Examples from recent work with K. Wodkiewicz, M. Jamanol and J. J. Yeh will be used to review the kinds of effects that may be expected when stochastic fluctuations are imposed on quantum and nonlinear optical processes.
Squeezing of radiation is a purely quantum mechanical phenomenon which has no classical counterpart. This quantum effect is expected to manifest itself in optical processes in which the nonlinear response of the system to the radiation field plays an important role. The concept of squeezing started in mid 1980s. Since then there has been an enormous upsurge of interest in this field owing to its low noise property. In the present paper various aspects of squeezing of radiation are studied and possible means of generation of squeezed light in which the quantum fluctuations are reduced below shot noise limit are investigated. The amplitude of the electric field of a mode of an electromagnetic field is always associated with quantum mechanical fluctuations. Squeezing states are characterised by reduced quantum fluctuations in one quadrature component of the field at the expense of increased fluctuations in the other noncommuting component. A fully quantum mechanical approach is followed. In the present paper we intend to review different aspects of squeezing and higher order squeezing in higher order Raman processes as well as in multiwave mixing processes. A comparative study between different processes are made which will pave a way for easier generation of squeezed light.
Recent studies have extensively explored chaotic dynamics in quantum optical systems through the mean-field approximation, which corresponds to an ideal, fluctuation-free scenario. However, the inherent sensitivity of chaos to initial conditions implies that even minute fluctuations can be amplified, thereby questioning the applicability of this approximation. Here, we analyze these chaotic effects using stochastic Langevin equations or the Lindblad master equation. For systems operating at frequencies of 105 to 107 Hz, we demonstrate that room-temperature thermal fluctuations are sufficient to suppress chaos at the level of expectation values, even under weak nonlinearity. Furthermore, nonlinearity induces deviations from Gaussian phase-space distributions of the quantum state, revealing attractor-like features in the Wigner function. With increasing nonlinearity, the noise threshold for chaos suppression decreases, approaching the scale of vacuum fluctuations. These results provide a bidirectional validation of the quantum mechanical suppression of chaos.
Recent studies have extensively explored chaotic dynamics in quantum optical systems through the mean-field approximation, which corresponds to an ideal, fluctuation-free scenario. However, the inherent sensitivity of chaos to initial conditions implies that even minute fluctuations can be amplified, thereby questioning the applicability of this approximation. Here, we analyze these chaotic effects using stochastic Langevin equations or the Lindblad master equation. For systems operating at frequencies of 105-107 Hz, we demonstrate that room-temperature thermal fluctuations are sufficient to suppress chaos at the level of expectation values, even under weak nonlinearity. Furthermore, nonlinearity induces deviations from Gaussian phase-space distributions of the quantum state, revealing attractor-like features in the Wigner function. With increasing nonlinearity, the noise threshold for chaos suppression decreases, approaching the scale of vacuum fluctuations. These results provide a bidirectional validation of the quantum mechanical suppression of chaos.