Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and General

Squeezed states in a quantum chaotic system

Karol Życzkowski

Published Dec 21, 1989• 7 citations
Publisher

Abstract

Time evolution of squeezed states in the quantum kicked rotator model is analysed. Squeezing influences the shape of quantum revivals obtained in the regime of classically regular motion, but does not facilitate the diffusion in angular momentum in the regime of classically chaotic motion. The speed of unlimited energy growth, which occurs in the case of quantum resonance, depends significantly on the squeezing parameter.

DOI
10.1088/0305-4470/22/24/003

Related papers

Squeezed states and quantum chaos

K. N. Alekseev, D. S. Priimak

We examine the dynamics of a wave packet that initially corresponds to a coherent state in the model of a quantum rotator excited by a periodic sequence of kicks. This model is the main model of quantum chaos and allows for a transition from regular behavior to chaotic in the classical limit. By doing a numerical experiment we study the generation of squeezed states in quasiclassical conditions and in a time interval when quantum-classical correspondence is well-defined. We find that the degree of squeezing depends on the degree of local instability in the system and increases with the Chirikov classical stochasticity parameter. We also discuss the dependence of the degree of squeezing on the initial width of the packet, the problem of stability and observability of squeezed states in the transition to quantum chaos, and the dynamics of disintegration of wave packets in quantum chaos.

arXiv:quant-ph/0111044•Journal of Experimental and Theoretical Physics•Jan 1, 1998•9 citations

Squeezed states and quantum chaos

Alekseev, K N, Primak, D S

We examine the dynamics of a wave packet that initially corresponds to a coherent state in the model of quantum kicked rotator. This main model of quantum chaos, which allows for a transition from regular to to chaotic behavior in the classical limit, may be realized in experiments with cold atoms. We study the generation of squeezed states in the quasiclassical limit and in a time interval when quantum-classical correspondence is yet well-defined. We find that the degree of squeezing depends on the degree of local instability in the system and increases with the Chirikov parameter of stochasticity. We discuss the dependence of the degree of squeezing on the initial width of the packet, the problems of stability and observability of squeezed states at the transition to quantum chaos, as well as the dynamics of wave packet destruction.

•Jan 1, 1998•8 citations

Dynamical evolution of squeezing and antibunching effects in a quantum chaotic system: The three-level Lipkin model

Rui-hua Xie, Gong-ou Xu

Time evolution of squeezing and antibunching effects in a nuclear model known as the three-level Lipkin model is analyzed. The two effects occur in the regime of classically regular motion, but disappear in the regime of classically chaotic motion, which is similar to that obtained in a spin-boson model (another quantum chaotic system). \textcopyright{} 1996 The American Physical Society.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Aug 1, 1996•6 citations

Chaos and squeezing in quantum optics

Alexander V. Gorokhov

Some quantum optical models possessing a transition from regular to chaotic dynamics and influence of `quantum chaos' to squeezing are investigated. Particular cases of semiclassical dynamics of a single atom and cooperative system of these atoms with (2j + 1)--equidistant levels interacting with a quantized photon mode in an ideal cavity were considered. Corresponding equations of motion are received without the rotation-wave approximation. Chaotic behavior and squeezing degree time dependence were obtained in computer simulations for coupling constant values or order of the atomic frequency.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 20, 2000•0 citations

Quantum Signatures of Anomalous Diffusion in Atom Optics

Bruce G. Klappauf, Windell H. Oskay, D. Steck +1 more

It is well established that classical chaotic motion is suppressed by quantum mechanics. The paradigm theoretical system has been the ?-kicked rotor, where the suppression manifests itself as dynamical localization. This effect is saturation of momentum growth after the quantum break time, with a resulting exponentially localized distribution. Classical analyses of this system have also identified regimes of anomalous diffusion, characterized by “Levy-type” flights in phase space [1]. This behavior is considerably more complex than simple diffusion and has attracted much interest in recent years. The quantum system was predicted to exhibit an increase in localization length near regions of anomalous diffusion [2], and recent theoretical work predicts very large growth of energy in this case, even for systems that are far from the semiclassical limit [3].

•May 3, 1998•0 citations

Spin squeezing properties in the quantum kicked top model

Lijun Song, Xiaoguang Wang, Dong Yan +1 more

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.

Journal of Physics B Atomic Molecular and Optical Physics•Jan 3, 2006•31 citations
Time evolution of squeezed states in the quantum kicked rotator model is analysed. Squeezing influences the shape of quantum revivals obtained in the regime of classically regular motion, but does not facilitate the diffusion in angular momentum in the regime of classically chaotic motion. The speed of unlimited energy growth, which occurs in the case of quantum resonance, depends significantly on the squeezing parameter.
We examine the dynamics of a wave packet that initially corresponds to a coherent state in the model of a quantum rotator excited by a periodic sequence of kicks. This model is the main model of quantum chaos and allows for a transition from regular behavior to chaotic in the classical limit. By doing a numerical experiment we study the generation of squeezed states in quasiclassical conditions and in a time interval when quantum-classical correspondence is well-defined. We find that the degree of squeezing depends on the degree of local instability in the system and increases with the Chirikov classical stochasticity parameter. We also discuss the dependence of the degree of squeezing on the initial width of the packet, the problem of stability and observability of squeezed states in the transition to quantum chaos, and the dynamics of disintegration of wave packets in quantum chaos.
We examine the dynamics of a wave packet that initially corresponds to a coherent state in the model of quantum kicked rotator. This main model of quantum chaos, which allows for a transition from regular to to chaotic behavior in the classical limit, may be realized in experiments with cold atoms. We study the generation of squeezed states in the quasiclassical limit and in a time interval when quantum-classical correspondence is yet well-defined. We find that the degree of squeezing depends on the degree of local instability in the system and increases with the Chirikov parameter of stochasticity. We discuss the dependence of the degree of squeezing on the initial width of the packet, the problems of stability and observability of squeezed states at the transition to quantum chaos, as well as the dynamics of wave packet destruction.
Some quantum optical models possessing a transition from regular to chaotic dynamics and influence of `quantum chaos' to squeezing are investigated. Particular cases of semiclassical dynamics of a single atom and cooperative system of these atoms with (2j + 1)--equidistant levels interacting with a quantized photon mode in an ideal cavity were considered. Corresponding equations of motion are received without the rotation-wave approximation. Chaotic behavior and squeezing degree time dependence were obtained in computer simulations for coupling constant values or order of the atomic frequency.
It is well established that classical chaotic motion is suppressed by quantum mechanics. The paradigm theoretical system has been the ?-kicked rotor, where the suppression manifests itself as dynamical localization. This effect is saturation of momentum growth after the quantum break time, with a resulting exponentially localized distribution. Classical analyses of this system have also identified regimes of anomalous diffusion, characterized by “Levy-type” flights in phase space [1]. This behavior is considerably more complex than simple diffusion and has attracted much interest in recent years. The quantum system was predicted to exhibit an increase in localization length near regions of anomalous diffusion [2], and recent theoretical work predicts very large growth of energy in this case, even for systems that are far from the semiclassical limit [3].
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.