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Journal of Changchun University

Study of Classical Phase Space in Two-component Bose-Einstein Condensate System

Lijun Song

Published Jan 1, 2011• 0 citations
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Abstract

Two-component Bose-Einstein condensate system impacted by pulses has chaotic dynamics behaviors in classical limit.By studying the corresponding classical phase space structure,we obtain the parameter scope of the transition of phase space from regular structure to chaotic structure.The results have important significance to the study of the stability of Bose-Einstein condensate.

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Two-component Bose-Einstein condensate system impacted by pulses has chaotic dynamics behaviors in classical limit.By studying the corresponding classical phase space structure,we obtain the parameter scope of the transition of phase space from regular structure to chaotic structure.The results have important significance to the study of the stability of Bose-Einstein condensate.
Spin squeezing of two-component Bose-Einstein condensate, which is impacted by the periodic impulses, is investigated. The results show that spin squeezing can reveal the underlying chaotic and regular structures of phase space, namely, spin squeezing vanishes after a very short time for an initial coherent state centred in a chaotic region, but spin squeezing exists for a long time for an initial coherent state centred in a regular region. In particular, with time evolution, distribution and swing of the mean spin direction is closely related to the structure of the space where the initial coherent state centred in. Finally, spin squeezing dynamics of initial states centred in the whole phase space is investigated and a better quantum-classical correspondence is obtained.
Quantum Fisher information,derived from the classical Fisher information, is closely related to the quantum entanglement in quantum information. The entanglement and the quantum information which are both associated with the classical phase space are investigated in a two-component Bose-Einstein condensate impacted by the impulses. The results reveal that the states regardless of disorder of the phase space after the first impulse are entangled. However, the quantum information is very sensitive to the state centred in the classical phase space, concretely, the value of the quantum information centred in the chaotic region is greater than in the regular region. By employing the good quantum-classical correspondence, we conclude that the quantum information can serve as a signature of the quantum chaos.
The influence of the quantum chaos on the single-particle coherence and the pairwise entanglement is investigated in a two-component Bose-Einstein condensate impacted by periodic impulses. The results reveal that the single-particle coherence decays strongly when driven by chaos and keeps a lower degree of coherence. Simultaneously, there apears the maximal pairwise entanglement and it disappears after a short time. By using the properties of the single-particle coherence, we can measure directly the structure of the phase space in which the chaos exists, and this contributes to prevent the collapse of a Bose-Einstein condensate and control the chaotic behavior.
We study the stability of a two-component Bose-Einstein condensate (BEC) in the parameter regime in which its classical counterpart has regular motion. The stability is characterized by the fidelity for both the same and different initial states. We study as initial states the Fock states with definite numbers of atoms in each component of the BEC. It is found that for some initial times the two Fock states with all the atoms in the same component of the BEC are more stable than Fock states with atoms distributed in the two components. An experimental scheme is discussed, in which the fidelity can be measured in a direct way.
For a weakly and periodically driven two-component Bose-Einstein condensate (BEC) the Melnikov chaotic solution and boundedness conditions are derived from a direct perturbation theory that leads to the chaotic regions in the parameter space. Differing from the usual results, the chaotic regions depend on the initial conditions directly and can be controlled by setting the initial phase and modulating the frequency and amplitude of laser. It is demonstrated that the order-chaos transitions can be controlled by tuning the laser frequency only.