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Physical Review A

Phase distribution and linewidth in the micromaser

William C. Schieve, Rebecca R. McGowan

Published Sep 1, 1993• 15 citations
Publisher

Abstract

The phase distribution function [after Pegg and Barnett, Phys. Rev. A 39, 1665 (1989)] is calculated for the micromaser and the lowest modal phase diffusion constant is compared to the linewidth calculation of Scully et al. [Phys. Rev. A 44, 5992 (1991)]. Utilizing the Fokker-Planck approach results in a linewidth which does not show ``trapping'' effects.

DOI
10.1103/physreva.48.2315

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Micromaser with injected atomic phase

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Both approximate and exact methods exist to determine the density matrix of the field inside an incoherently driven micromaser, but as of yet only a steady-state Fokker-Planck solution has been found for the micromaser with injected atomic phase [Phys. Rev. A 34, 2032 (1986)]. Since Fokker-Planck solutions have been shown not to represent the effect of trapping states on the cavity field adequately, other solutions must be sought. In this paper, we present both a highly accurate approximate analytical solution and a more computationally complex numerical solution based on the exact methods of Lu [Phys. Rev. A 47, 1347 (1993)], both of which demonstrate symmetry breaking in the phase. Since the spectra of the injected phase micromaser will be the same as that of the incoherently pumped case, we present numerical comparisons of our two solutions via the phase variance.

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Physical Review A•Jul 1, 1993•47 citations
The phase distribution function [after Pegg and Barnett, Phys. Rev. A 39, 1665 (1989)] is calculated for the micromaser and the lowest modal phase diffusion constant is compared to the linewidth calculation of Scully et al. [Phys. Rev. A 44, 5992 (1991)]. Utilizing the Fokker-Planck approach results in a linewidth which does not show ``trapping'' effects.
Both approximate and exact methods exist to determine the density matrix of the field inside an incoherently driven micromaser, but as of yet only a steady-state Fokker-Planck solution has been found for the micromaser with injected atomic phase [Phys. Rev. A 34, 2032 (1986)]. Since Fokker-Planck solutions have been shown not to represent the effect of trapping states on the cavity field adequately, other solutions must be sought. In this paper, we present both a highly accurate approximate analytical solution and a more computationally complex numerical solution based on the exact methods of Lu [Phys. Rev. A 47, 1347 (1993)], both of which demonstrate symmetry breaking in the phase. Since the spectra of the injected phase micromaser will be the same as that of the incoherently pumped case, we present numerical comparisons of our two solutions via the phase variance.
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.
We show how our recently proposed scheme for the measurement of the micromaser linewidth, which relates the phase diffusion dynamics of the cavity field to the population statistics of probe atoms, can be applied in the presence of trapping states, where the phase diffusion approximation does not strictly hold. This should allow the observation of the peculiar linewidth oscillations versus atomic pumping which are expected in this regime, and whose origin lies in the quantum nature of the cavity field.
We discuss a scheme to relate the phase diffusion dynamics of the micromaser field to the measured atomic population statistics. This can allow us to measure the linewidth of the micromaser spectrum and to solve a relevant decoherence problem in cavity quantum electrodynamics. The main steps are (i) a suitable preparation of the cavity field state to generate coherences, (ii) the transfer of information on the dynamics of field coherences to probe atoms by the action of an external resonant coherent field and (iii) the derivation of the phase diffusion rate, hence the micromaser linewidth, from the measured population statistics of the probe atoms. The method can be applied even in the presence of trapping states, where peculiar linewidth oscillations are expected for increasing pump rate, due to the quantum nature of the micromaser field.
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.