Calculation of the micromaser spectrum. I. Green’s-function approach and approximate analytical techniques

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Abstract
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.