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Chinese Physics B

Chaotic matter shock wave of an open system

Yan Deng, Wenhua Hai, Shiguang Rong, Honghua Zhong

Published Dec 1, 2010• 2 citations
Publisher

Abstract

We investigate a one-dimensional open Bose-Einstein condensate with attractive interaction, by considering the effect of feeding from nonequilibrium thermal cloud and applying the time-periodic inverted-harmonic potential. Using the direct perturbation method and the exact shock wave solution of the stationary Gross—Pitaevskii equation, we obtain the chaotic perturbed solution and the Melnikov chaotic regions. Based on the analytical and the numerical methods, the influence of the feeding strength on the chaotic motion is revealed. It is shown that the chaotic regions could be enlarged by reducing the feeding strength and the increase of feeding strength plays a role in suppressing chaos. In the case of "nonpropagated" shock wave with fixed boundary, the number of condensed atoms increases faster as the feeding strength increases. However, for the free boundary the metastable shock wave with fixed front density oscillates its front position and atomic number aperiodically, and their amplitudes decay with the increase of the feeding strength.

DOI
10.1088/1674-1056/19/12/120502

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We investigate a one-dimensional open Bose-Einstein condensate with attractive interaction, by considering the effect of feeding from nonequilibrium thermal cloud and applying the time-periodic inverted-harmonic potential. Using the direct perturbation method and the exact shock wave solution of the stationary Gross—Pitaevskii equation, we obtain the chaotic perturbed solution and the Melnikov chaotic regions. Based on the analytical and the numerical methods, the influence of the feeding strength on the chaotic motion is revealed. It is shown that the chaotic regions could be enlarged by reducing the feeding strength and the increase of feeding strength plays a role in suppressing chaos. In the case of "nonpropagated" shock wave with fixed boundary, the number of condensed atoms increases faster as the feeding strength increases. However, for the free boundary the metastable shock wave with fixed front density oscillates its front position and atomic number aperiodically, and their amplitudes decay with the increase of the feeding strength.
It is demonstrated that the well-known Smale-horseshoe chaos exists in the time evolution of the one-dimensional Bose-Einstein condensate (BEC) driven by the time-periodic harmonic or inverted-harmonic potential. A formally exact solution of the time-dependent Gross-Pitaevskii equation is constructed, which describes the matter shock waves with chaotic or periodic amplitudes and phases. When the periodic driving is switched off and the number of condensed atoms is conserved, we obtained the exact stationary states and nonstationary states. The former contains the stable ``nonpropagated'' shock wave, and in the latter the shock wave alternately collapses and grows for the harmonic trapping or propagates with exponentially increased shock-front speed for the antitrapping. It is revealed that the existence of chaos plays a role for suppressing the blast of matter wave. The results suggest a method for preparing the exponentially accelerated BEC shock waves or the stable stationary states.
We investigate the phase effects of a periodically driven Bose–Einstein condensate (BEC) held in a spatially two-dimensional (2D) harmonic or inverted-harmonic potential. A formally exact solution of the time-dependent Gross–Pitaevskii equation is found, which depicts the shock wave with chaotic or periodic amplitude and phase. The atomic densities are illustrated numerically, and the circularly symmetric distributions in the separable phase and the axially symmetric BEC clusters in the inseparable phase are shown. It is demonstrated that the periodic driving may lead to chaos for both phases, which plays a role in avoiding the escape of the solution and restraining the BEC collapse and blast. The results suggest a method for controlling the directed transports of the 2D BEC.
We investigate the dynamics of a weakly open Bose-Einstein condensate with attractive interaction in a magneto-optical double-well trap. A set of time-dependent ordinary differential equations describing the complex dynamics are derived by using a two-mode approximation. The stability of the stationary solution is analyzed and some stability regions on the parameter space are displayed. In the symmetric well case, the numerical calculations reveal that by adjusting the feeding from the nonequilibrium thermal cloud or the two-body dissipation rate, the system could transit among the periodic motions, chaotic self-trapping states of the Lorenz model, and the steady states with the zero relative atomic population or with the macroscopic quantum self-trapping (MQST). In the asymmetric well case, we find the periodic orbit being a stable two-sided limited cycle with MQST. The results are in good agreement with that of the direct numerical simulations to the Gross-Pitaevskii equation.
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.
Chaotic space-time evolution is investigated for the particle number density of a Bose-Einstein condensate with attractive interatomic interaction loaded into a traveling optical lattice. Melnikov chaos is studied and the weakly chaotic regime is presented analytically. Transitions from transient to stationary chaos in the space-time evolution are illustrated numerically. The results show that, on increasing the strength of the optical potential, the transient chaos falls onto several different attractors. Meanwhile, these attractors undergo a series of period-doubling bifurcations when the optical potential intensity is increased continuously, and eventually stationary chaos arises for a critical depth of the optical lattice. The obstructions to chaos caused by the damping and the motion of lattice are also demonstrated.