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Communications in Theoretical Physics

Spatial structure of a Bose–Einstein condensate in a combined trap*

Fei Li, Zhijian He, Wenwu Li

Published Dec 28, 2022• 4 citations
Publisher

Abstract

Abstract We study the spatial structure of a Bose–Einstein condensate (BEC) with a space-dependent s-wave scattering length in a combined trap. There exists a space-dependent nonlinear atomic current in the system. The atomic current has an important influence on the spatial structure of the BEC. Research findings reveal that a large chemical potential can effectively suppress the chaotic spatial structure in the BEC system. Due to the large chemical potential, a strong atomic current is necessary to make the system lose its periodic spatial structure and lead the system into a chaotic spatial structure. But when the atomic current intensity exceeds a critical value, the chaotic spatial structure of the BEC will be completely eliminated and the system will always be kept in a series of single-periodic states as the atomic current becomes stronger. For a very weak atomic current, the spatial structure of the BEC is very sensitive to the intensity of the atomic current and a very small change of the intensity can dramatically change the spatial structure of the BEC. The effects of the combined trap parameters on the spatial structure of BECs are also discussed.

DOI
10.1088/1572-9494/acaef8

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Abstract We study the spatial structure of a Bose–Einstein condensate (BEC) with a space-dependent s-wave scattering length in a combined trap. There exists a space-dependent nonlinear atomic current in the system. The atomic current has an important influence on the spatial structure of the BEC. Research findings reveal that a large chemical potential can effectively suppress the chaotic spatial structure in the BEC system. Due to the large chemical potential, a strong atomic current is necessary to make the system lose its periodic spatial structure and lead the system into a chaotic spatial structure. But when the atomic current intensity exceeds a critical value, the chaotic spatial structure of the BEC will be completely eliminated and the system will always be kept in a series of single-periodic states as the atomic current becomes stronger. For a very weak atomic current, the spatial structure of the BEC is very sensitive to the intensity of the atomic current and a very small change of the intensity can dramatically change the spatial structure of the BEC. The effects of the combined trap parameters on the spatial structure of BECs are also discussed.
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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 single-periodic 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.
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The spatial structure of a Bose-Einstein condensate loaded into an optical lattice potential is investigated, and spatially chaotic distributions of the condensates are revealed. By means of changing of the s-wave scattering length with a Feshbach resonance, the chaotic behavior can be well controlled to enter into periodicity. Numerical simulation shows that there are different periodic orbits according to different s-wave scattering lengths only if the maximal Lyapunov exponent of the system is negative.