotted (the remaining one oscillates weakly about zero),which make a series of close approaches to each other as K is increased.Solid lines in (a)and (c)(red online)denote the perturbative solutions,which agree well with the exact results (black circles).(b)At the points of close approach,the tunneling is suppressed and the localization peaks.For all ﬁeld strengths the tunneling is suppressed with respect to the undriven system,and the localization is thus enhanced.(c)At lower frequencies the behavior of the quasienergies changes dramati-cally.At ! 8the system is at the ﬁrst photon resonance (U !),and the behavior of the quasienergies is described extremely well by the perturbative solutions 0; 2J 1 K=! .(d)As before,the localization is peaked at the points of quasienergy crossing,but in contrast to (b)the peaks are extremely sharp.0K/ω00.51L o c a l i z a t i o nK/ω00.51L o c a l i z a t i o nsine wave square wave(a)(b)FIG.3(color online).Localization produced in a 7-site system (U 8)for two forms of periodic driving:(a)sinusoidal,(b)square wave.Both waveforms produce excellent localization at the ﬁrst photon resonance,! U ,shown by solid black lines.At the second photon resonance (2! U ),shown by dashed lines (red online),the localization produced by the sinusoidal driving is considerably smaller,but the square wave still pro-duces high peaks.This poor localization occurs because not all of the quasienergy crossings in the Floquet spectrum of a many-site system will occur at precisely the same value of K=!;instead the various crossings occur over an inter-val.Thus although at the peaks in the localization many pairs of Floquet states will be degenerate(and tunneling between them will be suppressed),other state-pairs will only be approximately degenerate and will permit a small, but nonzero,degree of tunneling to occur.The major factors inﬂuencing this effect arise from higher-order terms in the expansion of the single-period time-evolution opera-tor U T;0 ,which manifest as multiparticle tunneling and tunneling beyond nearest neighbors.CDT is a quantum interference effect,which occurs when the dynamical phase acquired by a particle in a period of driving produces destructive interference,thereby suppressing the particle’s dynamics.If,however,a‘‘clump’’of n1bosons tunnels between sites,the dynamical phase will be n1times largerthan that for a single boson.Similarly,if a boson tunnels between two sites separated by n2>1lattice spacings,the dynamical phase will be n2times larger.For sinusoidal driving,the single-particle tunneling is suppressed when J n K=! 0;for these higher-order processes also to be suppressed we therefore also require J n n1n2K=! 0 for integers n1;n2 1;2...N.Clearly this condition cannot be satisﬁed for sinusoidal driving,as the zeros of J n x are not equally spaced.Thus to observe good localization properties at high photon resonances we need to construct a drivingﬁeld f t such that the crossings in its Floquet spectrum are periodically spaced.This problem was confronted in a different context in Ref.[13],where it was shown that such aﬁeld must be discontinuous at changes of sign.Possibly the simplest ﬁeld of this type,and the most convenient for experiment, is a square waveﬁeld.In Fig.3(b)we show the localization obtained in a7-site system driven by a square ing the same perturba-tive approach as before,it may be shown that the quasi-energy degeneracies occur for K=! 2m 1or2m, depending on whether the order of the resonance n is odd or even.Unlike the case of sinusoidal driving,the n 2 resonance displays good localization,comparable to that obtained for n 1.A contour plot showing the localiza-tion as a function of both K=!and!ÿ1is presented in Fig.4.The prominent horizontal bands correspond to the photon resonances(!ÿ1 n=U),which are punctuated by a series of narrow peaks at which the localization is pre-served.This plot also clearly shows the division between the fairly featureless,poorly localized,‘‘weak-driving’’regime to the upper left,and the‘‘strong-driving’’regime which shows the resonance features.For the latter,the dynamics of the system are dominated by the combined effect of the drivingﬁeld and the Hubbard interaction,and thus is well described by our form of perturbation theory.Figure4allows us to locate the boundary between the two regimes quite accurately as K=!’ 2U =!.In summary,we have investigated the dynamics of the BH model under a periodic drivingﬁeld.For high frequen-cies[8]theﬁeld can be used to inhibit tunneling by means of CDT and thus stabilize the MI state.Lowering the frequency,however,reveals the existence of resonance effects which can be used to selectively destroy or preserve the MI state.Lower driving frequencies have the added advantages in experiment that they heat the condensate less,and will not drive transitions to higher Bloch bands thereby invalidating the single band model.The extremely narrow width of the resonance features indicates that it should be possible to control the Mott transition very precisely in thismanner.[1]O.Morsch and M.Oberthaler,Rev.Mod.Phys.78,179(2006).[2] D.Jaksch et al.,Phys.Rev.Lett.81,3108(1998).[3] D.Jaksch et al.,Phys.Rev.Lett.82,1975(1999).[4]M.Greiner et al.,Nature(London)415,39(2002).[5] F.Grossmann,T.Dittrich,P.Jung,and P.Ha¨nggi,Phys.Rev.Lett.67,516(1991).[6]M.Grifoni and P.Ha¨nggi,Phys.Rep.304,229(1998).[7]G.Hur,C.E.Crefﬁeld,P.H.Jones,and T.S.Monteiro,Phys.Rev.A72,013403(2005).[8] A.Eckardt,C.Weiss,and M.Holthaus,Phys.Rev.Lett.95,260404(2005).[9]H.Sambe,Phys.Rev.A7,2203(1973).[10]M.Holthaus,Z.Phys.B89,251(1992).[11] C.E.Crefﬁeld and G.Platero,Phys.Rev.B65,113304(2002);66,235303(2002).[12] A.Eckardt,T.Jinasundera,C.Weiss,and M.Holthaus,Phys.Rev.Lett.95,200401(2005).[13]M.M.Dignam and C.M.de Sterke,Phys.Rev.Lett.88,046806(2002).K0.1250.250.3750.5123n=n=n=n=4FIG.4(color online).The localization produced in a5-site system with U 8as a function of the frequency!of the square wave drivingﬁeld and its amplitude K.When n! U the localization is almost zero[the centers of the horizontal bands(blue online)]except at sharply deﬁned peaks(red back-ground online).Between the bands localization is good.The n 1,2,3,and4resonances are marked on the right.The upper-left triangle(blue online)displays poor localization and little struc-ture,corresponding to the nonperturbative regime.。

