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

Optica Acta International Journal of Optics

Exact Results for Photon Statistics of an Optical Bistability Type System

J.N. Elgin, Sarben Sarkar

Published Feb 1, 1984• 2 citations
Publisher

Abstract

An expression is obtained for the photon number distribution, p n, of light transmitted by a bistable cavity in the bad cavity limit, and under the assumption that single atom effects can be ignored. The result is exact, fully quantum mechanical and does not make any assumptions about decorrelations of correlation functions. Particular cases are discussed.

DOI
10.1080/713821481

Related papers

Single-atom cavity-enhanced absorption. I. Photon statistics in the bad-cavity limit

Perry R. Rice, H. J. Carmichael

The photon statistics of the transmitted light from a driven cavity containing a single resonant two-level atom are studied in the bad-cavity limit. For weak driving fields, the second-order intensity correlation function shows novel nonclassical behavior due to the interference of the driving field and forward reradiation from the atom. This behavior is related to squeezing in the cavity transmission. A physical interpretation is given in terms of the reduced quantum state of the coupled atom-field system following photodetection.>

IEEE Journal of Quantum Electronics•Jul 1, 1988•130 citations

Quantum theory of optical bistability. III. Atomic fluorescence in a low- Q cavity

H. J. Carmichael, Daniel F. Walls, P. D. Drummond +1 more

We specialize the quantum-statistical theory of optical bistability developed in "Optical Bistability. II" to a low-$Q$ cavity. From a linearized Fokker-Planck equation derived in the positive $P$ representation, the steady-state correlation matrix and spectrum of fluctuations are calculated. Expressions which normally assume a positive-definite diffusion matrix are shown to be valid for nonpositive-definite diffusion. For absorptive bistability we find agreement with results derived previously by quite different methods. More generally we extend previously published results by including atomic and cavity detunings. We compare the transmitted spectrum for dispersive bistability with that for absorptive bistability, and photon antibunching in dispersive bistability is discussed.

Physical Review A•Jun 1, 1983•35 citations

Photon correlations and spectra in the bimodal regime of single-atom cavity-enhanced absorption

P. M. Alsing, H. J. Carmichael, Perry R. Rice

We recently reported that the transmitted light from a driven optical cavity containing a single-atom absorber shows strong nonclassical features.1 Also, Savage and Carmichael2 have shown that this single-atom system can be operated in a regime in which the transmitted light has a bimodal photon-counting distribution; as the saturation photon number is increased this bimodality develops into a single-atom version of absorptive optical bistability. We present results for the degree of second-order coherence and the spectrum of the transmitted light in the operating regime at the onset of bimodality. In this regime we can study the onset of low frequency behavior associated with transitions between the local states defined by the peaks of the bimodal distribution. Our results are calculated numerically, using a supercomputer to solve matrix element equations derived in the Fock-state basis. Our numerical approach also allows us to extend our analytical study of nonclassical effects in single-atom cavity-enhanced absorption. Our analytical results are restricted either to the bad-cavity limit1 or to weak driving fields outside this limit. We can now study how the nonclassical effects identified in these analytical calculations are changed by using finite driving fields outside the bad-cavity limit.

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations

Atomic correlations in driven optical systems

L. A. Lugiato

We consider the one-mode quantum-statistical model of optical bistability, and show that atom-atom correlations are negligible in the good-cavity limit, in all effects that can be described by a linearized treatment. In the light of this result, we discuss the concept of ``atomic cooperation'' in quantum optical systems. In the purely absorptive case, the atomic polarization exhibits a squeezing effect which arises both in the good- and in the bad-cavity limit. This phenomenon has the same origin of the squeezing effect in resonance fluorescence.

Physical Review A•Jun 1, 1986•17 citations

Quantum theory of optical bistability with a spatially varying field mode in the good cavity limit

Xiao Min, H. J. Kimble, H. J. Carmichael

A straightforward but general extension of the quantum theory of optical bistability is made to include spatial variations of the field mode in the good cavity limit. The analysis proceeds by dividing the field mode into small sections which are each microscopically large in terms of the atomic number to allow truncation of the generalized Fokker-Planck equation but which are macroscopically small to justify the assumption of constant field amplitude. In a linearized approximation, analytic expressions are obtained for the ratio of incoherent to coherent intensity and for the intensity correlation function of the transmitted field for the two particular examples of a Gaussian-mode field in a ring cavity and a plane-wave field in a standing-wave cavity. In the weak field limit the results of the plane-wave ring cavity are recovered independent of the form of the spatial dependence of the cavity mode. However, more generally a nonuniform distribution tends to suppress certain quantum features such as photon antibunching.

