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arXiv:0801.0932 · Physical Review Letters

Optimum Spin Squeezing in Bose-Einstein Condensates with Particle Losses

Yun Li, Yvan Castin, Alice Sinatra

Published May 28, 2008• 135 citations
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Abstract

The problem of spin squeezing with a bimodal condensate in the presence of particle losses is solved analytically by the Monte Carlo wave function method. We find the largest obtainable spin squeezing as a function of the one-body loss rate, the two-body and three-body rate constants, and the s-wave scattering length.
DOI
10.1103/physrevlett.100.210401

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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.