核磁共振中常用的英文缩写和中文名称

NMR 中常用的英文缩写和中文名称收集了一些NMR 中常用的英文缩写,译出其中文名称,供初学者参考,不妥之处请指出,也请继续添加.相关附件NMR 中常用的英文缩写和中文名称APT Attached Proton Test 质子连接实验ASIS Aromatic Solvent Induced Shift 芳香溶剂诱导位移BBDR Broad Band Double Resonance 宽带双共振BIRD Bilinear Rotation Decoupling 双线性旋转去偶(脉冲)COLOC Correlated Spectroscopy for Long Range Coupling 远程偶合相关谱COSY ( Homonuclear chemical shift ) COrrelation SpectroscopY (同核化学位移)相关谱CP Cross Polarization 交叉极化CP/MAS Cross Polarization / Magic Angle Spinning 交叉极化魔角自旋CSA Chemical Shift Anisotropy 化学位移各向异性CSCM Chemical Shift Correlation Map 化学位移相关图CW continuous wave 连续波DD Dipole-Dipole 偶极-偶极DECSY Double-quantum Echo Correlated Spectroscopy 双量子回波相关谱DEPT Distortionless Enhancement by Polarization Transfer 无畸变极化转移增强2DFTS two Dimensional FT Spectroscopy 二维傅立叶变换谱DNMR Dynamic NMR 动态NMRDNP Dynamic Nuclear Polarization 动态核极化DQ(C) Double Quantum (Coherence) 双量子(相干)DQD Digital Quadrature Detection 数字正交检测DQF Double Quantum Filter 双量子滤波DQF-COSY Double Quantum Filtered COSY 双量子滤波COSYDRDS Double Resonance Difference Spectroscopy 双共振差谱EXSY Exchange Spectroscopy 交换谱FFT Fast Fourier Transformation 快速傅立叶变换FID Free Induction Decay 自由诱导衰减H,C-COSY 1H,13C chemical-shift COrrelation SpectroscopY 1H,13C 化学位移相关谱H,X-COSY 1H,X-nucleus chemical-shift COrrelation SpectroscopY 1H,X- 核化学位移相关谱HETCOR Heteronuclear Correlation Spectroscopy 异核相关谱HMBC Heteronuclear Multiple-Bond Correlation 异核多键相关HMQC Heteronuclear Multiple Quantum Coherence 异核多量子相干HOESY Heteronuclear Overhauser Effect Spectroscopy 异核Overhause 效应谱HOHAHA Homonuclear Hartmann-Hahn spectroscopy 同核Hartmann-Hahn 谱HR High Resolution 高分辨HSQC Heteronuclear Single Quantum Coherence 异核单量子相干INADEQUATE Incredible Natural Abundance Double Quantum Transfer Experiment 稀核双量子转移实验（简称双量子实验，或双量子谱）INDOR Internuclear Double Resonance 核间双共振INEPT Insensitive Nuclei Enhanced by Polarization 非灵敏核极化转移增强INVERSE H,X correlation via 1H detection 检测1H 的H,X 核相关IR Inversion-Recovery 反（翻）转回复JRES J-resolved spectroscopy J-分解谱LIS Lanthanide （chemical shift reagent ） Induced Shift 镧系（化学位移试剂）诱导位移LSR Lanthanide Shift Reagent 镧系位移试剂MAS Magic-Angle Spinning 魔角自旋MQ（C）Multiple-Quantum （ Coherence ）多量子（相干）MQF Multiple-Quantum Filter 多量子滤波MQMAS Multiple-Quantum Magic-Angle Spinning 多量子魔角自旋MQS Multi Quantum Spectroscopy 多量子谱NMR Nuclear Magnetic Resonance 核磁共振NOE Nuclear Overhauser Effect 核Overhauser 效应（NOE）NOESY Nuclear Overhauser Effect Spectroscopy 二维NOE 谱NQR Nuclear Quadrupole Resonance 核四极共振PFG Pulsed Gradient Field 脉冲梯度场PGSE Pulsed Gradient Spin Echo 脉冲梯度自旋回波PRFT Partially Relaxed Fourier Transform 部分弛豫傅立叶变换PSD Phase-sensitive Detection 相敏检测PW Pulse Width 脉宽RCT Relayed Coherence Transfer 接力相干转移RECSY Multistep Relayed Coherence Spectroscopy 多步接力相干谱REDOR Rotational Echo Double Resonance 旋转回波双共振RELAY Relayed Correlation Spectroscopy 接力相关谱RF Radio Frequency 射频ROESY Rotating Frame Overhauser Effect Spectroscopy 旋转坐标系NOE 谱ROTO ROESY-TOCSY Relay ROESY-TOCSY 接力谱SC Scalar Coupling 标量偶合SDDS Spin Decoupling Difference Spectroscopy 自旋去偶差谱SE Spin Echo 自旋回波SECSY Spin-Echo Correlated Spectroscopy 自旋回波相关谱SEDOR Spin Echo Double Resonance 自旋回波双共振SEFT Spin-Echo Fourier Tran sform Spectroscopy （with J modulati on）（J-调制）自旋回波傅立叶变换谱SELINCOR SELINQUATE SFORD SNR or S/NSelective Inverse Correlation 选择性反相关Selective INADEQUA TE 选择性双量子（实验）Single Frequency Off-Resonance Decoupling 单频偏共振去偶Signal-to-noise Ratio 信/ 燥比SQF Single-Quantum Filter 单量子滤波SRTCF TOCSY TORO TQF WALTZ-16 Saturation-Recovery 饱和恢复Time Correlation Function 时间相关涵数Total Correlation Spectroscopy 全(总)相关谱TOCSY-ROESY Relay TOCSY-ROESY 接力Triple-Quantum Filter 三量子滤波A broadband decoupling sequence 宽带去偶序列WATERGATE Water suppression pulse sequence 水峰压制脉冲序列WEFTZQ(C) ZQF T1T2 tmWater Eliminated Fourier Transform 水峰消除傅立叶变换Zero-Quantum (Coherence) 零量子相干Zero-Quantum Filter 零量子滤波Longitudinal (spin-lattice) relaxation time for MZ 纵向(自旋- 晶格)弛豫时间Transverse (spin-spin) relaxation time for Mxy 横向(自旋-自旋)弛豫时间T C rotational correlation time 旋转相关时间。

