Dynamics, correlations, and phases of the micromaser

Abstract

The micromaser possesses a variety of dynamical phase transitions parametrized by the flux of atoms and the time of flight of the atom within the cavity. We discuss how these phases may be revealed to an observer outside the cavity using the long-time correlation length in the atomic beam. Some of the phase transitions are not reflected in the average excitation level of the outgoing atom, which is the commonly used observable. The correlation length is directly related to the leading eigenvalue of the time evolution operator, which we study in order to elucidate the phase structure. We find that as a function of the time of flight the transition from the thermal to the maser phase is characterized by a sharp peak in the correlation length. For longer times of flight there is a transition to a phase where the correlation length grows exponentially with the flux. We present a detailed numerical and analytical treatment of the different phases and discuss the physics behind them.

The Deterministic Generation of Photons by Cavity Quantum Electrodynamics

“…Collapseand-revival in the presence of a thermal field was first observed by Rempe et al in 1987 [32]. Elmfors et al [33] subsequently performed a theoretical analysis of the experimental conditions and found excellent agreement between theory and experiment, thus clearly showing that the interpretation of the data as collapse-and-revival was accurate. In 1996, collapse-and-revival was also observed in the presence of a coherent field by Brune et al [34] (see also Sect.…”

Approach to equilibrium in the micromaser

“…Assuming that γτ ≪ 1, we neglect damping during the atom-photon interaction. The probability distribution for the photons just before the next atom enters the cavity is [3]:…”

“…We will refer to it as the discrete master equation. The analysis in [3] starts from a different master equation, which is called the continuous master equation. To derive the continuous master equation, Elmfors et al consider a situation where the flux of incoming atoms is large enough that the atoms have Poisson distributed arrival times, so that each atom has the same probability Rd t of arriving in an infinitesimal time d t. They further assume that the interaction within the cavity takes place in a time much less than this time interval (τ ≪ d t) which means that the interaction is essentially instantaneous.…”

“…In a recent paper, Elmfors et al [3] looked at long time correlations in the outgoing atomic beam and their relation to the various phases of the micromaser system. The properties they considered were associated with the equilibrium configuration of the cavity photon distribution, but there is a close connection between the correlation functions considered in [3] and the near equilibrium dynamical behaviour that we will be examining. As we will show, our results agree with those of [3] in the appropriate (i.e large N) limits.…”

Algebraic approach to the Tavis-Cummings problem

“…The results reported in [4] demonstrate that the physical assumptions underlying the JC model can indeed be experimentally realized. This triggered a lot of theoretical interest towards the one-atom micromaser(microlaser) (see [5,6,7] and references therein). The analysis of the JC model is greatly simplified by the fact that the eigenvalue problem of the Jaynes-Cummings Hamiltonian can be solved exactly.…”