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

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Fokker-Planck equation method and photon statistics in theory of one-atom maser

Alexander V. Gorokhov, Ilya E. Sinaiski

Published Apr 20, 2004• 1 citation
Publisher

Abstract

An exact analytical expression for a density matrix of atom + field system is obtained taking into account of the relaxation of photons and frequency detuning (Jaynes-Cummings model with dissipation). The photon mean number, atom population inversion and Fano Q - factor depending on initial states of the field and various parameters of the one-atom maser parameters are investigated.

DOI
10.1117/12.558819

Related papers

Exact solution of the Jaynes-Cummings model with relaxation

Alexander V. Gorokhov, Ilya E. Sinaiski

Exact analytical expression for the density matrix of atom + field system is obtained taking into account of the photons relaxation and frequency detuning (Jaynes-Cummings model with m-quantum transitions and dissipation). The photon mean number, atom population inversion and Fano Q - factor depending on initial states of the field and parameters of the one-atom maser are investigated.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jul 13, 2004•1 citation

Photon spectra and statistics in generalized Jaynes-Cummings model with photon losses and atom motion

Alexander V. Gorokhov, Ilya E. Sinaiski

The Jaynes-Cummings model (JCM) of two-level atom interacting with the photon mode in ideal cavity plays an essential role in modern quantum optics. In previous papers 1,2 an exact form of density matrix of the JCM with fixed atom position and photons dissipation was found. Here, taking into account the classical motion of the atom through the cavity, it is considered a case of nonideal cavity with zero temperature. We have obtained an exact expression for density matrix and calculated photon spectra and spectra of the mean number of photons in a cavity and and time dependencies of some values relevant for the one-atom maser theory.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 3, 2006•0 citations

One-atom maser theory: photon losses and spectra

Alexander V. Gorokhov, Ilya E. Sinaiski

The Jaynes-Cummings model (JCM) of two-level atom interacting with the photon mode in ideal cavity plays an essential role in modern quantum optics. In previous papers an exact form of density matrix of the JCM with photons dissipation was found. In this article it is considered a partial case of cavity with zero temperature and obtained an exact expression for photon spectra and spectra of the mean number of photons in a cavity.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 9, 2005•0 citations

Field statistics in some generalized Jaynes-Cummings models

Surendra Singh

Photon statistics in some fully quantized models of the interaction of a two-level atom with a single-mode radiation field have been studied using the operator equations of motion. Expressions for the photon number distribution and the mean photon number are presented for various initial conditions. It is found that the mean photon number may show decays and revivals of coherence similar to those of the atomic inversion in the coherent-state Jaynes-Cummings model. Application of these models to the study of multiphoton laser, absorption, and emission processes is also discussed.

Physical Review A•Jun 1, 1982•221 citations

Quantum Theory of a Simple Maser Oscillator

J. P. Gordon

We discuss the quantum theory of a simple model of a maser oscillator, consisting of one radiation-field mode interacting with a large number of stationary three-level atoms. The field and the atoms also interact with separate heat reservoirs which represent dissipation mechanisms and an incoherent pumping mechanism. The model is sufficiently simple that some analytical progress can be made with the nonlinear quantal equations before further approximation is necessary. We start from the quantal equation of motion of the field-atom density operator. We make immediate use of a diagonal coherent-state expansion for the field part of the density operator and a somewhat similar expansion for the atom part. This yields an exact equation of the Fokker-Planck form for a $c$-number weight distribution, which retains all the significance of the original operator equation, and which has the semiclassical equation for the same model as a first, fluctuation-free approximation. We make use of our basic Fokker-Planck equation in a variety of ways. We discuss the reduction of the equation under conditions that the atomic decay constants are large (large atomic linewidth), arriving finally at an equation of motion for a field-only weight function which serves to demonstrate the basic coherence properties of a maser. We derive and discuss the equation of motion of the generalized Wigner density for the maser model. The generalized Wigner density is a smoothed version (a convolution) of our basic weight distribution, and from it we derive an equivalent classical model including noise sources. Finally, we discuss other useful weight distributions and the number representation for the field. The equations we derive in these discussions make contact with the rate equations of Shimoda, Takahasi, and Townes, as well as with the more recent work of Lax and Louisell, Lax, and of Scully and Lamb.

