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

arXiv:1410.3113

A dynamical equation for a maser with non-poissonian injection statistics

Michael Fleischhauer

Published Oct 12, 2014• 0 citations
arXivHTMLPDF

Abstract

A derivation of the coarse grained dynamical equation for a maser with periodic injection of atoms suggested by Briegel and Englert [Phys.Rev.A. {\bf 52}, 2361 (1995)] from the microscopic masterequation is presented.
DOI
10.48550/arxiv.1410.3113

Related papers

Macroscopic dynamics of a maser with non-Poissonian injection statistics

Hans‐Jürgen Briegel, Berthold‐Georg Englert

We derive a master equation for the dynamics of a maser or laser with periodic injection of excited atoms. The model includes regular pumping with single atoms, but it also covers the case of periodic injection of groups of atoms, whose number may fluctuate. To obtain a quasicontinuous master equation for such a periodically kicked dynamics, we consider a macroscopic state of the field that is obtained from the true microscopic state by a time average over many periods. The master equation for that time-averaged state correctly describes both the stationary and the transient properties of the maser on a coarse, macroscopic scale. Numerical and analytical results based on this equation are compared with a microscopic, step-by-step resolution of the field's evolution along the periods. Deviations from the microscopic results only occur when frequencies of the order of the (mechanical) injection frequency of the pump become relevant. The recently predicted regularity-induced line splitting in the emission spectrum of a maser is an example for such a situation.

Physical Review A•Sep 1, 1995•28 citations

Suitability of the master-equation approach for micromasers with non-Poissonian pumping

L. Davidovich, S.-Y. Zhu, Antonio Zelaquett Khoury +1 more

The application to micromasers of a recently proposed generalized master equation, which takes into account the statistics of the pumping mechanism, may lead to incorrect results for non-Poissonian pumping, due to the violation of hypotheses regarding coarse graining and the independent action of gain and dissipation.

Physical Review A•Aug 1, 1992•14 citations

Pump statistics and micromaser dynamics

János A. Bergou, Mark S. Hillery

The realization of the micromaser prompted theoretical interest in the fundamental problems of laser physics. In particular, it has been shown that the usual quantum theory of the laser can be recovered from the micromaser theory if a Poissonian average with respect to the time intervals between subsequent injections is taken. The problem of general injection statistics has not been fully resolved but, instead, has been circumvented in the following ways. Instead of the time period between successive injections, the number of injected atoms during a fixed time interval was considered as a stochastic variable and was averaged with respect to a general sub-Poissonian distribution. This led to a closed-form master equa tion, but correction terms arise when the effect of cavity damping is significant. In another approach a stroboscopic theory has been developed: The system is observed when a full cycle of pumping, firing, and decay is completed. This assumes observation of the system on a nonuniform time scale. Here we carry out the averaging over the time interval between subsequent injections with sub-Poissonian distribution, suggest a new compact master equation, and exploit some of its consequences. We show that this approach reproduces the previous ones if the cavity damping is negligible. The surprising result of our approach is that altering the pump statistics affects both the gain and the loss part of the laser dynamics.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations

Theory of a microscopic maser

P. Filipowicz, Juha Javanainen, Pierre Meystre

We present the theory of a truly microscopic maser consisting of a single-mode high-Q resonator in which a monoenergetic beam of excited two-level atoms is injected at such a low flux that at most one atom at a time is present inside the cavity. Both a microscopic theory and a heuristic Fokker-Planck approach are presented. We show that the micromaser exhibits a number of novel features that are averaged out in usual masers and lasers. First, the field is in general sub-Poissonian, which reflects the quantization of both the field and its sources. Second, the onset of maser oscillations may be followed by a succession of abrupt transitions in the state of the field. Finally, as the atomic flux through the resonator is increased, the maser threshold acquires characteristics of a continuous phase transition, whereas the subsequent changes in the field distribution become analogous to first-order phase transitions.

Physical Review A•Oct 1, 1986•545 citations

One-atom maser with a periodic and noisy pump: An application of damping bases

Hans‐Jürgen Briegel, Berthold‐Georg Englert, Christian Ginzel +1 more

We study the one-atom maser with a periodic-pump scheme for the injected atoms. The dynamics of the system is solved also in a regime where the losses of the field cannot be neglected while the atom is inside the cavity, as is the situation in an optical maser. The time development of the maser field is described by a general evolution operator, whose matrix representation in the damping basis is known analytically for zero temperature. The numerical evaluation of this matrix yields the stationary as well as the transient properties of the maser. Noise-producing mechanisms of the pump are included explicitly in the evolution operator for the field. These are a finite efficiency of the pump laser, a velocity spread in the atomic beam, and spontaneous transitions between the atomic levels and to the ground state. We find that features such as trapped states and sub-Poissonian photon statistics also occur in the high-loss regime like in an optical resonator. The observation of such effects will, as in the ordinary micromaser experiments, depend very sensitively on the reduction of the pump noise. For highly regular excitation, we find a pronounced oscillation of the field-correlation function for a wide range of the transit time, which leads to a distinct line splitting in the spectrum of the field. The amount of the splitting is determined by the periodicity of the pump. For less regular excitation, and in particular in the Poissonian limit, these oscillations disappear.

