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Physical Review A

Quantum theory of the mazer. III. Spectrum

Michael Schröder, Karl Vogel, Wolfgang P. Schleich, Marlan O. Scully, HERBERT WALTHER

Published Nov 1, 1997• 71 citations
Publisher

Abstract

We calculate the spectrum of the micromaser with quantized motion of the pump atoms [M. O. Scully, G. M. Meyer, and H. Walther, Phys. Rev. Lett. 76, 4144 (1996)] in different velocity regimes. We show that when the kinetic energy of the pump atoms is comparable to the atom-field interaction energy the spectrum of the cavity field is no longer centered at the cavity frequency. In the case of very slow atoms huge broadenings and shifts occur in the vicinity of the mazer resonances. We present approximate analytical results for the spectrum that allow a comparison with the exact numerical calculations.

DOI
10.1103/physreva.56.4164

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We calculate the spectrum of the micromaser with quantized motion of the pump atoms [M. O. Scully, G. M. Meyer, and H. Walther, Phys. Rev. Lett. 76, 4144 (1996)] in different velocity regimes. We show that when the kinetic energy of the pump atoms is comparable to the atom-field interaction energy the spectrum of the cavity field is no longer centered at the cavity frequency. In the case of very slow atoms huge broadenings and shifts occur in the vicinity of the mazer resonances. We present approximate analytical results for the spectrum that allow a comparison with the exact numerical calculations.
The photon emission probability in a micromaser changes drastically when the kinetic energy of the pumping atoms is comparable to the atom-field interaction energy. In this situation, the atomic center-of-mass motion has to be treated quantum mechanically and the de Broglie wavelength of the atom inside the cavity is an important physical parameter. The interplay between reflection and transmission of the atoms leads to a new mechanism for induced emission. A photon is emitted by an excited atom when the de Broglie wavelength fits resonantly into the cavity. These resonances lead to the process of microwave amplification via zzz-motion-induced emission of radiation (mazer). We derive and illustrate a general expression for the emission probability and a master equation for the mazer. We note that the probability for emission by an excited thermal atom (stimulated maser emission) is very different from the emission probability as given by the de Broglie resonances (induced mazer emission).
A short review of the theoretical studies of the cold atom micromaser (mazer) is presented. Existing models are then improved by considering more general working conditions. Especially, the mazer physics is investigated in the situation where a detuning between the cavity mode and the atomic transition frequency is present. Interesting new effects are pointed out. Especially, it is shown that the cavity may slow down or speed up the atoms according to the sign of the detuning and that the induced emission process may be completely blocked by use of a positive detuning. The transmission probability of ultracold atoms through a micromaser is also studied and we generalize previous results established in the resonant case. In particular, it is shown that the velocity selection of cold atoms passing through the micromaser can be very easily tuned and enhanced using a nonresonant field inside the cavity. This manuscript is a summary of Martin's master thesis and articles [Phys. Rev. A 67, 053804 (2003)] and [Eur. Phys. J. D 29, 133 (2004)].
The spectrum of the micromaser injected with Λ-type three-level atoms is studied. The spectrum has a Lorentzian lineshape and its central frequency has a shift. The effects of various parameters (for example, the atomic center-of-mass velocity, the cavity-length, the one-photon detuning, the ratio of the atomic injection rate to the cavity decay rate and the number of thermal photons) on the linewidth and the frequency shift are examined. The spectrum shows very different features in different velocity regimes, i.e., in the fast-atom regime, in the intermediate-velocity-atom regime, and in the slow-atom regime.
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.
We study the spectrum of the micromaser injected with ultracold cascade three-level atoms. We examine the effects of the atomic centre-of-mass motion, the cavity length, the atom-field detuning, the ratio of the atomic injection rate to the cavity decay rate, and the number of photons in thermal equilibrium on the spectrum. We find that the micromaser injected with ultracold three-level atoms shows new spectral properties which are different from those of the micromaser injected with ultracold two-level atoms and the micromaser injected with thermal two- or three-level atoms. The main conclusions are that the linewidth can be broadened and the frequency can be either red-shifted or blue-shifted.
The equations for the micromaser are derived without assuming the validity of the rotating- wave approximation (RWA) in the Scully-Lamb model for a single-mode maser off resonance. The treatment is based on Swain's continued fractions approach, by which the eigenvalues and eigenvectors of the Hamiltonian describing the system of atoms plus cavity field can be iteratively determined to any desired order and then used to obtain the micromaser equations. These are valid to second order in the parameter g, the coupling constant of the atom-field interaction. The procedure can be extended, to any desired order in g, by successive iterations. Through numerically evaluating the micromaser spectrum we compare our results with those of the RWA. We predict a relative shift, stemming from the Bloch-Siegert shift, which in case of the spectra corresponding to two-photon correlations should be measurable through atomic selective field ionization.