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Physical Review A

Multiplicative noise-induced probability distributions in three-level atomic optical bistability

Haibin Wu, Surendra Singh, Min Xiao

Published Feb 26, 2009• 6 citations
Publisher

Abstract

Effects of multiplicative noise on optical bistability in a three-level atomic medium in a ring cavity are investigated experimentally and theoretically. Steady-state intensity distributions as well as switching and dwell times have been measured as functions of noise strength. System response to an external periodic signal is also explored. It is found that the probability for the system to stay in the upper state increases with increasing noise strength. When a small periodic signal is added to the input field, the probability for the upper state has a maximum as a function of multiplicative noise strength. A simple theoretical model based on nonlinear atomic susceptibility is presented to interpret the experimental observations.

DOI
10.1103/physreva.79.023835

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Effects of multiplicative noise on optical bistability in a three-level atomic medium in a ring cavity are investigated experimentally and theoretically. Steady-state intensity distributions as well as switching and dwell times have been measured as functions of noise strength. System response to an external periodic signal is also explored. It is found that the probability for the system to stay in the upper state increases with increasing noise strength. When a small periodic signal is added to the input field, the probability for the upper state has a maximum as a function of multiplicative noise strength. A simple theoretical model based on nonlinear atomic susceptibility is presented to interpret the experimental observations.
Stochastic resonance (SR) is experimentally demonstrated in an atomic optical bistable system consisting of three-level atoms in $\ensuremath{\Lambda}$-type configuration confined in an optical ring cavity. The optical bistable system with enhanced Kerr nonlinearity due to atomic coherence is driven by a periodic signal and a Gaussian white noise source with variable amplitude, and displays an improved output signal-to-noise ratio, a characteristic signature of SR. The measured results match qualitatively with the theoretical predictions of the generic model for the SR phenomenon.
The effect of correlated white noises on the optical bistability behavior of three-level atomic systems is theoretically investigated. Noise-induced bistability is demonstrated in an atomic optical bistable system consisting of three-level atoms in Λ-type configurations confined in an optical ring cavity. The output field as a result of enhanced Kerr nonlinearity induced by atomic coherence in the electromagnetically induced transparency system is variable due to the noises in laser parameters and the cooperativity parameter. Therefore, noise is mainly responsible for such induced bistability in the system. It is found that with the cross-correlation noises, the hysteresis loop of optical bistability can be clearly expanded in comparison with the deterministic case and the atomic system could show multistability behavior. This is specifically considerable for positive cross-correlated noises where it could expand the domain of the hysteresis loop. In the presented atomic system the numerical result shows that noise can induce bistability in the absence of spontaneously generated coherence. Furthermore, it is salient that the noise could induce bistability when the system is below its deterministic threshold for bistability.
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 propose an optical bistability (OB) model consisting of a five-level cascade electromagnetically induced transparency (EIT) medium placed in a unidirectional ring cavity. An input-output intensity relationship for a weak probe light field is derived as a function of parameters of a strong coupling light and cooperation C. The OB behaviors of the system are investigated with variation of the parameters. It has been shown that the OB behaviors occur simultaneously in three EIT windows. Furthermore, switching thresholds and the hysteresis loop can be controlled by the parameters of the coupling light and/or a cooperation of atomic medium. Such controllable OB behaviors can find interesting applications in bistable photonic devices working at low light intensity and multiple frequencies.