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Canadian Journal of Physics

Approach to equilibrium in the micromaser

D. Leary, S. Yau, M. E. Carrington, R. Kobes, G. Kunstatter

Published Jan 1, 2001• 0 citations
Publisher

Abstract

We examine the approach to equilibrium of the micromaser.Analytic methods are first used to show that for large times (i.e.many atoms) the convergence is governed by the next to leading eigenvalue of the corresponding discrete evolution matrix.The model is then studied numerically.The numerical results confirm the phase structure expected from analytic approximation methods and agree for large times with the analysis of Elmfors et al in terms of the "continuous master equation".For short times, however, we see evidence for interesting new structure not previously reported in the literature.

DOI
10.1139/cjp-79-5-783

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We examine the approach to equilibrium of the micromaser.Analytic methods are first used to show that for large times (i.e.many atoms) the convergence is governed by the next to leading eigenvalue of the corresponding discrete evolution matrix.The model is then studied numerically.The numerical results confirm the phase structure expected from analytic approximation methods and agree for large times with the analysis of Elmfors et al in terms of the "continuous master equation".For short times, however, we see evidence for interesting new structure not previously reported in the literature.
We examine the approach to equilibrium of the micromaser. Analytic methods are first used to show that for large times (i.e. many atoms) the convergence is governed by the next to leading eigenvalue of the corresponding discrete evolution matrix. The model is then studied numerically. The numerical results confirm the phase structure expected from analytic approximation methods and agree for large times with the analysis of Elmfors et al in terms of the continuous master equation. For short times, however, we see evidence for interesting new structure not previously reported in the literature.
We examine the approach to equilibrium of the micromaser. Analytic methods are first used to show that for large times (i.e., many atoms) the convergence is governed by the next-to-leading eigenvalue of the corresponding discrete evolution matrix. The model is then studied numerically. The numerical results confirm the phase structure expected from analytic approximation methods and agree for large times with the analysis of Elmfors et al. in terms of the ``continuous master equation.'' For short times, however, we see evidence for interesting new structure not previously reported in the literature. PACS No.: 42.55Sa
A detailed theoretical and experimental study of the atom-field interaction starting from first principles was made possible by the realization of the single-atom micromaser. The situation is very close to the ideal case of a single two-level atom interacting with a single quantized mode of a superconducting cavity. In spite of the considerable amount of work devoted to the study of the micromaser, it still remains to be established how the system behaves under coherent pumping. We present a comprehensive study of the coherently pumped micromaser; we develop an analytic method to obtain the steady-state solution of the master equation governing the time evolution of the cavity field. We illustrate this method with a simple example and present results for the photon distribution and purity of the steady state of the coherently pumped micromaser.
We first calculate the ``exact'' micromaser spectrum by solving numerically for the Green's function of the approximate master equation for the one-atom (micro-) maser. We then proceed to calculate approximate analytical expressions for the maser linewidth using (i) a phase-operator approach, (ii) an ansatz similar to the standard quantum theory of the laser, and (iii) a linear expansion of the correlation function. Novel features, quite distinct from the familiar Schawlow-Townes linewidth, are found, e.g., the linewidth decreases as the number of thermal photons increases.
In earlier papers, the linewidth of a micromaser was approximated by a phase diffusion rate that was obtained using a single decay rate assumption to model the decay of the electric field in the micromaser cavity. These methods gave analytic but approximate answers. Exact methods calculated the spectrum via the two-time correlation function, but required extensive numerical calculations. In this paper, we present an approximate analytic derivation of the micromaser spectrum via the two-time correlation function that is more accurate than other approximate analytic methods yet requires much less numerical calculation than the exact methods. We also review the other methods, both analytical and exact, and present numerical comparisons.