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arXiv:0808.1957 · Physical Review A

Relationship between spin squeezing and single-particle coherence in two-component Bose-Einstein condensates with Josephson coupling

Guangri Jin, C. K. Law

Published Dec 29, 2008• 37 citations
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Abstract

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 ${J}_{z}$ axis, indicating the appearance of an atom number-squeezed state. Power laws of the strongest squeezing and the optimal coupling with particle number $N$ are obtained based upon a wide range of numerical simulations.

DOI
10.1103/physreva.78.063620

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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.
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 present a detailed analysis of spin squeezing of the one-axis twisting model with a many-body phase dephasing, which is induced by external field fluctuation in a two-mode Bose-Einstein condensates. Even in the presence of the dephasing, our analytical results show that the optimal initial state corresponds to a coherent spin state ∣θ0,ϕ0⟩|\theta_{0}, \phi_0\rangle∣θ0​,ϕ0​⟩ with the polar angle θ0=π/2\theta_0=\pi/2θ0​=π/2. If the dephasing rate γ≪S−1/3\gamma\ll S^{-1/3}γ≪S−1/3, where SSS is total atomic spin, we find that the smallest value of squeezing parameter (i.e., the strongest squeezing) obeys the same scaling with the ideal one-axis twisting case, namely ξ2∝S−2/3\xi^2\propto S^{-2/3}ξ2∝S−2/3. While for a moderate dephasing, the achievable squeezing obeys the power rule S−2/5S^{-2/5}S−2/5, which is slightly worse than the ideal case. When the dephasing rate γ>S1/2\gamma>S^{1/2}γ>S1/2, we show that the squeezing is weak and neglectable.
Dynamical evolution of quantum mechanical squeezing and entanglement in a two-mode Bose-Einstein condensate (TBEC) with an adiabatic, time-varying Raman coupling is studied by finding analytical expressions for these quantities. In particular, we study the entanglement between the atoms in the condensate as well as that between the two modes. The nature of the enhanced quantum correlations in TBEC is clarified by considering squeezing and entanglement both with and without the nonlinear interaction turned on; it is found that entanglement approaching maximal value can be achieved with the nonlinear interactions present. Somewhat counterintuitively, greater squeezing is found in the absence of nonlinear interactions. This is due to the collapses and revivals of the TBEC quantum state induced by the nonlinear interactions. In addition, results involving the self-trapping phase state of TBEC indicate potential for creating a dynamically stable, macroscopic entangled quantum state which is relatively robust with respect to atom number fluctuations.