Theory of Fluctuations and Collisions in Quantum Optics.

Federico Casagrande, L. A. Lugiato

Darren Rand, Ken Steiglitz, Paul R. Prucnal

A fully quantum mechanical model of two-component Manakov solitons is developed in both the Heisenberg and Schr\"odinger representations, followed by an analytical, linearized quantum theory of Manakov solitons in the Heisenberg picture. This theory is used to analyze the vacuum-induced fluctuations of Manakov soliton propagation and collision. The vacuum fluctuations induce phase diffusion and dispersion in Manakov soliton propagation. Calculations of the position, polarization angle, and polarization state fluctuations show an increase in collision-induced noise with a decrease in the relative velocity between the two solitons, as expected because of an increase in the interaction length. Fluctuations in both the polarization angle and state are shown to be independent of propagation distance, opening up possibilities for communications, switching, and logic, exploiting these properties of Manakov solitons. Calculations of the phase noise reveal, surprisingly, that the collision-induced fluctuations can be reduced slightly below the level of fluctuations in the absence of collision, due to cross-correlation effects between the collision-induced phase and amplitude fluctuations of the soliton. The squeezing effect of Manakov solitons is also studied and proven, unexpectedly, to have the same theoretical optimum as scalar solitons.

F. T. Arecchi

K. Wódkiewicz

The theory of optical Bloch equations with stochastic coefficients is discussed in detail. It is shown that Bloch equations with stochastic fields lead to multiplicative stochastic processes for which exact solutions can be obtained. The steady state and the transient regimes of the phase-diffusion model of the laser bandwidth are treated, and exact solutions of Bloch equations are obtained. The case of fluctuation due to collisions is also discussed. A simple stochastic model of radiation-induced collisions is presented. For each stochastic model of incoherences formulas for the longitudinal and transverse lifetimes are derived exactly. It is shown that the finite bandwidths of light or the collision incoherences do not, in general, have a simple additive effect in atomic equations of motion.

Frank Vollmer, Deshui Yu

Fritz Haake, Lorenzo M. Narducci, Daniel F. Walls

This book presents the papers given at a conference on quantum optics. Topics considered at the conference included the growth of precipitates in a super saturated system, a space-time picture of relativistic propagation of medium energy hadrons through nuclei, lattice gauge theories, electron-nucleus scattering, short optical pulses, gaussons of the electromagnetic field, collision-induced coherence, spontaneous oscillations in a laser with injected signals, amplitude and phase in quantum optics, and Rydberg atoms in resonant cavities.