Spatial structure of a collisionally inhomogeneous Bose-Einstein condensate
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TOMS, MOLECULES, OPTICS
Spatial Structure of a Collisionally Inhomogeneous Bose–Einstein Condensate1 Fei Lia,b,*, Dongxia Zhangc, Shiguang Rongc, and Ying Xuc a
b
Department of Education Science, Hunan First Normal University, Changsha, 410205 China Key Laboratory of LowDimensional Quantum Structures and Quantum Control, Ministry of Education, Hunan Normal University, Changsha, 410081 China c Department of Physics, Hunan University of Science and Technology, Xiangtan, 411201 China *email: [email protected] Received April 28, 2013
Abstract—The spatial structure of a collisionally inhomogeneous Bose–Einstein condensate (BEC) in an optical lattice is studied. A spatially dependent current with an explicit analytic expression is found in the case with a spatially dependent BEC phase. The oscillating amplitude of the current can be adjusted by a Feshbach resonance, and the intensity of the current depends heavily on the initial and boundary conditions. Increasing the oscillating amplitude of the current can force the system to pass from a singleperiodic spatial structure into a very complex state. But in the case with a constant phase, the spatially dependent current disappears and the Melnikov chaotic criterion is obtained via a perturbative analysis in the presence of a weak optical lattice potential. Numerical simulations show that a strong optical lattice potential can lead BEC atoms to a state with a chaotic spatial distribution via a quasiperiodic route. DOI: 10.1134/S1063776113130141 1
1. INTRODUCTION
Ever since Dalian et al. successfully loaded Bose– Einstein condensates (BECs) in optical lattices [1, 2], the rich and interesting phenomena of BECs in optical lattices attract more and more attention. This is because BECs in optical lattices open up numerous new research aspects for both fundamental and applied problems in quantum mechanics. An optical lattice can be created by the interference of two or more laser beams [3]. Many important phenomena following from the interactions between BECs and optical lattices have been profoundly investigated, both experimentally and theoretically. A quantum phase transition in a BEC with repulsive interactions, confined in a threedimensional optical lattice poten tial, was found in [4]. As the potential depth increases, a transition is observed from a current to a Mottinsu lator phase [4]. In onedimensional (1D) offreso nance optical lattices, for small values of the lattice well depth, Bloch oscillations were observed [5]. Using the Holstein–Primakoff (HP) transformation, Xie and coworkers theoretically found that the dark and bright magnetic solitons can exist in spinor BECs in a 1D optical lattices in different parameter regions [6]. Up to date, the intriguing BEC phenomena investi gated experimentally or theoretically in optical lattices include current and dissipative dynamics [7], arrays of 1
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Josephson junctions [8], Landau–Zener tunneling [2, 9–12], squeezed states [13], chaos [14–30], and so on. In recent yea
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