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

Physical Review A

Squeezed vacuum states in a nonlinear medium modulated by periodic kicking

Christopher C. Gerry, R. Grobe, Edward R. Vrscay

Published Jan 1, 1991• 11 citations
Publisher

Abstract

In this paper we study the dynamics of a nonlinear quantum-optical system subjected to a periodic modulation in the form of kicks. The system consists of a nonabsorbing anharmonic medium related to optical bistability, a degenerate parametric amplifier with a classical pump field that is modulated by a periodic sequence of kicks, and the initial state is taken to be a squeezed vacuum state. Using the related SU(1,1) coherent states (which are squeezed vacuum states), we study and compare the quantum and classical dynamics of the system. The ``classical'' motion in this case means the motion projected onto the phase space defined by the parameter labeling the generalized coherent states. For certain values of the coupling constants, we obtain both regular and chaotic motion in the classical phase space. In the quantum dynamics of the system, the manifestation of the classical chaos turns out to be rather weak, at least in the regime numerically accessible to us. We study the time evolution of the initial-state population probability, the average photon number in the field, and the squeezing of the field. We also briefly discuss the level statistics of the evolution operator.

DOI
10.1103/physreva.43.361

Related papers

Squeezed vacuum states in optically bistable two-photon media

Christopher C. Gerry, Edward R. Vrscay

The time evolution of squeezed vacuum states, taken to be SU(1,1) coherent states, interacting with a two-photon medium is examined using numerical methods. The non-photon-conserving medium is modeled by a Hamiltonian which consists of the free-field term, a non-photon-conserving term in the form of a degenerate parametric amplifier, and an anharmonic term which gives rise to optical bistability. This system has previously been shown to produce enhanced squeezing when interacting with ordinary coherent light. In the present work we find that the squeezing property is generally revoked by the anharmonic term and increased by the nonconserving term. The combined effects are not additive, however, and a quantum interference effect is observed in the calculations.

Physical Review A•Jun 1, 1988•20 citations

Long-time classical dynamics of the periodically driven system with a Kerr nonlinearity

T Lisowski

We examine the classical dynamics of a parametric amplifier driven by periodic `kicks' of the pump field inside a cavity filled with the Kerr medium. The time evolution of the initial SU(1,1) generalized coherent state is investigated, and the classification of the possible maps is presented. New features of these maps are observed if the evolution is continued after the initial few thousand iterations.

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Feb 1, 1997•1 citation

Quantum coherence and classical chaos in a pulsed parametric oscillator with a Kerr nonlinearity

Gerard J Milburn, Catherine A. Holmes

We consider a parametric amplifier driven by a periodically pulsed pump field inside a cavity containing a Kerr nonlinearity. The dynamics of the device is modeled as a kicked nonlinear system. The pulsed parametric amplifier constitutes the kick. In between kicks the dynamics is determined by the Kerr nonlinearity and damping. In the absence of damping, a classical description of the device exhibits a rich phase-space structure including fixed points of multiple period and chaos. We contrast the classical behavior of the mean intensity with that predicted by quantum dynamics. The mean photon number inside the cavity is shown to undergo regular collapse and revival in the regular region of the phase space and irregular revivals in the chaotic region. When damping is included, the quantum recurrences are rapidly suppressed, and the classical behavior is restored. In this case a stable steady state is possible. The damping represents the effect of photon-number measurements on the system. We also discuss the photon statistics in the steady state.

Physical Review A•Oct 1, 1991•83 citations

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

Time evolution of an anharmonic oscillator in an initial Holstein-Primakoff SU(1,1) coherent state

Vladimír Bužek

We have studied the interaction of the squeezed light with the nonabsorbing nonlinear medium in the framework of the model of an anharmonic oscillator initially in a Holstein-Primakoff SU(1,1) coherent state. We have shown that the initial squeezing reappears periodically. Furthermore, due to the interaction with the nonlinear medium, the squeezing can be enhanced.

Physical Review A•May 1, 1989•15 citations

Coherence and chaos in a quantum optical system

Gerard J Milburn

A nonlinear, kicked quantum optical system, which classically exhibits regions of regular and chaotic motion, is proposed as a possible experimental test of quantum chaos. The mean photon number is shown to undergo regular collapse and revival in the regular region of phase space and irregular revivals in the chaotic region.

Physical Review A•Jun 1, 1990•27 citations
In this paper we study the dynamics of a nonlinear quantum-optical system subjected to a periodic modulation in the form of kicks. The system consists of a nonabsorbing anharmonic medium related to optical bistability, a degenerate parametric amplifier with a classical pump field that is modulated by a periodic sequence of kicks, and the initial state is taken to be a squeezed vacuum state. Using the related SU(1,1) coherent states (which are squeezed vacuum states), we study and compare the quantum and classical dynamics of the system. The ``classical'' motion in this case means the motion projected onto the phase space defined by the parameter labeling the generalized coherent states. For certain values of the coupling constants, we obtain both regular and chaotic motion in the classical phase space. In the quantum dynamics of the system, the manifestation of the classical chaos turns out to be rather weak, at least in the regime numerically accessible to us. We study the time evolution of the initial-state population probability, the average photon number in the field, and the squeezing of the field. We also briefly discuss the level statistics of the evolution operator.
The time evolution of squeezed vacuum states, taken to be SU(1,1) coherent states, interacting with a two-photon medium is examined using numerical methods. The non-photon-conserving medium is modeled by a Hamiltonian which consists of the free-field term, a non-photon-conserving term in the form of a degenerate parametric amplifier, and an anharmonic term which gives rise to optical bistability. This system has previously been shown to produce enhanced squeezing when interacting with ordinary coherent light. In the present work we find that the squeezing property is generally revoked by the anharmonic term and increased by the nonconserving term. The combined effects are not additive, however, and a quantum interference effect is observed in the calculations.
We consider a parametric amplifier driven by a periodically pulsed pump field inside a cavity containing a Kerr nonlinearity. The dynamics of the device is modeled as a kicked nonlinear system. The pulsed parametric amplifier constitutes the kick. In between kicks the dynamics is determined by the Kerr nonlinearity and damping. In the absence of damping, a classical description of the device exhibits a rich phase-space structure including fixed points of multiple period and chaos. We contrast the classical behavior of the mean intensity with that predicted by quantum dynamics. The mean photon number inside the cavity is shown to undergo regular collapse and revival in the regular region of the phase space and irregular revivals in the chaotic region. When damping is included, the quantum recurrences are rapidly suppressed, and the classical behavior is restored. In this case a stable steady state is possible. The damping represents the effect of photon-number measurements on the system. We also discuss the photon statistics in the steady state.
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.