PhysRevA_78_033617

where ␻ fg is the frequency of the transition between the instantaneous eigenstates ͉ f ͑t͒͘ and ͉g͑t͒͘. Due to its fundamental importance in quantum theory and applications of quantum state control, the adiabatic theorem has been very actively studied under various practical conditions in the past years. Very recently, Pu and co-workers proposed an elegant way to derive an approximated adiabatic condition for a specific mean-field nonlinear system—i.e., the coherent creation of homonuclear diatomic molecules from a dilute ultracold Bose-condensed atomic gas under the collisionless limit ͓2͔. The basic idea of their method is to first find the coherent population trapping ͑CPT͒ state of the system by using the stimulated Raman adiabatic passage ͑STIRAP͒ technique, and then the deviations from the CPT evolution can form a set of linearized differential equations, which is quite easily solved to obtain an adiabaticity parameter ͓2͔. Then, by taking account of the particles collisions ͓3͔, Ling et al. confirmed the validity of the method of Pu et al. by achieving again a similar adiabatic condition. These pioneering works have motivated us to further study and compare the adiabatic conditions in coherent atom–heteronuclear-diatomic- or -triatomic-molecule conversions. The specific example of atom–homonuclear-dimer conversion considered by Pu et al. ͓2,3͔ is closely related to the fact that considerable interest has been stimulated recently in making and probing an ultracold molecular gas or even a molecular Bose-Einstein condensate ͑BEC͒ ͓4͔. By using a magnetic Feshbach resonance ͑FR͒ ͓5͔ or an optical photoassociation ͑PA͒ technique ͓6͔ within an atomic BEC, the coherent atom-dimer conversion has been extensively studied as a novel matter-wave analog of the simplest nonlinear quantum optical system ͑second-harmonic generation͒ ͓7,8͔. For example, Winkler et al. ͓9͔ experimentally studied the coherent two-color PA “superchemistry” process ͑Boseenhanced free-quasibound-bound transition͒ ͓10͔. By com1050-2947/2008/78͑3͒/033617͑8͒
PHYSICAL REVIEW A 78, 033617 ͑2008͒
Adiabatic condition for coherent atom–heteronuclear-molecule conversion
Department of Physics, Henan Normal University, Xinxiang 453007, People’s Republic of China 2 Institute and Department of Physics, The University of Arizona, Tucson, Arizona 85721, USA ͑Received 19 May 2008; revised manuscript received 12 August 2008; published 25 September 2008͒ Recently, Pu et al. developed an efficient strategy to find the adiabatic condition of a nonlinear system—i.e., the atom-homonuclear dimer conversion ͓Phys. Rev. Lett. 98, 050406 ͑2007͔͒. Here, by applying their method, we extend it to study the adiabatic condition of coherent atom–heteronuclear-diatomic- or -triatomic-molecule conversion. The different adiabatic evolutions in creating the homo- or heteronuclear dimers are compared. The impact of the two different reaction paths on the adiabatic conditions in creating the heteronuclear triatomic molecules is also discussed. DOI: 10.1103/PhysRevA.78.033617 PACS number͑s͒: 03.75.Pp, 42.50.Ϫp, 03.70.ϩk
1
H. Jing,1,2 F. Zheng,1 Y. Jiang,1 and Z. Geng1
I. INTRODUCTION
பைடு நூலகம்
The standard adiabatic theorem in quantum mechanics ͓1͔ is derived generally for a linear system with a sufficiently slowly changed Hamiltonian in comparison with typical level spacings, i.e., ˙ ͉ Ӷ ប͉␻ ͉ ͉H fg ͑for any f g͒ , ͑1͒
bining magneto-optic techniques, Ling et al. proposed a generalized atom-dimer dark-state method to achieve an efficient and stable atom-dimer conversion by minimizing the meanfield shift of particle collisions ͓11,12͔. We note that, although the focus of current research on coherent atom-molecule conversion has been largely on the atom-dimer coupling ͓13–18͔, more and more efforts are currently directed towards the assembly and manipulation of ultracold objects of increasing complexity, such as the atomtrimer conversion ͓19͔: 3a ͑or 2a + b͒ → g, where a ͑b͒ and d ͑g͒ denote atom a ͑b͒ and dimer ͑trimer͒. In fact, evidence of Efimov triatomic resonances ͓20,21͔ or tetramer molecules Cs4 ͓22͔ was observed recently. In view of their novel anisotropic properties ͓23,24͔, the formation and quantum control of heteronuclear trimers is of particular interest. A notable two-path quantum interference effect was also revealed in creating the heteronuclear trimers ͓25͔. The purpose of this paper is to study the adiabatic conditions of coherent atom–heteronuclear-molecule conversion, including the formation of heteronuclear diatomic or triatomic molecules ͑with two different reaction paths͒. In particular, we study the coherent assembly of the same type of heteronuclear trimers A2B from a two-species atomic Bose condensate via two different paths with an intermediate homonuclear or heteronuclear dimer state A2 or AB. An atom-molecule dark state is exploited to keep the dimer number as zero in the conversion process ͓11,13–15,20,25͔. This enables us to compare the adiabatic conditions of atom– heteronuclear-molecule conversions with that of creating homonuclear dimers ͓2͔.