Optical bistability in a resonant two-photon absorber

Abstract

Optical bistabflity as a kind of first-order phase transition has been suggested and experimentally observed in an optical feedback system (1) as well as in a resonant absorber within an interferomcter ([ 2). A multiple-pass interferometer with a suitable nonlinear dispersive or absorptive mechanism can behave as a bistable optical system. The first suggestion was made by SZ6K~ et al. (1), and different versions have been shown to work with the nonlinearity due either to an atomic medium at resonance with the impinging field (2) or to an external feed-back system (3). We are here interested in the optical bistability arising from the collective behaviour of an atomic system. A general theory has been formulated in a series of papers by BONIFACIO and LVGIATO (4) to obtain absorptive and dispersive atomic bistability. As is well known from the first approaches (3) a difficulty of atomic bistability consists in inhomogeneous broadening due to the Doppler contribution of atom in a cell. We show here evidence of a bistable behaviour of an interferometer filled with a two-photon absorber and working in a travelling wave mode. This is the first step to derive, afterwards, a Doppler free atomic bistability (6) by absorbing photons from opposite directions and getting rid of the inhomogeneous line. We consider an n-level atom (fig. 1) where two relevant levels a and b with the same pari ty can be coupled by two-photon processes via all the other intermediate levels of suitable pari ty to satisfy the selection rules for one-photon processes. We introduce an interaction with a classical field that we write in the slowly varying envelope approximation as