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

The European Physical Journal D

Generalized master equation for systems in nonideal cavities with squeezed baths

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

Published Jan 1, 1998• 2 citations
Publisher

Abstract

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.

DOI
10.1007/pl00021583

Related papers

Generalization of damping theory for cavities with mirrors of finite transmittivity

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

Standard damping theory is generalized to incorporate the effects of finite mirror transmittivity. The correction to the standard Langevin equation for the quasimode annihilation operator is determined in first order in the transmittivity of the mirrors. From the Langevin equation an effective master equation is derived. As an example, we study the decay of a single two-level atom at a fixed position in a nonideal cavity. For this case we find a modification of the damped Rabi oscillations, which depends on the atomic position. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Mar 1, 1996•16 citations

Spontaneous emission from an atom in a nonideal cavity: Application of a generalized master equation

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

The decay of an excited two-level atom in a cavity with mirrors of finite transmittivity is studied with the help of a generalized multimode master equation that has been established recently. The time evolution of the decaying atom is obtained by accounting for the interaction with infinitely many quasimodes. The analytical and numerical results are compared with those of the standard multimode master equation and of a universe-mode approach. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Sep 1, 1996•3 citations

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

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.

Modern Physics Letters B•Jun 28, 2018•2 citations

Squeezing for Intracavity generated light in the master equation approach

H. J. Carmichael

Master equation methods provide useful tools for analyzing the statistics of quantum optical systems. They focus attention on a simple system of interest (a single cavity mode, for example), accounting for its interaction with its environment in parameters describing decay rates and environmental fluctuations. Intracavity systems for generating squeezed light are prime candidates for analysis by these methods. It has been shown, however, that it is important in such analysis to distinguish between the statistics of the intracavity field and the statistics of the field generated outside the cavity by transmission through the cavity mirrors.1,2 It is desirable to perform calculations with the single mode inside the cavity. Then the statistics of the multimode field outside the cavity must be related to those of the internal mode. The situation is analogous to that in resonance fluorescence, where the statistics of the fluorescent field can be calculated in terms of the source dipole operator. In this paper the field outside an optical cavity is expressed in terms of the intracavity oscillator as a source. The measurement of squeezing in the external field is then related to the correlation properties of the cavity source operator. Measurement by photon counting of homodyned light is related to the spectrum of squeezing calculated by Walls and co-workers.

Annual Meeting Optical Society of America•Jan 1, 1986•0 citations

Unified GKLS quantum master equation beyond the secular approximation

Anton Sergeevich Trushechkin

Derivation of a quantum master equation for a system weakly coupled to a bath which takes into account non-secular effects, but, nevertheless, has the mathematically correct Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form (in particular, preserves positivity of the density operator) and also satisfies the standard thermodynamic properties is a known long-standing problem in theory of open quantum systems. The non-secular terms are important when some energy levels of the system or their differences (Bohr frequencies) are nearly degenerate. We provide a fully rigorous derivation of such equation based on a formalization of the weak-coupling limit for the general case.

•Mar 22, 2021•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 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
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.
Standard damping theory is generalized to incorporate the effects of finite mirror transmittivity. The correction to the standard Langevin equation for the quasimode annihilation operator is determined in first order in the transmittivity of the mirrors. From the Langevin equation an effective master equation is derived. As an example, we study the decay of a single two-level atom at a fixed position in a nonideal cavity. For this case we find a modification of the damped Rabi oscillations, which depends on the atomic position. \textcopyright{} 1996 The American Physical Society.
Master equation methods provide useful tools for analyzing the statistics of quantum optical systems. They focus attention on a simple system of interest (a single cavity mode, for example), accounting for its interaction with its environment in parameters describing decay rates and environmental fluctuations. Intracavity systems for generating squeezed light are prime candidates for analysis by these methods. It has been shown, however, that it is important in such analysis to distinguish between the statistics of the intracavity field and the statistics of the field generated outside the cavity by transmission through the cavity mirrors.1,2 It is desirable to perform calculations with the single mode inside the cavity. Then the statistics of the multimode field outside the cavity must be related to those of the internal mode. The situation is analogous to that in resonance fluorescence, where the statistics of the fluorescent field can be calculated in terms of the source dipole operator. In this paper the field outside an optical cavity is expressed in terms of the intracavity oscillator as a source. The measurement of squeezing in the external field is then related to the correlation properties of the cavity source operator. Measurement by photon counting of homodyned light is related to the spectrum of squeezing calculated by Walls and co-workers.
Derivation of a quantum master equation for a system weakly coupled to a bath which takes into account non-secular effects, but, nevertheless, has the mathematically correct Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form (in particular, preserves positivity of the density operator) and also satisfies the standard thermodynamic properties is a known long-standing problem in theory of open quantum systems. The non-secular terms are important when some energy levels of the system or their differences (Bohr frequencies) are nearly degenerate. We provide a fully rigorous derivation of such equation based on a formalization of the weak-coupling limit for the general case.
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.