什么是量子点量子线量子棒

-----WORD格式--可编辑--专业资料-----量子点(quantum dot)是准零维(quasi-zero-dimensional)的纳米材料，由少量的原子所构成。

由于量子局限效应会导致类似原子的不连续电子能阶结构，因此量子点又被称为「人造原子」(artificial atom)。

科学家已经发明许多不同的方法来制造量子点，并预期这种纳米材料在二十一世纪的纳米电子学(nanoelectronics)上有极大的应用潜力。

量子棒指的是在两个维度方向上都受到量子限域效应影响的一种一维材料。

块体是三维的立方体，如果其中一个维度非常薄，几个纳米厚，另外两个方向比较厚，就是薄膜，也就是量子阱；如果其中两个维度都很小，只有一个方向比较大，就是纳米线，足够细的就是量子棒；如果三个维度都很小，就是纳米颗粒，也就是量子点。

在凝聚态物理中,量子线指导电性质受到量子效应影响的导线.由于传导电子在切向上受到量子束缚,切向能量呈现量子化:E0 ("基态" 能量), E1,... (另见量子谐振子).量子化的主要后果是量子线的电阻不能用传统公式，量子线电阻必须通过对横向能量的精确计算而获得,而且必然是量子化的。

纳米线的直径越小,这种量子效应就愈加明显。

半导体线的电阻在直径100纳米左右开始显示可观测的量子性,而金属要在原子量级才能显现.碳纳米管被视作最具有可行性的量子线。

polaron带电粒子在极性介质中受到屏蔽，在带电粒子周围有感应产生的极化云占据，这种感应的极化云将随带电粒子一起运动。

朗道将这种带电粒子及其感应的极化云作为整体称为极化子[1]。

在离子晶体或极性半导体中的传导电子是典型的极化子，是导电聚合物中的一种重要的电荷载流子。

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