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Physical Review Letters

Subnarrow linewidth, hole, and split in micromaser spectrum

Ning Lu

Published Feb 15, 1993• 19 citations
Publisher

Abstract

By calculating the two-time correlation function of a one-photon micromaser, we study the line shapes and linewidth of the micromaser spectrum. We find that the half-width at half maximum of the spectrum can be less than the smallest decay rate of the off-diagonal density-matrix elements ${\mathrm{\ensuremath{\rho}}}_{\mathit{n},}$${\mathit{n}}_{+1}$, that a hole can appear in the spectrum, and that the spectrum can be split by shifted spectral components.

DOI
10.1103/physrevlett.70.912

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By calculating the two-time correlation function of a one-photon micromaser, we study the line shapes and linewidth of the micromaser spectrum. We find that the half-width at half maximum of the spectrum can be less than the smallest decay rate of the off-diagonal density-matrix elements {\mathrm{\ensuremath{\rho}}}_{\mathit{n},}$${\mathit{n}}_{+1}, that a hole can appear in the spectrum, and that the spectrum can be split by shifted spectral components.
We study the spectrum of a one-photon micromaser through the approach of the two-time correlation function. First, we derive two general formulas for the two-time correlation function and for the micromaser spectrum. Then, we focus our attention on trapped states of the micromaser. We examine the line shapes and linewidth of the micromaser spectrum. We find that the half width at half maximum of the spectrum can be less than the smallest decay rate of the off-diagonal density matrix elements ${\mathrm{\ensuremath{\rho}}}_{\mathit{n},}$n+1{\mathit{n}}_{+1}n+1​(t), that a hole can appear at the center of the spectrum, and that the spectrum can be split by shifted spectral components. Using a simple example in which the micromaser spectrum is exactly Lorentzian, we also show that two very close photon-number distributions can correspond to two very different natural linewidths.
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 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 this paper, we study the influence of atomic decay on the linewidth of a two-photon micromaser using an exact Hamiltonian approach. We consider a three-level cascade atomic system (where each level has a finite lifetime) interacting with a single mode of the radiation field. The intermediate level is considered to be off resonant with the field. We calculate the linewidth for both small- and large-detuning limits. In both cases, the well known oscillatory behaviour of the linewidth vanishes for large decay rates. We also find a reduction in the linewidth in certain regions of interaction times. In the limit of small decay rates, we recover the linewidth of the ordinary two-photon micromaser. We also compare the results under the large-detuning limit with the results obtained using a phenomenological Hamiltonian approach.