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

Master equation for dissipative dynamics of a two-level atom in the superintense field: Field-dependent relaxation

Gautam Gangopadhyay, Deb Shankar Ray

Published Aug 1, 1991• 5 citations
Publisher

Abstract

We derive a generalized master equation on the basis of system-reservoir theory where the system is a two-level atom interacting with a superintense classical electromagnetic field within the Born and Markov approximations. We show that the usual assumption of independence of the atom-field coupling and the atomic decay processes breaks down and the relaxation becomes field dependent in the superintense regime. This results in significant deviation from the exponential decay of the Bloch vector components.

DOI
10.1103/physreva.44.2206

Related papers

Generalized master equation for a two-level atom in a strong field and tailored reservoirs

A. Kowalewska-Kudłaszyk, R. Tanaś

The generalized master equation for a two-level atom driven by a strong classical field and damped into a ‘tailored’ reservoir with a non-flat density of modes is derived under the Born-Markov approximation. To derive the master equation the dressing transformation on the atomic operators is performed first and next the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The modifications introduced by a strong field and/or by the reservoir with the non-flat density of modes lead to non-standard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs. The optical Bloch equations based on this generalized master equation are obtained and solved for the steady state. The solutions are discussed from the point of view of both bare and dressed atoms. Analytical formulas for the fluorescence and probe absorption spectra are obtained and illustrated graphically.

Journal of Modern Optics•Feb 1, 2001•35 citations

Markovian master equation for a two-level atom in a strong field and/or a tailored reservoir

A. Kowalewska-Kudłaszyk, R. Tanaś

The master equation for a two-level atom driven by a strong classical field and damped into a tailored reservoir with nonflat density of modes is derived under the Born-Markov approximation. To derive the master equation, the dressing transformation on the atomic operators is performed first, and, next, the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The effects of a strong field and/or structured reservoir are seen as nonstandard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs. The master equation leads to the generalized optical Bloch equations that can easily be solved for the steady state and, together with the quantum regression theorem, allow for analytical expressions for the fluorescence, as well as absorption spectra.

Optics and Spectroscopy•Sep 1, 2001•2 citations

Two-level atom-field interaction: Exact master equations for non-Markovian dynamics, decoherence, and relaxation

Charis Anastopoulos, B. L. Hu

We perform a first-principles derivation of the general master equation to study the non-Markovian dynamics of a two-level atom (2LA) interacting with an electromagnetic field (EMF). We use the influence functional method, which can incorporate the full back reaction of the field on the atom, while adopting Grassmannian variables for the 2LA and the coherent-state representation for the EMF. We find exact master equations for the cases of a free quantum field and a cavity field in the vacuum. In response to the search for mechanisms to preserve maximal coherence in quantum computations in ion trap prototypes, we apply these equations to analyze the decoherence of a 2LA in an EMF, and find that decoherence time is close to relaxation time. This is at variance with the claims by authors who studied the same system but used a different coupling model. We explain the source of difference and argue that, contrary to common belief, the EMF, when resonantly coupled to an atom, does not decohere it as efficiently as a bath does on a quantum Brownian particle. The master equations for non-Markovian dynamics derived here are expected to be useful for exploring new regimes of 2LAEMF interaction, which is becoming physically important experimentally.

arXiv:quant-ph/9901078•Physical Review A•Aug 18, 2000•93 citations

Generalized master equation for a two-level atom in a strong é eld and tailored reservoirs

Anna KOWALEWSKA-KUDè Aszyk

The generalized master equation for a two-level atom driven by a strong classical e eld and damped into a 'tailored' reservoir with a non-e at density of modes is derived under the Born-Markov approximation. To derive the master equation the dressing transformation on the atomic operators is performed e rst and next the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The modie cations introduced by a strong e eld and/or by the reservoir with the non-e at density of modes lead to non-standard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs. The optical Bloch equations based on this generalized master equation are obtained and solved for the steady state. The solutions are discussed from the point of view of both bare and dressed atoms. Analytical formulas for the e uorescence and probe absorption spectra are obtained and illustrated graphically.

•Jan 1, 2001•0 citations

Two-level atom in a structured reservoir

A. Kowalewska-Kudłaszyk, R. Tanaś

A two level atom driven by a strong resonant field and coupled to a structured reservoir is studied. The generalized master equation describing the evolution of the atom is derived under the Born-Markov approximation. To derive the master equation the dressing transformation on the atomic operators is performed first and next the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The modifications introduced by a strong field and/or by the reservoir with non-flat density of modes lead to non-standard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs although the reservoir is not a squeezed vacuum. The optical Bloch equations based on this generalized master equation are obtained and solved for the steady state. The resonance fluorescence spectra of the atom are shortly discussed.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 7, 2001•0 citations

