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Physica Scripta

On the numerical calculation of the micromaser spectrum

F. De Zela

Published Dec 1, 1995• 2 citations
Publisher

Abstract

A powerful numerical algorithm is described for calculating the micromaser spectrum. The method can be extended as a tool for computing the dynamics of the field density matrix which describes the photon field inside the micromaser cavity. An expression for the micromaser spectrum is also discussed, from which the role played by the initial state in the build-up of the spectrum becomes clearly distinguished from the micromaser dynamics.

DOI
10.1088/0031-8949/52/6/011

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A powerful numerical algorithm is described for calculating the micromaser spectrum. The method can be extended as a tool for computing the dynamics of the field density matrix which describes the photon field inside the micromaser cavity. An expression for the micromaser spectrum is also discussed, from which the role played by the initial state in the build-up of the spectrum becomes clearly distinguished from the micromaser dynamics.
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 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.