Non-Markovian Stochastic Resonance in a Tunable Optical Microcavity

Abstract

In this Thesis we analyze, both in theory and experiment, the phenomenon of stochastic resonance in an optical microcavity with a non-instantaneous nonlinearity. Such a non-instantaneous nonlinearity is found, for example, in media that heat and cool in finite time under constant illumination. Starting from a driven-dissipative Kerr model, we develop a new theory modeling the field in such media by introducing a memory kernel that assigns a timescale to the nonlinearity. The memory kernel makes the state of system explicitly depend on its complete history, and not only on its immediate past. The deviation from a Markovian approximation is characterized by the residence time distribution, which we find is no longer an exponential on timescales comparable to the characteristic timescale of the nonlinearity. This is an indication of level crossings which are correlated in time, a signature of non-Markovian dynamics. The model successfully reproduces experimental results demonstrating dynamical hysteresis in an optical microcavity with a thermal nonlinear medium inside. We furthermore explore the concept of stochastic resonance in this new model. This effect manifests itself in a resonance-like peak in the signal-to-noise ratio as a function of the noise intensity. The role of the thermal relaxation time is also studied and is found to shift the peak in the signal-to-noise ratio to larger noise strengths. We finally report the first experimental observation of stochastic resonance in a thermal nonlinear medium. Comparing experimental results with simulations, we find a good agreement between theory and experiment.