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

Fluctuation phenomena in a multibranch potential

M. I. Dykman, D. G. Luchinsky, P. V. E. McClintock, Norman D Stein, Nigel G. Stocks

Published Jun 1, 1992• 3 citations
Publisher

Abstract

Fluctuation phenomena, to be anticipated in all systems for which the internal fluctuating variable is a multivalued function of the observable quantity, are reported. Analog electronic experiments on a model optically bistable Fabry-P\'erot cavity have shown that the observable may be described in terms of a Boltzmann distribution with a multibranch effective potential. The distribution was observed to possess up to four peaks (two twin peaks) within the range of bistability, and to become singular at outer boundaries corresponding to the branching points of the potential. The experimental results are compared with theory.

DOI
10.1103/physreva.45.r7678

Related papers

Fluctuational transitions and related phenomena in a passive all-optical bistable system

M. I. Dykman, G. P. Golubev, D. G. Luchinsky +2 more

Fluctuational transitions between stable states of an all-optical lumped-parameter bistable system have been observed. The dependences of the transition probabilities, and of the statistical distribution of the transmitted-light intensity, on the intensities of incident light and noise have been investigated. Two types of stochastic modulation, that of the incident-light intensity and that of the device itself, have been used. They correspond to multiplicative and additive noise for the intracavity-phase gain and give rise to qualitatively different pictures of the fluctuations. In particular, for the latter type of noise the logarithm of the statistical distribution of the transmitted-light intensity is described by a multibranch function, and the peaks of the distribution are strongly asymmetric. The onset of a zero-frequency peak in the power spectrum of the transmitted light in the range of the kinetic phase transition has been observed. The experimental data are in good qualitative and quantitative agreement with the theory.

Physical Review A•Aug 1, 1991•8 citations

Absorptive Optical Bistability with Laser Amplitude Fluctuations

Marek Kuś, K. Wódkiewicz, Jason A. C. Gallas

In this paper we discuss the influence of laser fluctuations on the hysteresis cycle in Optical Bistability. For the simplest case of an Absorptive Optical Bistability in a good cavity driven by an external laser light with non-white Gaussian amplitude fluctuations we derive a Fokker-Planck equation in the limit of large laser linewidth and good amplitude stabilization. This Fokker-Planck equation has a nonconstant diffusion term which shifts the most probable values of the steady state probability distribution from its deterministic positions. From the form of the steady state solution of the Fokker-Planck equation with non-white amplitude fluctuations we discuss the relative stability of the bistable branches. As in the case of quantum fluctuations the random amplitude of the laser field leads to a small range of values of the injected laser intensity in which the two bistable peaks have a comparable area. The transmitted field averaged with respect to the stationary distribution function coincides with one of the two deterministic branches except on the narrow transition region where we have large fluctuations.

Topical Meeting on Optical Bistability (OB)•Jan 1, 1983•0 citations

Noise Effects In Transient Optical Bistability

R. Deserno, Rolf Kumme, Fedor M. Mitschke +2 more

The effect of external noise of different spectral distributions on the dynamic behaviour of an intrinsic optical bistable device is studied. Our experiments are performed under absorptive conditions in a sodium-filled nonlinear Fabry-Perot in the bad cavity limit. Alternatively, a bistable electronic circuit (Schmitt trigger) is shown to exhibit the same type of noise phenomena while admitting more detailed investigations.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 8, 1987•5 citations

Optical extinction theorem theory of optical multi-stability bifurcations and turbulence in the Fabry-Perot interferometer

R. Bullough, Saad S. M. Hassan, G. P. Hildred +1 more

We have reported two different aspects of this work already [1,2]. Nevertheless as the point of view is unconventional we review it here strictly within the context of the theory of optical bistability and optical multistability. We are concerned to connect the envelope Maxwel1-Bloch equations with optical bistability (multistability) in a Fabry-Perot (FP) cavity in a rigorous and potentially quantitative way. One problem in this connection is an adequate statement about standing waves. We present methods which derive the standing wave equations of motion completely as a part of a comprehensive non-linear refractive index theory of multistabi1ity inside the FP cavity. The theory is a c-number one — but a comparable quantum theory seems possible. A key feature of the argument is generalisation of the famous 'optical extinction theorem' [1,2,3] to this non-linear regime. In practice it means we do not invoke any boundary conditions at the surfaces of the FP cavity — only conditions at infinity — and this offers advantages for the quantitative description as we show.

Topical Meeting on Optical Bistability (OB)•Jan 1, 1983•0 citations

Absorptive Optical Bistability

Yutaka Fukuyama

A gas of two-level atoms in a Fabry-Perot cavity injected with a coherent resonant electric field is considered.Adopting a projector elimination of irrelevant degree-of-freedom in multiplicative stochastic process a stationary distribution for optical bistability is derived.The results derived from the stationary distribution.

