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Physical Review A

Quantum Fisher information and spin squeezing of the non-Hermitian one-axis twisting model and the effect of dephasing

Tie-Jun Hou

Published Jan 13, 2017• 7 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.95.013824

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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 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.
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.
In the absence of decay, the conditional dynamics for an open system is often describable by a non-Hermitian Hamiltonian. This study investigates spin squeezing (SS) in a non-Hermitian one-axis twisting (OAT) model. Somewhat surprisingly, SS close to the limit of Hermitian two-axis counter twisting (TACT) Hamiltonian is achievable for some parameters, which significantly improves upon the optimal value realizable by the Hermitian OAT model. The drawback is like with all conditional schemes, it takes on average longer time to evolve into a steady state, and the probability of no decay or success decreases as the number of atoms (spins) increases. The result above for the steady-state SS in a non-Hermitian OAT Hamiltonian is thus limited to small systems. For other parameter regimes, however, desirable SS arrives dynamically before a steady state is achieved, with a greatly shortened evolution time and enhanced probability of success, while still remains significantly improved over the limit of Hermitian OAT.
We investigate spin squeezing (SS) and the quantum Fisher information (QFI) for the Jaynes-Cummings Dicke (JC-Dicke) model in a two component atomic Bose-Einstein condensate (BEC) inside an optical cavity. Analytical expressions for spin squeezing and the reciprocal of the quantum Fisher information per particle (RMQFI) are derived using the frozen spin approximation. It is shown that in the superradiant phase near the critical point, maximum squeezing and maximum quantum entanglement occurs. The present study is relevant to quantum information processing and precision spectroscopy.