Statistical Treatment of Quantum Optical Systems and Squeezing Effect

Abstract

The analysis of fluctuations in quantum optical systems has been a subject of outstanding interest since Glauber¹ formulated his theory of quantum coherence. Haken and coworkers², Lamb and Scully³, Risken⁴, Lax and Louisell⁵ performed fundamental works on laser noise, thereby elaborating a number of useful and flexible techniques. Even if these studies remain basic for the present understanding of fluctuations, in the recent years it clearly emerged the need of a further elaboration of the methods involved. The reasons for that can be easily understood by considering that the main objective in the sixties was the analysis of fluctuations in the laser threshold region. In this problem the results are quite insensible to the approximations used, and completely different procedures lead to the same or to equivalent final equations. This is no longer true in the case of some problems considered more recently, as e.g. optical bistability. In partiçular, attention fogused on nonclassical effects as antibunching⁶,⁷ and “squeezing”⁸. The possibility of generating squeezed states of light, in which the noise in one quadrature component is reduced with respect to coherent Glauber states, has given rise to remarkable interest in the fields of optical communication, interferometry, gravitational wave detection. Now, the analysis of these purely quantum effects requires using the most refined techniques available, because any inaccurate approximation is likely to alter or even destroy them.