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Physical Review A

Generalized Bose-Einstein distributions and multistability of a laser-cooled gas

J. I. Cirac, Maciej Lewenstein, P. Zoller

Published Apr 1, 1995• 9 citations
Publisher

Abstract

We study the dynamics of a system of atoms undergoing laser cooling in a microtrap. Using a simple model, we show that the stationary state of the system can be different from the standard Bose-Einstein distribution. In particular, it can exhibit infinite sequences of phase transitions as a function of laser detuning, as well as multistable behavior. This is due to the combination of quantum statistical phenomena and other effects related to the laser-cooling process.

DOI
10.1103/physreva.51.2899

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We study the dynamics of a system of atoms undergoing laser cooling in a microtrap. Using a simple model, we show that the stationary state of the system can be different from the standard Bose-Einstein distribution. In particular, it can exhibit infinite sequences of phase transitions as a function of laser detuning, as well as multistable behavior. This is due to the combination of quantum statistical phenomena and other effects related to the laser-cooling process.
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After reviewing the interpretation of laser operation as a nonequilibrium Bose-Einstein condensation phase transition, we illustrate the novel features arising from the nonequilibrium nature of photon and polariton Bose-Einstein condensates recently observed in experiments. We then propose a quantitative criterion to experimentally assess the equilibrium versus nonequilibrium nature of a specific condensation process, based on fluctuation-dissipation relations. The power of this criterion is illustrated on two models which show very different behaviors. Historical and Conceptual Introduction The first introduction of concepts of nonequilibrium statistical mechanics into the realm of optics dates back to the early 1970s with pioneering works by Graham and Haken [1] and by DeGiorgio and Scully [2], who proposed a very insightful interpretation of the laser threshold in terms of a spontaneous breaking of the U( 1 ) symmetry associated with the phase of the emitted light. Similar to what happens to the order parameter at a second-order phase transition, such an optical phase is randomly chosen every time the device is switched on and remains constant for macroscopic times. Moreover, a long-range spatial order is established, as light emitted by a laser device above threshold is phase-coherent on macroscopic distances. While textbooks typically discuss this interpretation of laser operation in terms of a phase transition for the simplest case of a single-mode laser cavity, rigorously speaking this is valid only in spatially infinite systems. In fact, only in this case one can observe nonanalytic behaviors of the physical quantities at the transition point. In particular, the long-range order is typically assessed by looking at the long-distance behavior of the correlation function of the order parameter, which, for a laser, corresponds to the first-order spatial coherence of the emitted electric field, the spontaneous symmetry breaking is signaled by this quantity becoming nonzero (see Chapter 5). The average is taken on the stationary density matrix of the system. In order to be able to probe this long-distance behavior, experimental studies need devices with a spatially extended active region.
In this paper, we present a method for simulating the kinetic evolution of a dilute gas of atoms that are cooled below the critical temperature for Bose-Einstein condensation. Our method gives insight into the formulation of physical kinetics by illustrating directly the decomposition of the distribution function into an infinite sum of single-particle trajectories. This approach is valid for the entire range of phase-space densities, although we limit the discussion here to exclude the region where the condensate fraction is close to unity and the effect of the mean field is significant. We present explicit calculations of finite number effects on equilibrium, the dynamic build-up of the ground state, and simulations of evaporative cooling.