Annual Meeting Optical Society of America•Jan 1, 1985•0 citations

Single atom optical bistability

Craig M. Savage, H. J. Carmichael

Absorptive optical bistability is shown to exist for a single two-level atom inside a resonant optical cavity. Solutions for the quantum-mechanical density operator are obtained numerically for a parameter regime at the interface between the quantum limit, in which quantum-mechanical noise invalidates the semiclassical prediction of bistability, and the classical limit, in which quantum noise is a negligible perturbation on semiclassical results. Bimodal photon number distributions and Q functions are obtained, and two-state transition rates are calculated.>

IEEE Journal of Quantum Electronics•Aug 1, 1988•134 citations
An expression is obtained for the photon number distribution, p n, of light transmitted by a bistable cavity in the bad cavity limit, and under the assumption that single atom effects can be ignored. The result is exact, fully quantum mechanical and does not make any assumptions about decorrelations of correlation functions. Particular cases are discussed.
The photon statistics of the transmitted light from a driven cavity containing a single resonant two-level atom are studied in the bad-cavity limit. For weak driving fields, the second-order intensity correlation function shows novel nonclassical behavior due to the interference of the driving field and forward reradiation from the atom. This behavior is related to squeezing in the cavity transmission. A physical interpretation is given in terms of the reduced quantum state of the coupled atom-field system following photodetection.>
We specialize the quantum-statistical theory of optical bistability developed in "Optical Bistability. II" to a low-QQQ cavity. From a linearized Fokker-Planck equation derived in the positive PPP representation, the steady-state correlation matrix and spectrum of fluctuations are calculated. Expressions which normally assume a positive-definite diffusion matrix are shown to be valid for nonpositive-definite diffusion. For absorptive bistability we find agreement with results derived previously by quite different methods. More generally we extend previously published results by including atomic and cavity detunings. We compare the transmitted spectrum for dispersive bistability with that for absorptive bistability, and photon antibunching in dispersive bistability is discussed.
We recently reported that the transmitted light from a driven optical cavity containing a single-atom absorber shows strong nonclassical features.1 Also, Savage and Carmichael2 have shown that this single-atom system can be operated in a regime in which the transmitted light has a bimodal photon-counting distribution; as the saturation photon number is increased this bimodality develops into a single-atom version of absorptive optical bistability. We present results for the degree of second-order coherence and the spectrum of the transmitted light in the operating regime at the onset of bimodality. In this regime we can study the onset of low frequency behavior associated with transitions between the local states defined by the peaks of the bimodal distribution. Our results are calculated numerically, using a supercomputer to solve matrix element equations derived in the Fock-state basis. Our numerical approach also allows us to extend our analytical study of nonclassical effects in single-atom cavity-enhanced absorption. Our analytical results are restricted either to the bad-cavity limit1 or to weak driving fields outside this limit. We can now study how the nonclassical effects identified in these analytical calculations are changed by using finite driving fields outside the bad-cavity limit.
We consider the one-mode quantum-statistical model of optical bistability, and show that atom-atom correlations are negligible in the good-cavity limit, in all effects that can be described by a linearized treatment. In the light of this result, we discuss the concept of ``atomic cooperation'' in quantum optical systems. In the purely absorptive case, the atomic polarization exhibits a squeezing effect which arises both in the good- and in the bad-cavity limit. This phenomenon has the same origin of the squeezing effect in resonance fluorescence.
A straightforward but general extension of the quantum theory of optical bistability is made to include spatial variations of the field mode in the good cavity limit. The analysis proceeds by dividing the field mode into small sections which are each microscopically large in terms of the atomic number to allow truncation of the generalized Fokker-Planck equation but which are macroscopically small to justify the assumption of constant field amplitude. In a linearized approximation, analytic expressions are obtained for the ratio of incoherent to coherent intensity and for the intensity correlation function of the transmitted field for the two particular examples of a Gaussian-mode field in a ring cavity and a plane-wave field in a standing-wave cavity. In the weak field limit the results of the plane-wave ring cavity are recovered independent of the form of the spatial dependence of the cavity mode. However, more generally a nonuniform distribution tends to suppress certain quantum features such as photon antibunching.
Absorptive optical bistability is shown to exist for a single two-level atom inside a resonant optical cavity. Solutions for the quantum-mechanical density operator are obtained numerically for a parameter regime at the interface between the quantum limit, in which quantum-mechanical noise invalidates the semiclassical prediction of bistability, and the classical limit, in which quantum noise is a negligible perturbation on semiclassical results. Bimodal photon number distributions and Q functions are obtained, and two-state transition rates are calculated.>