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arXiv:cond-mat/0111573 · Physical Review A

Dynamics of a strongly driven two-component Bose-Einstein condensate

Grant Leonard Salmond, Catherine A. Holmes, Gerard J Milburn

Published Feb 28, 2002• 52 citations
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Abstract

We consider a two-component Bose-Einstein condensate in two spatially localized modes of a double-well potential, with periodic modulation of the tunnel coupling between the two modes. We treat the driven quantum field using a two-mode expansion and define the quantum dynamics in terms of the Floquet Operator for the time periodic Hamiltonian of the system. It has been shown that the corresponding semiclassical mean-field dynamics can exhibit regions of regular and chaotic motion. We show here that the quantum dynamics can exhibit dynamical tunneling between regions of regular motion, centered on fixed points (resonances) of the semiclassical dynamics.

DOI
10.1103/physreva.65.033623

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We study the effects of chaotic dynamics on atomic tunneling between two weakly coupled Bose-Einstein condensates driven by a double-frequency periodic field. Under the Melnikov's chaos criterion, we divide the parameter space into three parts of different types, regular region, low-chaoticity region, and high-chaoticity region, and give the accurate boundaries between the different regions. It is found that the atomic tunneling can be enhanced in the presence of chaos. Particularly, in the high-chaoticity regions, the chaos-induced inversion of the population imbalance is observed numerically.
We theoretically study binary Bose-Einstein condensates trapped in a single-well harmonic potential to probe the dynamics of collective atomic motion. The idea is to choose tunable scattering lengths through Feshbach resonances such that the ground-state wave function for two types of the condensates are spatially immiscible where one of the condensates, located at the center of the potential trap, can be effectively treated as a potential barrier between bilateral condensates of the second type of atoms. In the case of small wave-function overlap between bilateral condensates, one can parametrize their spatial part of the wave functions in the two-mode approximation together with the time-dependent population imbalance zzz and the phase difference $\ensuremath{\phi}$ between two wave functions. The condensate in the middle can be approximated by a Gaussian wave function with the displacement of the condensate center $\ensuremath{\xi}$. As driven by the time-dependent displacement of the central condensate, we find the Josephson oscillations of the collective atomic motion between bilateral condensates as well as their anharmonic generalization of macroscopic self-trapping effects. In addition, with the increase in the wave-function overlap of bilateral condensates by properly choosing tunable atomic scattering lengths, the chaotic oscillations are found if the system departs from the state of a fixed point. The Melnikov approach with a homoclinic solution of the derived $z, \ensuremath{\phi}$, and $\ensuremath{\xi}$ equations can successfully justify the existence of chaos. All results are consistent with the numerical solutions of the full time-dependent Gross-Pitaevskii equations.
We examine the nonlinear dynamical behavior of a spinor Bose-Einstein condensate in a double-well potential. Considering a condensate with large number of atoms, such that it can be described using the mean field theory, we separate the spinor dynamics from the spatial dynamics under the single-mode approximation. We limit ourselves to certain initial conditions under which the spatial mode is frozen so that we can focus on the spinor dynamics only. Identifying collective spin variables of our system, we derive the corresponding nonlinear equations of motion for them. Employing standard stability analysis, we find and characterize fixed points of the system. For a wide range of physical parameters such as tunneling strength and non-linear interactions, as well as for various initial preparations of the system, we identify qualitatively different dynamical regimes possible in the system. In particular, complete and incomplete oscillations of spin variables between quantum wells are found. We also show that by bringing some fixed points close to each other in the phase space of the system, it is possible to induce amplitude modulation to those otherwise regular tunneling oscillations.
We consider the quantum dynamics of a neutral atom Bose- Einstein condensate in a double-well potential, including hard-sphere particle interactions. Using a mean-field factorization we show that the coherent oscillations due to tunnelling are suppressed when the number of atoms exceeds a critical value. An exact quantum solution, in a two-mode approximation, shows that the mean-field solution is modulated by a quantum collapse and revival sequence. Chaotic dynamics results when the potential is modulated.
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