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Physical Review A

Squeezing and entanglement of a Bose-Einstein condensate in optical lattices

X. P. Liu, P. T. Leung

Published Jan 23, 2008• 2 citations
Publisher

Abstract

The squeezing and entanglement properties of a one-component Bose-Einstein condensate trapped in optical lattices are theoretically studied. A two-mode squeezing parameter for the system is found, which is identical with Einstein-Podolsky-Rosen correlation, indicating the quantum correlation between excitation modes. Its dynamics and relation to the Hamiltonian parameters are quantitatively shown, and some constructive relation between squeezing and condensation is pointed out. For entanglement, the entanglement of formation of the two-mode system is also presented. For the probing of such a correlation, relevant experimental issues about atom shot noise are also discussed.

DOI
10.1103/physreva.77.013615

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The Hamiltonian operator of two-mode light field interacting with Bose-Einstein condensate(BEC) of two-level atoms is improved in terms of the lattice-liquid model,and the squeezing properties of two-mode squeezed field interacting with Bose-Einstein condensate of two-level atoms are studied.The results show that two quadrature components of light can be squeezed periodically,the maximum depth of squeezing is closely correlated to the initial squeezing parameter of light,and the duration is determined by the frequency of the light field.
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The entanglement in the system which consists of two-mode squeezed vacuum state and Bose- Einstein condensate in two-photon process is investigated.The entanglement of field-atom and the entangle- ment between the two-mode field are investigated using the quantum reduced entropy and quantum relative entropy,respectively.The influences of the initial squeezed parameter of field and the interaction between atoms on the evolution of the entanglement of field-atom and one of two modes of field are discussed.
The Hamiltonian operator of a system of single-mode light field interacting with Bose-Einstein condensate (BEC) of two-level atoms is discussed in terms of the lattice-liquid model. It is indicated that the contribution of the interaction between atoms to the Hamiltonian was irrationally overestimated in the literature, so the Hamiltonian operator is improved in the present paper. Based on the improved Hamiltonian, the equations of motion of the photon and atomic operators are derived analytically. The relevant parameters in the model are estimated in connection with the BEC experimental conditions. The influence of the interaction between atoms in the BEC on the squeezing of light field and the atomic lasers is studied. The results show that the dependence of squeezing factor with atom number in BEC is different from that given in literature. and the fluctuations of two quadrature components of light evolve periodically with cosine law and the fluctuations of two quadrature components of the atomic laser can be squeezed.
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