The atomic damping basis and the collective decay of interacting two-level atoms

William Alvarez-Giron, Pablo Barberis-Blostein

Abstract We find analytical solutions to the evolution of interacting two-level atoms when the master equation is symmetric under the permutation of atomic labels. The master equation includes atomic independent dissipation. The method to obtain the solutions is: first, we use the system symmetries to describe the evolution in an operator space whose dimension grows polynomially with the number of atoms. Second, we expand the solutions in a basis composed of eigenvectors of the dissipative part of the master equation that models the independent dissipation of the atoms. This atomic damping basis is an atomic analog to the damping basis used for bosonic fields Briegel and Englert (1993 Phys. Rev. A 47 3311–29). The solutions show that the system decays as a sum of sub- and super-radiant exponential terms.

arXiv:2008.11056•Journal of Physics A Mathematical and Theoretical•Aug 24, 2020•4 citations
We derive a generalized master equation on the basis of system-reservoir theory where the system is a two-level atom interacting with a superintense classical electromagnetic field within the Born and Markov approximations. We show that the usual assumption of independence of the atom-field coupling and the atomic decay processes breaks down and the relaxation becomes field dependent in the superintense regime. This results in significant deviation from the exponential decay of the Bloch vector components.
The generalized master equation for a two-level atom driven by a strong classical field and damped into a ‘tailored’ reservoir with a non-flat density of modes is derived under the Born-Markov approximation. To derive the master equation the dressing transformation on the atomic operators is performed first and next the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The modifications introduced by a strong field and/or by the reservoir with the non-flat density of modes lead to non-standard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs. The optical Bloch equations based on this generalized master equation are obtained and solved for the steady state. The solutions are discussed from the point of view of both bare and dressed atoms. Analytical formulas for the fluorescence and probe absorption spectra are obtained and illustrated graphically.
The master equation for a two-level atom driven by a strong classical field and damped into a tailored reservoir with nonflat density of modes is derived under the Born-Markov approximation. To derive the master equation, the dressing transformation on the atomic operators is performed first, and, next, the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The effects of a strong field and/or structured reservoir are seen as nonstandard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs. The master equation leads to the generalized optical Bloch equations that can easily be solved for the steady state and, together with the quantum regression theorem, allow for analytical expressions for the fluorescence, as well as absorption spectra.
We perform a first-principles derivation of the general master equation to study the non-Markovian dynamics of a two-level atom (2LA) interacting with an electromagnetic field (EMF). We use the influence functional method, which can incorporate the full back reaction of the field on the atom, while adopting Grassmannian variables for the 2LA and the coherent-state representation for the EMF. We find exact master equations for the cases of a free quantum field and a cavity field in the vacuum. In response to the search for mechanisms to preserve maximal coherence in quantum computations in ion trap prototypes, we apply these equations to analyze the decoherence of a 2LA in an EMF, and find that decoherence time is close to relaxation time. This is at variance with the claims by authors who studied the same system but used a different coupling model. We explain the source of difference and argue that, contrary to common belief, the EMF, when resonantly coupled to an atom, does not decohere it as efficiently as a bath does on a quantum Brownian particle. The master equations for non-Markovian dynamics derived here are expected to be useful for exploring new regimes of 2LAEMF interaction, which is becoming physically important experimentally.
The generalized master equation for a two-level atom driven by a strong classical e eld and damped into a 'tailored' reservoir with a non-e at density of modes is derived under the Born-Markov approximation. To derive the master equation the dressing transformation on the atomic operators is performed e rst and next the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The modie cations introduced by a strong e eld and/or by the reservoir with the non-e at density of modes lead to non-standard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs. The optical Bloch equations based on this generalized master equation are obtained and solved for the steady state. The solutions are discussed from the point of view of both bare and dressed atoms. Analytical formulas for the e uorescence and probe absorption spectra are obtained and illustrated graphically.
A two level atom driven by a strong resonant field and coupled to a structured reservoir is studied. The generalized master equation describing the evolution of the atom is derived under the Born-Markov approximation. To derive the master equation the dressing transformation on the atomic operators is performed first and next the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The modifications introduced by a strong field and/or by the reservoir with non-flat density of modes lead to non-standard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs although the reservoir is not a squeezed vacuum. The optical Bloch equations based on this generalized master equation are obtained and solved for the steady state. The resonance fluorescence spectra of the atom are shortly discussed.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Abstract We find analytical solutions to the evolution of interacting two-level atoms when the master equation is symmetric under the permutation of atomic labels. The master equation includes atomic independent dissipation. The method to obtain the solutions is: first, we use the system symmetries to describe the evolution in an operator space whose dimension grows polynomially with the number of atoms. Second, we expand the solutions in a basis composed of eigenvectors of the dissipative part of the master equation that models the independent dissipation of the atoms. This atomic damping basis is an atomic analog to the damping basis used for bosonic fields Briegel and Englert (1993 Phys. Rev. A 47 3311–29). The solutions show that the system decays as a sum of sub- and super-radiant exponential terms.