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

Modern Physics Letters B

Exact solution of degenerate and nondegenerate optical parametric oscillator coupled with a squeezed thermal bath

Braulio Misael Villegas-Martínez, H. M. Moya-Cessa, Francisco Soto

Published Jun 28, 2018• 2 citations
Publisher

Abstract

We solve exactly the master equation of the degenerate and nondegenerate parametric oscillator in the presence of a squeezed reservoir. We show that the formal solutions of both systems can be obtained in terms of the density operator by applying squeeze transformations and using the superoperators formalism.
DOI
10.1142/s0217984918502470

Related papers

Analytic solution to the nonlinear generation of squeezed states in a thermal bath

Paul R. B. Hughes, Marc M. Dignam

We model squeezed state generation in a lossy optical cavity in the presence of a thermal bath using the Lindblad master equation. We show that in the undepleted-pump approximation, the exact solution is a squeezed thermal state, where thermal photons arise both from loss and from the thermal bath. We derive a closed-form solution for the evolution of the quadrature uncertainty arising from pulsed degenerate spontaneous parametric down conversion in the cavity under the parametric oscillation threshold. We apply this solution under different pump conditions and show in detail how the thermal environment reduces quadrature squeezing as well as the second-order coherence function.

Physical Review A•Dec 24, 2024•2 citations

Analytic solution to the nonlinear generation of squeezed states in a thermal bath

Paul R. B. Hughes, Marc M. Dignam

We model squeezed state generation in a lossy optical cavity in the presence of a thermal bath using the Lindblad master equation. We show that the exact solution is a squeezed thermal state, where thermal photons arise both from loss and from the thermal bath. We derive an exact, closed-form solution for the evolution of the quadrature uncertainty arising from pulsed degenerate spontaneous parametric down conversion in the cavity. We apply this solution under different pump conditions and show in detail how the thermal environment reduces quadrature squeezing as well as the second order coherence function.

arXiv:2406.18694•Jun 26, 2024•0 citations

Superposed Degenerate Parametric Oscillator with Coherent Light

Yimenu Yeshiwas

In this paper, we have studied the statistical and squeezing properties of the light produced by superposed light beams generating by a pair of degenerate parametric oscillator whose cavity mode is driven by a coherent light and is coupled to a vacuum reservoir via a single port mirror. We obtain c-number Langevin equation associated with the normal ordering using the pertinent master equation. Employing the solution of the c-number Langevin equation and the density operator, we have determined the mean and the variance photon number, quadrature variances and squeezing spectrum of the superposed light beams.

Advances in physics theories and applications•Jan 1, 2018•0 citations

Solution to the Master Equation of a Free Damped Harmonic Oscillator with Linear Driving

Yang Jie, Huai-Xin Lu, Bo Zhao +2 more

We use the Lie algebra representation theory for superoperators to solve the master equation for a harmonic oscillator with a linear driving term in a squeezed thermal reservoir. By using the quantum displacement transformation and squeeze transformation, we show that the master equation has an su (1,1) Lie algebra structure, with which we obtain the explicit solution to the master equation. A simple but typical example is given to illustrate our method.

Chinese Physics Letters•May 16, 2003•7 citations

Solution to the Master Equation for Nondegenerate Parametric Amplification with Thermal Reservoir

Zhong-Jie Wang Zhong-Jie Wang, Xiao-Dong Zhang

By using Lie dynamical algebra representation theory, we have solved the master equation for the nondegenerate parametric amplifier model in a thermal reservoir. Applying a series of transformations, we show that the master equation has multiple commuted SU(1,1) Lie algebra structures. The explicit solution to the master equation has been obtained.

The Journal of Atomic and Molecular Sciences•Oct 20, 2010•0 citations

Generalized master equation for systems in nonideal cavities with squeezed baths

R.W.F. van der Plank, L.G. Suttorp

The master equation for the density operator of a system in a lossy cavity, which is coupled to a squeezed bath, is generalized so as to include the effects of an enhanced loss through a mirror of finite transmittivity. As compared to the standard master equation, which is valid for a nearly-perfect cavity, the generalized master equation is found to contain additional terms that account for an effective squeezed-light mixing at the nonideal mirror and for the interplay of the photon loss and the interaction within the cavity. As an example, the new master equation is used to study the influence of the enhanced losses on the photon statistics of a localized degenerate parametric oscillator. It is found that considerable changes in the photon distribution can occur as soon as the quality of the mirror becomes less than perfect.

The European Physical Journal D•Jan 1, 1998•2 citations
We model squeezed state generation in a lossy optical cavity in the presence of a thermal bath using the Lindblad master equation. We show that in the undepleted-pump approximation, the exact solution is a squeezed thermal state, where thermal photons arise both from loss and from the thermal bath. We derive a closed-form solution for the evolution of the quadrature uncertainty arising from pulsed degenerate spontaneous parametric down conversion in the cavity under the parametric oscillation threshold. We apply this solution under different pump conditions and show in detail how the thermal environment reduces quadrature squeezing as well as the second-order coherence function.
We model squeezed state generation in a lossy optical cavity in the presence of a thermal bath using the Lindblad master equation. We show that the exact solution is a squeezed thermal state, where thermal photons arise both from loss and from the thermal bath. We derive an exact, closed-form solution for the evolution of the quadrature uncertainty arising from pulsed degenerate spontaneous parametric down conversion in the cavity. We apply this solution under different pump conditions and show in detail how the thermal environment reduces quadrature squeezing as well as the second order coherence function.
In this paper, we have studied the statistical and squeezing properties of the light produced by superposed light beams generating by a pair of degenerate parametric oscillator whose cavity mode is driven by a coherent light and is coupled to a vacuum reservoir via a single port mirror. We obtain c-number Langevin equation associated with the normal ordering using the pertinent master equation. Employing the solution of the c-number Langevin equation and the density operator, we have determined the mean and the variance photon number, quadrature variances and squeezing spectrum of the superposed light beams.
The master equation for the density operator of a system in a lossy cavity, which is coupled to a squeezed bath, is generalized so as to include the effects of an enhanced loss through a mirror of finite transmittivity. As compared to the standard master equation, which is valid for a nearly-perfect cavity, the generalized master equation is found to contain additional terms that account for an effective squeezed-light mixing at the nonideal mirror and for the interplay of the photon loss and the interaction within the cavity. As an example, the new master equation is used to study the influence of the enhanced losses on the photon statistics of a localized degenerate parametric oscillator. It is found that considerable changes in the photon distribution can occur as soon as the quality of the mirror becomes less than perfect.