Photon statistics of a bistable absorber

Year: 1978

Authors: Bonifacio R., Gronchi M., Lugiato L.A.

Autors Affiliation: Istituto di Fisica dell’Università di Milano;
Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, Italy

Abstract: We discuss the quantum-statistical properties of a system of absorbing atoms in a ring cavity under the action of a resonant classical field. At a semiclassical level, this system exhibits a bistable behavior in the sense that the transmitted light ET is a discontinuous function of the incident light EI with a hysteresis cycle, which resembles a first-order phase transition. Here we specify this analogy stressing the nonthermodynamic properties of this coherently driven system. The quantized field ET is described by a Glauber P function, which obeys to a Fokker-Planck equation. This equation is derived from a very general master equation in the case of a good quality cavity by neglecting derivatives of order higher than second. A remarkable feature of this equation is that the diffusion coefficient is a nonlinear function of the field intensity. The steady-state solution of the Fokker-Planck equation has the following features. The P function can be single or double peaked according to the value of EI. In fact, our Fokker-Planck equation is like the one of a Brownian particle moving in a potential which presents one minimum or minima separated by a barrier, depending on the value of EI. The peaks of the P function correspond to the minima of the potential. In the double-peaked case, the peaks have different widths. The maxima of the p function occur at values of ET, which coincide with the classical stationary solutions that are stable according to the linear stability analysis. These semiclassical solutions give a discontinuous two-valued function of ET vs EI (hysteresis cycle). On the contrary, the mean value 〈ET〉 is a continuous single-valued function of EI, which behaves similarly to the Maxwell construction of a first-order phase transition: 〈ET〉 jumps from low to high values in a very sharp transition region of EI, which lies between the discontinuity points of the hysteresis cycle. However, the Maxwell rule that we obtain is quite different from that of equilibrium thermodynamics. The mean-square fluctuations of ET are always very small except in the transition region where they are quite remarkable. We also present an exact expression of the stationary P function, which takes into account all higher-order derivatives, and we show that the Fokker-Planck approximation is very good for calculating mean values and mean-square fluctuations. Finally, we discuss the connections which link bistable absorption to the laser with injected signal and to the laser with a saturable absorber.

Journal/Review: PHYSICAL REVIEW A

Volume: 18 (5)      Pages from: 2266  to: 2279

KeyWords: optical bistability
DOI: 10.1103/PhysRevA.18.2266

Citations: 105
data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-11-17
References taken from IsiWeb of Knowledge: (subscribers only)
Connecting to view paper tab on IsiWeb: Click here
Connecting to view citations from IsiWeb: Click here