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arXiv:1312.3743 · Quantum Information and Computation

Spin squeezing of one-axis twisting model in the presence of phase dephasing

Chen-Gang Ji, Yong‐Chun Liu, Guangri Jin

Published Mar 1, 2013• 4 citations

Abstract

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 $|\theta_{0}, \phi_0\rangle$ with the polar angle $\theta_0=\pi/2$. If the dephasing rate $\gamma\ll S^{-1/3}$, where $S$ 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 $\xi^2\propto S^{-2/3}$. While for a moderate dephasing, the achievable squeezing obeys the power rule $S^{-2/5}$, which is slightly worse than the ideal case. When the dephasing rate $\gamma>S^{1/2}$, we show that the squeezing is weak and neglectable.

DOI: 10.26421/qic13.3-4-7

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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

|\theta_{0}, \phi_0\rangle

with the polar angle

\theta_0=\pi/2

. If the dephasing rate

\gamma\ll S^{-1/3}

, where

S

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

\xi^2\propto S^{-2/3}

. While for a moderate dephasing, the achievable squeezing obeys the power rule

S^{-2/5}

, which is slightly worse than the ideal case. When the dephasing rate

\gamma>S^{1/2}

, we show that the squeezing is weak and neglectable.

A detailed analysis of the quantum Fisher information (QFI) and spin squeezing (SS) of the non-Hermitian one-axis twisting model is conducted. The results show that the non-Hermitian model achieves significant entanglement in many-body systems, which is quite different from the Hermitian case, and achieves more SS than the optimal value of the Hermitian counterpart. Furthermore, we investigate the effect of dephasing, which is induced by external field fluctuations, and find out to what extent it weakens QFI and SS of the non-Hermitian one-axis twisting model.

We investigate the dependence of spin squeezing on the polar angle of the initial coherent spin state |θ 0 , ϕ 0 ⟩ in a generalized one-axis twisting model, where the detuning δ is taken into account. We show explicitly that regardless of δ and ϕ 0 , previous results of the ideal one-axis twisting are recovered as long as θ 0 =π/2. For a small departure of θ 0 from π/2, however, the achievable variance ( V − ) min ∼ N 2/3 , which is larger than the ideal case N 1/3 . We also find that the maximal squeezing time t min scales as N −5/6 . Analytic expressions of ( V − ) min and t min are presented and they agree with numerical simulations.

We investigate the dependence of the average parameter estimation precision (APEP), which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state |θ0, φ0〉 in a one-axis twisting model. Jin et al. [New J. Phys. 11 (2009) 073049] found that the spin squeezing sensitively depends on the polar angle θ0 of the initial coherent spin state. We show explicitly that the APEP is robust to the initial polar angle θ0 in the vicinity of π/2 and a near-Heisenberg limit ∝ 2/N in quantum single-parameter estimation may still be achieved for states created with the nonlinear evolution of the nonideal coherent spin states θ0 ∼ π/2. Based on this model, we also consider the effects of the collective dephasing on spin squeezing and the APEP.

We investigate the dependence of the average parameter estimation precision (APEP), which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state |θ 0 , φ 0 〉 in a one-axis twisting model. Jin et al. [ New J. Phys. 11 (2009) 073049 ] found that the spin squeezing sensitively depends on the polar angle θ 0 of the initial coherent spin state. We show explicitly that the APEP is robust to the initial polar angle θ 0 in the vicinity of π/2 and a near-Heisenberg limit ∝ 2/ N in quantum single-parameter estimation may still be achieved for states created with the nonlinear evolution of the nonideal coherent spin states θ 0 ∼ π/2. Based on this model, we also consider the effects of the collective dephasing on spin squeezing and the APEP.

We study the spin squeezing in a spin-1/2 Bose-Einstein condensates (BEC) with Raman-induced spin-orbit coupling (SOC). Under the condition of two-photon resonance and weak Raman coupling strength, the system possesses two degenerate ground states, using which we construct an effective two-mode model. The Hamiltonian of the two-mode model takes the form of the one-axis-twisting Hamiltonian, which is known to generate spin squeezing. More importantly, we show that the SOC provides a convenient control knob to adjust the spin nonlinearity responsible for spin squeezing. Specifically, the spin nonlinearity strength can be tuned to be comparable to the two-body density-density interaction, and hence is much larger than the intrinsic spin-dependent interaction strength in conventional two-component BEC systems such as

^{87}\mathrm{Rb}

and

^{23}\mathrm{Na}

in the absence of the SOC. We confirm the spin squeezing by carrying out a fully beyond-mean-field numerical calculation using the truncated Wigner method. Additionally, the experimental implementation is also discussed.