Spin squeezing, negative correlations, and concurrence in the quantum kicked top model

Xiaoqian Wang, Jian Ma, Lijun Song, Xihe Zhang, and Xiaoguang Wang

Phys. Rev. E 82, 056205 – Published 12 November 2010

Abstract

We study spin squeezing, negative correlations, and concurrence in the quantum kicked top model. We prove that the spin squeezing and negative correlations are equivalent for spin systems with only symmetric Dicke states populated. We numerically analyze spin squeezing parameters and concurrence in this model and find that the maximal spin squeezing direction, which refers to the minimal pairwise correlation direction, is strongly influenced by quantum chaos. Entanglement (spin squeezing) sudden death and sudden birth occur alternatively for the periodic and quasiperiodic cases, while only entanglement (spin squeezing) sudden death is found for the chaotic case.

Received 13 July 2010

DOI:https://doi.org/10.1103/PhysRevE.82.056205

Authors & Affiliations

Xiaoqian Wang^1,2, Jian Ma², Lijun Song³, Xihe Zhang¹, and Xiaoguang Wang^2,*

¹Department of Physics, Changchun University of Science and Technology, Changchun 130022, People’s Republic of China
²Department of Physics, Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, People’s Republic of China
³School of Science, Changchun University, Changchun 130022, People’s Republic of China

^*xgwang@zimp.zju.edu.cn

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Vol. 82, Iss. 5 — November 2010

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Images

Figure 1
(Color online) Stroboscopic phase-space map of the classical kicked top with $κ = 3$ and $p = π / 2$ . We choose 200 random initial states and each evolves 200 kicks. A triangle at $(θ, ϕ) = (2.25, 0.63)$ is at the fixed point, namely, in the periodic region. A diamond at $(θ, ϕ) = (2.25, - 2.35)$ is in the quasiperiodic region. A circle at $(θ, ϕ) = (2.25, - 1)$ is in the chaotic region.Reuse & Permissions
Figure 2
(Color online) Dynamical evolutions of the parameters $ξ_{T}^{2}$ , $ξ_{KU}^{2}$ , and $ξ_{\vec{n}}^{2}$ with different initial states. We choose $N = 50$ . In the periodic region (a), $(θ, ϕ) = (2.25, 0.63)$ , $ξ_{KU}^{2}$ and $ξ_{T}^{2}$ are almost the same, while $ξ_{\vec{n}}^{2}$ is very large. This implies that, the maximal spin squeezing is around the ${\vec{n}}_{⊥}$ direction. However, in the chaotic region (b), $(θ, ϕ) = (2.25, - 1)$ , the differences between $ξ_{KU}^{2}$ and $ξ_{T}^{2}$ are obvious, that means, the maximal spin squeezing is not restricted to the ${\vec{n}}_{⊥}$ direction. The dashed line corresponds to 1.Reuse & Permissions
Figure 3
(Color online) Directions of the maximal spin squeezing. The dots on the unit sphere represent the end points of the directions of maximal spin squeezing. And the axis label $\vec{n}$ denotes the mean spin direction, ${\vec{n}}_{1}$ and ${\vec{n}}_{2}$ are two orthogonal directions which are perpendicular to $\vec{n}$ . In the left plot, the initial state is in the periodic region, with $(θ, ϕ) = (2.25, 0.63)$ . And in the right plot, the initial state is in the chaotic region, with $(θ, ϕ) = (2.25, - 1)$ .Reuse & Permissions
Figure 4
(Color online) Evolutions of $ξ_{T}^{2}$ , $ξ_{KU}^{2}$ , and $ξ_{C}^{2}$ with different initial states, and we choose $N = 50$ . In (a) and (b), the initial state is in the periodic region, at $(θ, ϕ) = (2.25, 0.63)$ . The values of $ξ_{T}^{2}$ and $ξ_{C}^{2}$ are almost the same except for the first two kicks, but there are small differences between $ξ_{KU}^{2}$ and $ξ_{C}^{2}$ . In (c) and (d), we choose $(θ, ϕ) = (2.25, - 1)$ , which is centered in the chaotic region. There are small differences between $ξ_{T}^{2}$ and $ξ_{C}^{2}$ , but the differences between $ξ_{KU}^{2}$ and $ξ_{C}^{2}$ are large. The dashed line corresponds to 1.Reuse & Permissions
Figure 5
(Color online) Dynamical evolutions of concurrence in the QKT model for (a) the periodic case $(θ, ϕ) = (2.25, 0.63)$ , (b) the quasiperiodic case $(θ, ϕ) = (2.25, - 2.35)$ , and (c) the chaotic case $(θ, ϕ) = (2.25, - 1)$ . Here, we choose $N = 50$ .Reuse & Permissions
Figure 6
(Color online) Dynamical evolutions of spin squeezing in the QKT model with (a) the periodic case $(θ, ϕ) = (2.25, 0.63)$ , (b) the quasiperiodic case $(θ, ϕ) = (2.25, - 2.35)$ , and (c) the chaotic case $(θ, ϕ) = (2.25, - 1)$ . Here, we choose $N = 50$ .Reuse & Permissions

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