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Journal of Atomic and Molecular Physics

Regular and chaoticdistribution of Bose-Einstein condensed atoms with a space-dependent nonlinear interaction

Yong Gao

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

This paper studies the regular and chaotic spatial distribution of Bose-Einstein condensed atoms with a space-dependent nonlinear interaction.There exists a steady atomic current in the system due to the space-dependent phase of condensate.For the system with a positive chemical potential and repulsive interatomic interaction,we construct the general solution of the 1st-order equation,whose boundedness conditions contain the famous Mel'nikov chaotic criterion.When the system doesn't satisfy the perturbation conditions,numerical simulations reveal that increasing the atomic current can destroy the spatial symmetry of the distributional structure of condensed atoms,whether the condensed atoms in a chaotic or regular distribution.

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This paper studies the regular and chaotic spatial distribution of Bose-Einstein condensed atoms with a space-dependent nonlinear interaction.There exists a steady atomic current in the system due to the space-dependent phase of condensate.For the system with a positive chemical potential and repulsive interatomic interaction,we construct the general solution of the 1st-order equation,whose boundedness conditions contain the famous Mel'nikov chaotic criterion.When the system doesn't satisfy the perturbation conditions,numerical simulations reveal that increasing the atomic current can destroy the spatial symmetry of the distributional structure of condensed atoms,whether the condensed atoms in a chaotic or regular distribution.
In this paper, we study the spatially chaotic distribution of atoms in a Bose-Einstein condensate system, trapped in an asymmetric periodic potential. For a constant phase of condensate, without atom currents in the system, the space distributed structure of condensated atoms can be described by an undamped Duffing equation with double drivers. Through theoretical analyses, the Mel'nikov chaotic criterion for the system with a repulsive interatomic interaction is presented. Numerical simulations show that an increasing chemical potential can exert considerable suppression on the chaotic distribution of condensated atoms and even completely eliminate chaos. For a system with an attractive interatomic interaction, under some specific parametric conditions, adjusting the ratio between optical lattice potential amplitudes will force the condensated atoms from a periodic state into a spatially chaotic distribution; with the increase of chemical potential, the spatially chaotic distribution is completely suppressed.
Abstract We investigate the chaotic and regular spatial structures of Bose–Einstein condensates (BECs) with a spatially modulated atom-atom interaction and without an external trapping potential. A BEC with a spatially modulated atom-atom interaction is equivalent to being constrained by a nonlinear optical lattice. Theoretical analyses show the existence of a steady atomic current in the BEC with a spatially varying phase. Under perturbative conditions, the Melnikov chaos criteria of BECs with a spatially varying phase and a constant one are theoretically obtained, respectively. When the perturbative conditions cannot be satisfied, for a repulsive BEC with a spatially varying phase, numerical simulations demonstrate that changing the initial condition can eliminate the chaotic spatial structure and then the system transitions into a biperiodic spatial structure. Increasing the chemical potential can result in a transition from the biperiodic spatial structure to a single-periodic spatial structure. For an attractive BEC with a spatially varying phase, numerical simulations show that decreasing the chemical potential can lead to a high atomic density, but when the wave number of the laser inducing the optical Feshbach resonance exceeds a critical value, the atomic density falls back to a finite range. Regardless of whether the BEC has a spatially varying phase or a constant one, modulating the laser wave number can effectively suppress the chaotic spatial structure in the BEC and then force it into a regular spatial structure.
The spatial chaos of Bose–Einstein condensates in a cigar-shaped trap is studied. For a system with a steady current, we construct the general solution of the 1st-order equation. From the boundedness condition of the general solution, we obtain the Melnikov function predicting the onset of chaos. The unpredictability of the system's distribution of atom density is also theoretically analyzed. For a 23 Na system meeting the perturbation condition, numerical simulations show the existence of chaos, which is in accordance with our analytical results. Numerical simulations of a 87 Rb system dissatisfying the perturbation condition also demonstrate that there exists chaos in the system. The case without a current is also investigated.
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.
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.
We study the nonlinear dynamics of two-component Bose–Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross–Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.