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arXiv:0912.0444 · Journal of Physics B Atomic Molecular and Optical Physics

Atom-number squeezing and bipartite entanglement of two-component Bose–Einstein condensates: analytical results

Guangri Jin, X W Wang, D Li, Yanwu Lü

Published Jan 25, 2010• 17 citations
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Abstract

We investigate spin dynamics of a two-component Bose-Einstein condensates with weak Josephson coupling. Analytical expressions of atom-number squeezing and bipartite entanglement are presented for atom-atom repulsive interactions. For attractive interactions, there is no number squeezing; however, the squeezing parameter is still useful to recognize the appearance of Schrödinger's cat state.

DOI
10.1088/0953-4075/43/4/045301

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We investigate spin dynamics of a two-component Bose-Einstein condensates with weak Josephson coupling. Analytical expressions of atom-number squeezing and bipartite entanglement are presented for atom-atom repulsive interactions. For attractive interactions, there is no number squeezing; however, the squeezing parameter is still useful to recognize the appearance of Schrödinger's cat state.
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We investigate spin squeezing dynamics in a two-component Bose–Einstein condensate (BEC) in the presence of the nonlinear interatomic interaction, interspecies interaction and Josephson-like tunneling interaction. In particular, we are interesting in the dependence of spin squeezing parameter on the interspecies interaction and the numbers of atom. By adopting the two-mode approximation and the rotating wave approximation, we succeed in obtaining analytical solutions for the optimally squeezed angle and spin squeezing parameter. It is shown that the stronger interspecies interaction induces faster spin squeezing and the more atoms or the larger population imbalance induces stronger squeezing; while the Josephson-like tunneling gives vanishing contribution to spin squeezing.
We investigate spin squeezing of a two-mode boson system with a Josephson coupling. An exact relation between the squeezing and the single-particle coherence at the maximal-squeezing time is discovered, which provides a more direct way to measure the squeezing by readout of the coherence in atomic interference experiments. We prove explicitly that the strongest squeezing is along the Jz{J}_{z}Jz​ axis, indicating the appearance of an atom number-squeezed state. Power laws of the strongest squeezing and the optimal coupling with particle number NNN are obtained based upon a wide range of numerical simulations.
Based on the exact solution of the time-dependent Schrödinger equation for two-species Bose–Einstein condensates (BECs) consisting of two hyperfine states of the atoms coupled by a tuned adiabatic and time-varying Raman coupling, we obtain analytically the entanglement dynamics of the system with various initial states, particularly the SU(2) coherent state, for both of cases with and without the nonlinear interactions. It is shown that the effect of nonlinear interaction on the entanglement appears only in a longer time period depending on the BEC parameters.