Physical Review A•Jun 1, 1994•29 citations

Dressed-state lasers and masers

G. S. Agarwal

We show that laser and maser action is possible using atoms that have been prepared in dressed states. We develop the microscopic theory and derive the Fokker-Planck equation for the field distribution for such a laser (maser) system.

Physical Review A•Jul 1, 1990•44 citations
We derive a master equation for the dynamics of a maser or laser with periodic injection of excited atoms. The model includes regular pumping with single atoms, but it also covers the case of periodic injection of groups of atoms, whose number may fluctuate. To obtain a quasicontinuous master equation for such a periodically kicked dynamics, we consider a macroscopic state of the field that is obtained from the true microscopic state by a time average over many periods. The master equation for that time-averaged state correctly describes both the stationary and the transient properties of the maser on a coarse, macroscopic scale. Numerical and analytical results based on this equation are compared with a microscopic, step-by-step resolution of the field's evolution along the periods. Deviations from the microscopic results only occur when frequencies of the order of the (mechanical) injection frequency of the pump become relevant. The recently predicted regularity-induced line splitting in the emission spectrum of a maser is an example for such a situation.
The realization of the micromaser prompted theoretical interest in the fundamental problems of laser physics. In particular, it has been shown that the usual quantum theory of the laser can be recovered from the micromaser theory if a Poissonian average with respect to the time intervals between subsequent injections is taken. The problem of general injection statistics has not been fully resolved but, instead, has been circumvented in the following ways. Instead of the time period between successive injections, the number of injected atoms during a fixed time interval was considered as a stochastic variable and was averaged with respect to a general sub-Poissonian distribution. This led to a closed-form master equa tion, but correction terms arise when the effect of cavity damping is significant. In another approach a stroboscopic theory has been developed: The system is observed when a full cycle of pumping, firing, and decay is completed. This assumes observation of the system on a nonuniform time scale. Here we carry out the averaging over the time interval between subsequent injections with sub-Poissonian distribution, suggest a new compact master equation, and exploit some of its consequences. We show that this approach reproduces the previous ones if the cavity damping is negligible. The surprising result of our approach is that altering the pump statistics affects both the gain and the loss part of the laser dynamics.
We present the theory of a truly microscopic maser consisting of a single-mode high-Q resonator in which a monoenergetic beam of excited two-level atoms is injected at such a low flux that at most one atom at a time is present inside the cavity. Both a microscopic theory and a heuristic Fokker-Planck approach are presented. We show that the micromaser exhibits a number of novel features that are averaged out in usual masers and lasers. First, the field is in general sub-Poissonian, which reflects the quantization of both the field and its sources. Second, the onset of maser oscillations may be followed by a succession of abrupt transitions in the state of the field. Finally, as the atomic flux through the resonator is increased, the maser threshold acquires characteristics of a continuous phase transition, whereas the subsequent changes in the field distribution become analogous to first-order phase transitions.
We study the one-atom maser with a periodic-pump scheme for the injected atoms. The dynamics of the system is solved also in a regime where the losses of the field cannot be neglected while the atom is inside the cavity, as is the situation in an optical maser. The time development of the maser field is described by a general evolution operator, whose matrix representation in the damping basis is known analytically for zero temperature. The numerical evaluation of this matrix yields the stationary as well as the transient properties of the maser. Noise-producing mechanisms of the pump are included explicitly in the evolution operator for the field. These are a finite efficiency of the pump laser, a velocity spread in the atomic beam, and spontaneous transitions between the atomic levels and to the ground state. We find that features such as trapped states and sub-Poissonian photon statistics also occur in the high-loss regime like in an optical resonator. The observation of such effects will, as in the ordinary micromaser experiments, depend very sensitively on the reduction of the pump noise. For highly regular excitation, we find a pronounced oscillation of the field-correlation function for a wide range of the transit time, which leads to a distinct line splitting in the spectrum of the field. The amount of the splitting is determined by the periodicity of the pump. For less regular excitation, and in particular in the Poissonian limit, these oscillations disappear.