長崎大学教育学部自然科学研究報告•Feb 28, 1981•0 citations

Fluctuational Transitions and Critical Phenomena in a Noise-Driven Optically Bistable Device

M. I. Dykman, G. P. Golubev, V. P. Golubchenko +3 more

Fluctuational transitions between the stable states of a passive optically bistable device have been observed and investigated theoretically and experimentally in the absence of spatial effects (for a lumped-parameter system). The problem of calculation of transition probabilities in dynamical systems driven by weak Gaussian noise has been reduced to logarithmic accuracy to a variational problem which is solved for some types of colored noise. The procedure of the experimental determination of the transition probabilities from the data on transmitted intensity is proposed for the case of a broad-band noise in the intensity of incident radiation. The onset of an extremely narrow peak in the power spectrum of the system in the range of the kinetic phase transition is revealed.

Nonlinear Dynamics in Optical Systems•Jan 1, 1990•0 citations
Fluctuation phenomena, to be anticipated in all systems for which the internal fluctuating variable is a multivalued function of the observable quantity, are reported. Analog electronic experiments on a model optically bistable Fabry-P'erot cavity have shown that the observable may be described in terms of a Boltzmann distribution with a multibranch effective potential. The distribution was observed to possess up to four peaks (two twin peaks) within the range of bistability, and to become singular at outer boundaries corresponding to the branching points of the potential. The experimental results are compared with theory.
Fluctuational transitions between stable states of an all-optical lumped-parameter bistable system have been observed. The dependences of the transition probabilities, and of the statistical distribution of the transmitted-light intensity, on the intensities of incident light and noise have been investigated. Two types of stochastic modulation, that of the incident-light intensity and that of the device itself, have been used. They correspond to multiplicative and additive noise for the intracavity-phase gain and give rise to qualitatively different pictures of the fluctuations. In particular, for the latter type of noise the logarithm of the statistical distribution of the transmitted-light intensity is described by a multibranch function, and the peaks of the distribution are strongly asymmetric. The onset of a zero-frequency peak in the power spectrum of the transmitted light in the range of the kinetic phase transition has been observed. The experimental data are in good qualitative and quantitative agreement with the theory.
In this paper we discuss the influence of laser fluctuations on the hysteresis cycle in Optical Bistability. For the simplest case of an Absorptive Optical Bistability in a good cavity driven by an external laser light with non-white Gaussian amplitude fluctuations we derive a Fokker-Planck equation in the limit of large laser linewidth and good amplitude stabilization. This Fokker-Planck equation has a nonconstant diffusion term which shifts the most probable values of the steady state probability distribution from its deterministic positions. From the form of the steady state solution of the Fokker-Planck equation with non-white amplitude fluctuations we discuss the relative stability of the bistable branches. As in the case of quantum fluctuations the random amplitude of the laser field leads to a small range of values of the injected laser intensity in which the two bistable peaks have a comparable area. The transmitted field averaged with respect to the stationary distribution function coincides with one of the two deterministic branches except on the narrow transition region where we have large fluctuations.
We have reported two different aspects of this work already [1,2]. Nevertheless as the point of view is unconventional we review it here strictly within the context of the theory of optical bistability and optical multistability. We are concerned to connect the envelope Maxwel1-Bloch equations with optical bistability (multistability) in a Fabry-Perot (FP) cavity in a rigorous and potentially quantitative way. One problem in this connection is an adequate statement about standing waves. We present methods which derive the standing wave equations of motion completely as a part of a comprehensive non-linear refractive index theory of multistabi1ity inside the FP cavity. The theory is a c-number one — but a comparable quantum theory seems possible. A key feature of the argument is generalisation of the famous 'optical extinction theorem' [1,2,3] to this non-linear regime. In practice it means we do not invoke any boundary conditions at the surfaces of the FP cavity — only conditions at infinity — and this offers advantages for the quantitative description as we show.
Fluctuational transitions between the stable states of a passive optically bistable device have been observed and investigated theoretically and experimentally in the absence of spatial effects (for a lumped-parameter system). The problem of calculation of transition probabilities in dynamical systems driven by weak Gaussian noise has been reduced to logarithmic accuracy to a variational problem which is solved for some types of colored noise. The procedure of the experimental determination of the transition probabilities from the data on transmitted intensity is proposed for the case of a broad-band noise in the intensity of incident radiation. The onset of an extremely narrow peak in the power spectrum of the system in the range of the kinetic phase transition is revealed.