Physical Review•Sep 10, 1967•107 citations

Quantum properties of one-atom maser radiation in the presence of thermal photons

T. B. Karlovich, S. Ya. Kilin

The effect of thermal photons on the radiative properties of a one-atom maser is investigated. Stationary P and Q distribution functions are determined analytically in the approximation of strong interaction between an atom and a cavity field mode. The generation conditions are found for a one-atom maser. It is shown that taking into account thermal photons leads to a decrease in the threshold value of incoherent pumping. It is demonstrated that generation may occur in the absence of population inversion in the atomic subsystem and when losses exceed the intensity of incoherent pumping. A formula is proposed for the Fano factor of a one-atom maser in the form of the sum of the Fano factors of the microcavity radiation in the absence of thermal photons and the thermal radiation.

Optics and Spectroscopy•Dec 1, 2004•1 citation
An exact analytical expression for a density matrix of atom + field system is obtained taking into account of the relaxation of photons and frequency detuning (Jaynes-Cummings model with dissipation). The photon mean number, atom population inversion and Fano Q - factor depending on initial states of the field and various parameters of the one-atom maser parameters are investigated.
The Jaynes-Cummings model (JCM) of two-level atom interacting with the photon mode in ideal cavity plays an essential role in modern quantum optics. In previous papers 1,2 an exact form of density matrix of the JCM with fixed atom position and photons dissipation was found. Here, taking into account the classical motion of the atom through the cavity, it is considered a case of nonideal cavity with zero temperature. We have obtained an exact expression for density matrix and calculated photon spectra and spectra of the mean number of photons in a cavity and and time dependencies of some values relevant for the one-atom maser theory.
Photon statistics in some fully quantized models of the interaction of a two-level atom with a single-mode radiation field have been studied using the operator equations of motion. Expressions for the photon number distribution and the mean photon number are presented for various initial conditions. It is found that the mean photon number may show decays and revivals of coherence similar to those of the atomic inversion in the coherent-state Jaynes-Cummings model. Application of these models to the study of multiphoton laser, absorption, and emission processes is also discussed.
We discuss the quantum theory of a simple model of a maser oscillator, consisting of one radiation-field mode interacting with a large number of stationary three-level atoms. The field and the atoms also interact with separate heat reservoirs which represent dissipation mechanisms and an incoherent pumping mechanism. The model is sufficiently simple that some analytical progress can be made with the nonlinear quantal equations before further approximation is necessary. We start from the quantal equation of motion of the field-atom density operator. We make immediate use of a diagonal coherent-state expansion for the field part of the density operator and a somewhat similar expansion for the atom part. This yields an exact equation of the Fokker-Planck form for a ccc-number weight distribution, which retains all the significance of the original operator equation, and which has the semiclassical equation for the same model as a first, fluctuation-free approximation. We make use of our basic Fokker-Planck equation in a variety of ways. We discuss the reduction of the equation under conditions that the atomic decay constants are large (large atomic linewidth), arriving finally at an equation of motion for a field-only weight function which serves to demonstrate the basic coherence properties of a maser. We derive and discuss the equation of motion of the generalized Wigner density for the maser model. The generalized Wigner density is a smoothed version (a convolution) of our basic weight distribution, and from it we derive an equivalent classical model including noise sources. Finally, we discuss other useful weight distributions and the number representation for the field. The equations we derive in these discussions make contact with the rate equations of Shimoda, Takahasi, and Townes, as well as with the more recent work of Lax and Louisell, Lax, and of Scully and Lamb.
The effect of thermal photons on the radiative properties of a one-atom maser is investigated. Stationary P and Q distribution functions are determined analytically in the approximation of strong interaction between an atom and a cavity field mode. The generation conditions are found for a one-atom maser. It is shown that taking into account thermal photons leads to a decrease in the threshold value of incoherent pumping. It is demonstrated that generation may occur in the absence of population inversion in the atomic subsystem and when losses exceed the intensity of incoherent pumping. A formula is proposed for the Fano factor of a one-atom maser in the form of the sum of the Fano factors of the microcavity radiation in the absence of thermal photons and the thermal radiation.