Mixtures of Bose gases confined in concentrically coupled annular traps

arXiv:0911.2355v2 [cond-mat.quant-gas] 16 Dec 2009 Mixtures of Bose gases confined in concentrically coupled annular traps F. Malet1, G. M. Kavoulakis2, and S. M. Reimann1 1Mathematical Physics, Lund Institute of Technology, P.O. Box 118, SE-22100 Lund, Sweden 2Technological Education Institute of Crete, P.O. Box 1939, GR-71004, Heraklion, Greece (Dated: October 29, 2018) A two-component Bose-Einstein condensate confined in an axially-symmetric potential with two local minima, resembling two concentric annular traps, is investigated. The system shows a number of phase transitions that result from the competition between phase coexistence, and radial/azimuthal phase separation. The ground-state phase diagram, as well as the rotational prop- erties, including the (meta)stability of currents in this system, are analysed. PACS numbers: 05.30.Jp, 03.75.Lm, 67.60.Bc I. INTRODUCTION The field of cold atoms has expanded dramatically over the last 15 years. It has now reached a stage where ex- perimentalists are capable of designing the form of the confining potential. Going to extreme aspect ratios, con- ditions of quasi-one- and quasi-two-dimensional behavior have been achieved. In other experiments, it has also become possible to design toroidal trapping potentials [1, 2, 3, 4, 5], in which persistent currents have been observed [3]. Recent theoretical studies have examined Bose- Einstein condensates in one-dimensional annular traps. For example, quantum-tunneling-related effects in verti- cally [6] and concentrically [7] coupled double-ring traps were investigated. Also, the rotational properties of a mixture of two distinguishable Bose gases that are con- fined in a single ring were addressed [8]. One of the basic points of the above studies is the fact that the ability to design traps, control and manipulate the atoms with a very high accuracy, may allow the investigation of novel quantum phenomena, like quantum phase transitions, for example. In the present work we consider a mixture of two dis- tinguishable Bose gases [9, 10] which interact via an effectively-repulsive contact potential, and are confined in a two-dimensional concentric double-ring-like trap, as shown in Fig. 1. Using the mean-field approximation, we investigate two main questions: First, we identify the various phases in the ground state of the system, varying the interaction strength between the atoms. In the trap- ping potential that we consider, we observe that the two gases separate radially via discontinuous transitions; in this case, each gas resides in one of the two minima of the trapping potential, preserving the circular symmetry of the trapping potential. We also observe the expected az- imuthal (and continuous) phase separation between the two gases in each potential minimum [11, 12, 13]. A sim- ilar effect has also been studied in the case of a single ring [8]; see also [11, 12, 13]. The second main question that we examine are the ro- tational properties of this system, including its response to some rotational frequency of the trap Ω, as well as the stability of the persistent currents for variable couplings, and variable relative populations of the two components. The expectation value of the angular momentum of the system as a function of Ωshows an interesting structure, reflecting the various phase transitions that take place with increasing Ω. Regarding the (meta)stability of the currents, it is re- markable that for equal populations between the two components the vast majority of the coupling strengths that we have examined yield metastable states, except for a very small range where all the coupling strengths are exactly or nearly equal. It is worth mentioning that analogous single and con- centric ring geometries have been addressed in semicon- ductor heterostructures, both theoretically and experi- mentally, see e.g. [14], and also [15] for reviews on the subject. In these systems, the applied external mag- netic field plays the same role as the trap rotation in the present problem and allows the investigation of, e.g., electron localization effects and persistent electron cur- rents in field-free regions. In what follows we first describe in Sec. II our model. In Sec. III we present the results for the ground state of the system, identifying the states where the species coexist, or separate, either radially or azimuthally. In Sec. IV we examine the rotational properties for a fixed rotational frequency of the trap, and the (meta)stability of the per- sistent currents. We study the stability as a function of the coupling between the atoms, as well as of the ratio of the populations of the two components. Finally, in Sec. V we present a summary and our conclusions. II. MODEL AND METHOD We consider two distinguishable kinds of bosonic atoms, labelled as A and B, which are trapped in a two- dimensional potential of the form V (ρ) = min 1 2 Mω2 i (ρ −Ri)2 , 1 2 Mω2 o (ρ −Ro)2  , (1) where ρ is the usual radial coordinate in cylindric

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