Quantum fluctuations in nonlinear optical systems

Abstract

The subject of quantum structures in nonlinear optics is a quite recent interdisciplinary field. It deals with the quantum properties of electromagnetic radiation in self-organized spatial structures. Until the decade of 1980 the areas of quantum optics and self-organized patterns were investigated by two different communities: • Most of the literature about pattern formation was concerned with classical features of the phenomenon [Haken, Cross & Hohenberg]. The effects of fluctuations in the process of pattern formation have been analyzed at length [Garc´ıa-Ojalvo & Sancho, San Miguel & Toral]. In fact, fluctuations allow for the exploration of several states, even producing new states, absent in a deterministic scenario (noise-induced states). However, there are only few studies about classical correlations functions and long-range spatial correlations in patterns. In addition, the possibility of quantum correlations in pattern formation was not investigated in detail. • Theoretical and experimental results concerning quantum phenomena in optics were obtained neglecting the spatial effects associated with the transverse profile of light beams [Walls & Milburn, Mandel & Wolf]. Only a spatial mode of the electromagnetic field at a frequency was generally considered (single-mode field). These models describe the experimental situation in which the whole light beam is detected with a single photodetector. Temporal fluctuations were mostly investigated, neglecting any spatial effects in the transverse area of the light beam.