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Physical Review A

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

M. I. Dykman, G. P. Golubev, D. G. Luchinsky, A. L. Velikovich, S. V. Tsuprikov

Published Aug 1, 1991• 8 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.44.2439

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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.
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.
The transient properties of a three-level atomic optical bistable system in the presence of multiplicative and additive noises are investigated. The explicit expressions of the mean first-passage time (MFPT) of the transition from the high intracavity intensity state to the low one are obtained by numerical computations. The impacts of the intensities of the multiplicative noise D M and the additive noise D A , the intensity of correlation between two noises λ, and the intensity of the incident light y on the MFPT are discussed, respectively. Our results show: (i) for the case of no correlation between two noises (λ = 0.0), the increase in D M and D A can lead to an increase in the probability of the transition to the low intracavity intensity state, while the increase in y can lead to a retardation of the transition; and (ii) for the case of correlation between two noises (λ = 0.0), the increase in λ can cause an increase in the probability of the transition, and the increase in D A can cause a retardation of the transition firstly and then an increase in the probability of the transition, i.e., the noise-enhanced stability is observed for the case of correlation between two noises.
We consider the dynamical behavior of the (nonlinear) amplitude fluctuations in the transmitted radiation of the optical bistability in the transition region. A Fokker-Planck model with nonlinear diffusion coefficient (multiplicative Gaussian white noise) is used to describe the system in the "good-quality" cavity limit. Choosing a parameter set corresponding to a numerically small but tractable tunneling rate between the stable and metastable states we study, as functions of the external coherent field and system size, the spectrum and the response to a small additional injected coherent signal. The numerical calculations are facilitated by the construction of complex-valued continued-fraction representations for the spectrum of amplitude fluctuations and for the response function. This representation allows us to discuss the memory effects caused by deviations from a simple Gaussian-Markov behavior around the transition region. In addition, such a representation enables the construction of "a posteriori" error bounds on the power spectrum.
A quantum description of the transmitted field is given. In the bistable situation, the stationary Glauber quasi probability distribution has two peaks thereby producing a first-order phase transition. For small incident field the linewidth of the transmitted light is proportional to the atomic density and becomes very narrow as the field approaches some critical value from below. Crossing this value the spectrum splits discontinuously into a triplet (dynamical Stark shift) where the central peak is as high as twice the side-bands.
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.