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Acta Physica Sinica

Quantum Fisher information and chaos in the system of Bose-Einstein condensate

Lijun Song, Dong Yan, Liu Yie

Published Jan 1, 2011• 6 citations
Publisher

Abstract

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.

DOI
10.7498/aps.60.120302

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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.
Fisher information is an important concept in estimation theory, which has recently been found closely related with the criteria of the entanglement in quantum information. Under the condition of non-rotating wave approximation, the classical phase space of the Dicke model displays chaotic dynamic properties. This paper studies the quantum Fisher information and the dynamic properties of spin squeezing in the interaction system of light and matter described in the Dicke model. Results reveal that, in the short-time instant state, wherever the initial state is, in a regular region or a chaotic region, the system displays entanglement; but in the long-time stable state, when the initial state is in the regular region, the system entanglement disappears, however, when the initial state is in the chaotic region, the system is always entangled. Compared with the spin-squeezing dynamic properties of the system, Fisher information is found to be able to effectively characterize quantum chaos. On further examination on the dynamic evolvement properties of the density matrix and purity of the system when in the regular and chaotic regions, we find that chaos gives rise to decoherence of the system, showing that quantum information become more sensitive to chaos.
We investigate both classical and quantum chaotic dynamics of a two-mode Bose-Einstein condensate driven by a continuously periodic field. We calculate the quantities, including quantum Fisher information (QFI), fidelity, and linear entropy, to characterize the quantum chaos and compare these quantities with the maximum Lyapunov exponent (MLE) of the corresponding classical system. The behaviors of the quantum quantities and the classical quantity show a strong correspondence regardless of the classical regular and chaotic regions in the parameter space. A quantitative link between the MLE and the short-time dynamics of the QFI is established. Particularly, we find that our continuously driven model is significantly superior to other models in accelerating entanglement generation through chaos, which is evidenced by the shorter time required for the QFI to reach the Heisenberg limit. We briefly discuss the underlying mechanism of this finding and its application in saving time costs and improving measurement accuracy as well.
We study the particle-entanglement dynamics witnessed by the quantum Fisher information (QFI) of a trapped Bose-Einstein condensate governed by the kicked rotor Hamiltonian. The dynamics is investigated with a beyond-mean-field approach. We link the time scales of the validity of this approximation in both classical regular and chaotic regions, with the maximum Lyapunov exponents of the classical system. This establishes an effective connection between the classical chaos and the QFI. We finally study the critical point of a quantum phase transition using the beyond-mean-field approximation by considering a two-mode bosonic Josephson junction with attractive interparticle interaction.
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.
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 is related to the problem of parameter estimation. Recently, a criterion has been proposed for entanglement in multipartite systems based on quantum Fisher information. This paper studies the behaviours of quantum Fisher information in the quantum kicked top model, whose classical correspondence can be chaotic. It finds that, first, detected by quantum Fisher information, the quantum kicked top is entangled whether the system is in chaotic or in regular case. Secondly, the quantum Fisher information is larger in chaotic case than that in regular case, which means, the system is more sensitive in the chaotic case.