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

Quantum fluctuations of light at the output of a cavity with absorptive bistability for arbitrary input-photon statistics

A. S. Troshin, N. A. Vasil’ev

Published Jan 14, 2000• 0 citations
Publisher

Abstract

The general expression of the output-light Mandel parameter(xi) out is obtained in case of purely absorptive bistability, for arbitrary value of (xi) in of incident light. Calculations are based on stochastic rate equations. No adiabatic elimination of atomic variables is made; the coherent nature of 'incoming' of incident photon is into a cavity is correctly taken into account. On condition of bistability, although the strongly sub-Poisson input-photon statistics generally reduces the output noise as compared to the case of coherent input, the inequality (xi) out > 0 still near the switching points.

DOI
10.1117/12.375339

Related papers

Possibility of suppressing quantum light fluctuations when excess photon fluctuations occur inside a cavity

Yu. M. Golubev, I. V. Sokolov, Mikhail I. Kolobov

Using the optical excitation of a high-Q cavity as an example, it is shown that when light is observed at the output of this cavity, effective suppression of the photocurrent shot noise below the quantum limit is in general independent of the parameters of the stationary state of the field oscillator (in particular, it is independent of the rms photon fluctuations) inside the cavity and can occur not only at any allowed negative value but even at a positive value of the Mandel parameter. It was assumed in solving the problem that the cavity is optically excited by superimposing the radiation of a sub-Poisson laser and a laser with excess photon noise. A formal solution was obtained in terms of the kinetic equation for the density matrix of the actual fields (inside the laser cavities and the empty cavity), which is derived here on the basis of the Heisenberg-Langevin quantum equations, taking into account directed propagation of the field from the laser cavities inside the empty cavity. The resulting kinetic equation can also be used to solve other physical problems, since it is applicable to optical systems that contain, in principle, an arbitrary number of coupled cavities and interference mixers.

Journal of Experimental and Theoretical Physics•May 1, 1997•2 citations

Quantum fluctuations in absorptive bistability without adiabatic elimination

H. J. Carmichael

A linearized theory of fluctuations for absorptive bistability based on the positive P representation is developed without adiabatic elimination of the atoms or the field. An analytic expression for the steady-state covariance matrix is derived from which the size of quantum-statistical effects can be estimated without restriction to the good- or the bad-cavity limit. When the atom and field relaxation rates are similar the intensity correlation function of the transmitted light exhibits an oscillatory relaxation associated with vacuum Rabi splitting.

Physical Review A•May 1, 1986•108 citations

Sub-Poissonian laser output due to optical pumping by squeezed light

Monika A. M. Marte, P. Zoller

A recent analysis of the influence of the pump statistics on the laser output fluctuations is applied to the experimentally feasible case of a laser being pumped by light coming from a separate pump field cavity that is driven by a broad-band squeezed vacuum plus a coherent driving field. In contrast to the 'squeezed-reservoir laser', where a reservoir of squeezed modes coming from all directions coupled to the dipole moment of the lasing transition and leads to atomic phase decay inhibition and phase locking of the laser field, here the squeezed light merely pumps the gain atoms, that is gives rise to inversion of the laser transition. In analogy to photodetection theory the photon statistics of the laser output is calculated as a function of the photon statistics of the absorbed squeezed pump light. For the case of a squeezed pump field chosen to display sub-Poissonian statistics, it is demonstrated that the Mandel Q-parameter of the laser cavity output can theoretically reach the optimum value of Q=- 1 / 2 , similar to the case of a deterministic pumping mechanism.

Quantum Optics Journal of the European Optical Society Part B•Jun 1, 1990•14 citations

Quantum theory of optical bistability. II. Atomic fluorescence in a high- Q cavity

P. D. Drummond, Daniel F. Walls

A quantum treatment of a coherently driven cavity with a medium of two-level atoms is given. The system displays both absorptive and dispersive bistability. Quantum fluctuations are included via a Fokker-Planck equation in a generalized $P$ representation, after adiabatic elimination of the atomic variables. The transmitted spectrum and correlation function is calculated in a linearized (Gaussian) approximation. In the limit of large detuning and radiative damping, the quantum fluctuations are identical to those of a simple nonlinear polarizability theory. An analysis is given of the nonclassical statistical properties of the intensity-correlation spectrum.

Physical Review A•May 1, 1981•194 citations

Quantum statistical properties of a quantum theory of optical bistability

G. P. Hildred, S. S. Hassan, Ravinder Rupchand Puri +1 more

Abstract The strictly quantum driven Dicke model of N two-level atoms on the same site shows conventional optical bistability if and only if cavity feedback is included. In this model we find that for N->oo the photon statistics of the transmitted field are Poisson on the lower branch of the output-input curve, but on the upper branch approach Bose-Einstein in the hysteresis region, with reversion to Poisson only for very strong input fields.

Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences•Dec 18, 1984•0 citations

Collective atomic correlations in absorptive optical bistability without adiabatic elimination: Exemplifying nonclassicality from a linearized treatment of fluctuations

Th. K. Mavrogordatos

We determine the incoherent spectrum, squeezing properties, and second-order correlation function of the collective atomic degrees of freedom in absorptive optical bistability. This is accomplished via a linearized Fokker-Planck equation in the positive $P$ representation, guided by the analysis of H. J. Carmichael [Phys. Rev. A 33, 3262 (1986)] which does not resort to adiabatic elimination. We focus on the regimes of weak and strong intracavity excitation, addressing the good-cavity and bad-cavity limits as well as the limit of collective strong coupling. Adiabatic elimination of the intracavity field sustained by an auxiliary resonator coupled to the ensemble is used to probe the atomic correlations via the formation of a collective emission channel. We compare to the corresponding expressions for the forward-scattered light with reference to experimental results, discussing key differences between the lower and upper branch of the steady-state semiclassical bistability curve. Our analysis is carried out around the stable states situated far away from the turning points, where analytical expressions can be obtained self-consistently, demonstrating a clear departure from classical behavior.

arXiv:2010.05808•Physical Review A•Nov 6, 2020•2 citations
The general expression of the output-light Mandel parameter(xi) out is obtained in case of purely absorptive bistability, for arbitrary value of (xi) in of incident light. Calculations are based on stochastic rate equations. No adiabatic elimination of atomic variables is made; the coherent nature of 'incoming' of incident photon is into a cavity is correctly taken into account. On condition of bistability, although the strongly sub-Poisson input-photon statistics generally reduces the output noise as compared to the case of coherent input, the inequality (xi) out > 0 still near the switching points.
Using the optical excitation of a high-Q cavity as an example, it is shown that when light is observed at the output of this cavity, effective suppression of the photocurrent shot noise below the quantum limit is in general independent of the parameters of the stationary state of the field oscillator (in particular, it is independent of the rms photon fluctuations) inside the cavity and can occur not only at any allowed negative value but even at a positive value of the Mandel parameter. It was assumed in solving the problem that the cavity is optically excited by superimposing the radiation of a sub-Poisson laser and a laser with excess photon noise. A formal solution was obtained in terms of the kinetic equation for the density matrix of the actual fields (inside the laser cavities and the empty cavity), which is derived here on the basis of the Heisenberg-Langevin quantum equations, taking into account directed propagation of the field from the laser cavities inside the empty cavity. The resulting kinetic equation can also be used to solve other physical problems, since it is applicable to optical systems that contain, in principle, an arbitrary number of coupled cavities and interference mixers.
A linearized theory of fluctuations for absorptive bistability based on the positive P representation is developed without adiabatic elimination of the atoms or the field. An analytic expression for the steady-state covariance matrix is derived from which the size of quantum-statistical effects can be estimated without restriction to the good- or the bad-cavity limit. When the atom and field relaxation rates are similar the intensity correlation function of the transmitted light exhibits an oscillatory relaxation associated with vacuum Rabi splitting.
A recent analysis of the influence of the pump statistics on the laser output fluctuations is applied to the experimentally feasible case of a laser being pumped by light coming from a separate pump field cavity that is driven by a broad-band squeezed vacuum plus a coherent driving field. In contrast to the 'squeezed-reservoir laser', where a reservoir of squeezed modes coming from all directions coupled to the dipole moment of the lasing transition and leads to atomic phase decay inhibition and phase locking of the laser field, here the squeezed light merely pumps the gain atoms, that is gives rise to inversion of the laser transition. In analogy to photodetection theory the photon statistics of the laser output is calculated as a function of the photon statistics of the absorbed squeezed pump light. For the case of a squeezed pump field chosen to display sub-Poissonian statistics, it is demonstrated that the Mandel Q-parameter of the laser cavity output can theoretically reach the optimum value of Q=- 1 / 2 , similar to the case of a deterministic pumping mechanism.
A quantum treatment of a coherently driven cavity with a medium of two-level atoms is given. The system displays both absorptive and dispersive bistability. Quantum fluctuations are included via a Fokker-Planck equation in a generalized PPP representation, after adiabatic elimination of the atomic variables. The transmitted spectrum and correlation function is calculated in a linearized (Gaussian) approximation. In the limit of large detuning and radiative damping, the quantum fluctuations are identical to those of a simple nonlinear polarizability theory. An analysis is given of the nonclassical statistical properties of the intensity-correlation spectrum.
We determine the incoherent spectrum, squeezing properties, and second-order correlation function of the collective atomic degrees of freedom in absorptive optical bistability. This is accomplished via a linearized Fokker-Planck equation in the positive PPP representation, guided by the analysis of H. J. Carmichael [Phys. Rev. A 33, 3262 (1986)] which does not resort to adiabatic elimination. We focus on the regimes of weak and strong intracavity excitation, addressing the good-cavity and bad-cavity limits as well as the limit of collective strong coupling. Adiabatic elimination of the intracavity field sustained by an auxiliary resonator coupled to the ensemble is used to probe the atomic correlations via the formation of a collective emission channel. We compare to the corresponding expressions for the forward-scattered light with reference to experimental results, discussing key differences between the lower and upper branch of the steady-state semiclassical bistability curve. Our analysis is carried out around the stable states situated far away from the turning points, where analytical expressions can be obtained self-consistently, demonstrating a clear departure from classical behavior.