Transition to chaos in Bose-Einstein condensates: role of inter-component interactions on wavepacket breathing

摘要

Recently a great number of theoretical and experimental efforts have been devoted to Bose-Einstein condensates (BECs). As well as single-component BECs, the trapping techniques can create multi-component condensates which involve inter-component nonlinear interactions. The multi-component BEC, far from being a trivial extension of the single-component one, presents novel and fundamentally different scenarios for its ground state and excitations. In particular, it has been observed that BEC can reach an equilibrium state characterized by the separation of the species in different domains. BEC has a dual aspect of waves and particles. The wave nature is high-lightened in the phenomenon of interference leading to fringe patterns. On the other hand, the particle nature of BECs can be seen in typical localized states like vortices and solitons. In fact solitons were observed in the quasi-one dimensional BEC.%閉じ込めポテンシャルを持つ2次元の多成分BECのダイナミクスを、集団座標の方法の観点から考察する。一成分BECのダイナミクスではエーレンフェストの定理が成立し、ガウス型波束は安定であり波束幅は特徴的振動数で振動する。しかし、成分間に非線形相互作用を取り入れると、波束幅は不安定成長して波束間干渉が生じ、多成分BECに対する粒子描像が完全にこわれる。しかし、振動型の成分間非線形相互作用を採用すると、ガウス型波束は安定性を回復する。さらに、振動型相互作用の振幅を増加きせると規則振動からカオス振動への遷移が生じる。3成分BECのダイナミクス（3体問題）を例にとり、このシナリオを具体的に示す。