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International Conference on Mechatronic Science, Electric Engineering and Computer

Properties of spin squeezing in the quantum kicked tops model

Yongchao Wang

Published Aug 1, 2011• 0 citations
Publisher

Abstract

In this paper, by using QKT model, we give the changing relation between chaotic coefficient k and spin squeezing coefficient of two different definitions by numerical simulation calculation. The results show that the regular regions are stronger than chaotic ones in the classical phase space, the spin squeezed behavior is very strong, and the chaotic regions are stronger than regular ones in the classical phase space, the spin squeezed behavior is very weak, which indicate the spin squeezing is very sensitive to the corresponding classical chaos. Through the comparison we also know that the spin squeezing coefficient defined by Wineland is more sensitive to the classical chaos than the one by Kitagawa and Ueda, so the quantum chaos can be described by spin squeezing.

DOI
10.1109/mec.2011.6025635

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In this paper, by using QKT model, we give the changing relation between chaotic coefficient k and spin squeezing coefficient of two different definitions by numerical simulation calculation. The results show that the regular regions are stronger than chaotic ones in the classical phase space, the spin squeezed behavior is very strong, and the chaotic regions are stronger than regular ones in the classical phase space, the spin squeezed behavior is very weak, which indicate the spin squeezing is very sensitive to the corresponding classical chaos. Through the comparison we also know that the spin squeezing coefficient defined by Wineland is more sensitive to the classical chaos than the one by Kitagawa and Ueda, so the quantum chaos can be described by spin squeezing.
The quantum information is a new interdisciplinary science in the 21st century, and it has become a research field which attracts strongly much attention in the world. Recently, the study of the quantum computer is in the ascendant. In the process of finding a scheme for quantum computation, quantum chaos aroused much attention. It has been shown that it is possible to induce quantum chaos when running quantum computer and consequently it may destroy the operational condition of the quantum computer. The relationship between quantum entanglement and quantum chaos has already been investigated, and the spin squeezing is regarded as another classical quantum property indeed, then is there a natural relationship between quantum chaos and spin squeezing? In this paper a very typical QKT model in the quantum chaos has been discussed,and the properties of spin squeezing in the quantum chaotic system has been studied. The relation between spin squeezing parameters and chaotic parameter in the two different definitions is worked out by numerical calculation. The stronger that the regular regions are than chaotic ones, which are chosen firstly, in the classical phase space, the stronger the spin system which the initial states locate at the centre of elliptical regions as a result. If the initial states are chosen another condition, the contrary result is obtained naturally. It indicates the spin squeezing is very sensitive to the classical chaos and the classical chaos suppresses the spin squeezing. It is interesting that the definition by Wineland is more sensitive than the one by Kitagawa and Ueda, consequently a conclusion, which the quantum chaos can be described by spin squeezing, is acquired.
We study spin squeezing, an intrinsically quantum property, in the quantum kicked top model exhibiting chaotic behaviours in the classical limit. We show that spin squeezing can reveal the underlying chaotic and regular structures in phase space given by a sphere with a unit radius, namely, spin squeezing vanishes after a very short time for an initial spin coherent state centred in a chaotic region of the phase space, whereas spin squeezing occurs over a long period of time for the coherent state centred in an elliptic fixed point. We also study the distribution of the mean spin directions when quantum dynamics take places and give a comparison between the dynamics of spin squeezing and quantum entanglement.
A quantum dicke model exhibits chaotic dynamic characters with the classical limit.By studying the quantum entanglement and quantum spin squeezing,such results are obtained :linear entropy that measuring the power of quantum entanglement,according to different initial states which corresponding to the different regions in phase space,have different behaviors: the power of quantum entanglement strengthen in the chaotic regions obviously and it is weak in the regular regions by contraries;the spin squeezing express difference between regular and chaotic regions in phase space,and the little probabilities of existing spin squeezing are in the regular regions absolutely.In the same conditions,there are exactly similar varieties of the linear entropies and the squeezing parameters.
The quantum kicked top (QKT) is one of the most widely studied models in quantum chaos, providing a minimal yet powerful framework for exploring the relationship between classical nonlinear dynamics and quantum behavior. Unlike many chaotic systems with infinite-dimensional Hilbert spaces, the QKT possesses a finite-dimensional Hilbert space, making it analytically and numerically controllable while still showing a rich dynamical phenomena. In this chapter, we present a comprehensive introduction to the QKT as a paradigmatic model of quantum chaos. Starting from the classical kicked top, we derive the discrete nonlinear map governing the dynamics on the unit sphere and analyze its phase space structure through fixed points, stability analysis, bifurcations and Lyapunov exponents. We then discuss the role of symmetries, including rotational and time-reversal symmetry, and how their breaking modifies the dynamics. The quantum description is developed using Floquet theory, where the periodically driven spin system is represented by a unitary Floquet operator acting on a (2j+1)(2j+1)(2j+1)-dimensional Hilbert space. Within this framework, signatures of quantum chaos such as spectral statistics, entanglement generation and recurrences are discussed. The model also admits an interpretation as a system of interacting qubits, enabling explicit few-qubit realizations and direct connections with quantum information measures through reduced density matrices and entanglement entropy. By linking classical phase space structures with quantum dynamical indicators, the QKT provides a clear setting to investigate the emergence of chaotic behavior in the semiclassical limit. The chapter, therefore, highlights the quantum kicked top as a bridge between nonlinear classical dynamics, quantum chaos and modern quantum information science.
In this paper, we investigate the effects of spin squeezing on two-coupled quantum kicked tops, which have been previously shown to exhibit a quantum signature of chaos in terms of entanglement dynamics. Our results show that initial spin squeezing can lead to an enhancement in both the entanglement rate and the asymptotic entanglement for kicked tops when the initial state resides in the regular islands within a mixed classical phase space. On the other hand, we found a reduction in these two quantities if we were to choose the initial state deep inside the chaotic sea. More importantly, we have uncovered that an application of periodic spin squeezing can yield the maximum attainable entanglement entropy, albeit this is achieved at a reduced entanglement rate.
We study spin squeezing, an intrinsic quantum property, in the Dicke model without the rotating-wave approximation. We show that the spin squeezing can reveal the underlying chaotic and regular structures in phase space given by a Poincaré section, namely, it acts as an indicator of quantum chaos. Spin squeezing vanishes after a very short time for an initial coherent state centered in a chaotic region, whereas it persists over a longer time for the coherent state centered in a regular region of the phase space. We also study the distribution of the mean spin directions when quantum dynamics takes place. Finally, we discuss relations among spin squeezing, bosonic quadrature squeezing, and two-qubit entanglement in the dynamical processes.