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Physical Review A

Theory of a two-level quantum-beat laser

Nadeem A. Ansari, Muhammad Suhail Zubairy

Published Nov 1, 1989• 11 citations
Publisher

Abstract

The theory of a two-level quantum-beat laser is presented within the framework of the quantum theory of multiwave mixing. The diffusion coefficients for the relative and the mean of phase angles of the two modes are derived. It is shown that under suitable conditions the diffusion coefficient for the mean angle of the field modes vanishes.

DOI
10.1103/physreva.40.5690

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The theory of a two-level quantum-beat laser is presented within the framework of the quantum theory of multiwave mixing. The diffusion coefficients for the relative and the mean of phase angles of the two modes are derived. It is shown that under suitable conditions the diffusion coefficient for the mean angle of the field modes vanishes.
Multiphoton transitions are of great interest in laser spectroscopy because they permit the study of new physical phenomena and because of their potential applications. Malcuit et al.1 studied two-photon transitions in atomic sodium and showed that for appropriate phase-matching four-wave mixing can overcome the usual spontaneous decay processes. We have recently developed a quantum theory2 to treat such multiwave mixing processes in two-photon media. Because of the greater complexity of two-photon transitions, many effects arise that are absent in the one-photon case, some of which have important consequences in the generation of squeezed states. For the two-photon two-level model, the field modes have frequencies approximately one-half the frequency difference between the levels. We find that our coefficients differ from the corresponding one-photon theory in that dynamic Stark shifts have a major effect and that the pump-induced coherence between the two levels has a new term in the conjugate coupling terms, which leads to improved squeezing.
We present a comprehensive quantum theory of correlated-emission lasers (CEL's) in a combination-mode approach, which is valid for both the quantum-beat laser and the CEL with injected atomic coherence. We first show that, under certain conditions, the linear master equation of the CEL's breaks down into two uncoupled equations in the combination modes, which are linear combinations of two CEL modes. One combination mode that is above threshold represents the average phase and the average amplitude of two CEL modes (called the sum mode), whereas the other that is below threshold represents the relative phase and the relative amplitude of the two CEL modes (called the relative mode). When the relative mode is in its vacuum state, the normally ordered variances of two Hermitian operators corresponding, respectively, to the relative phase and the relative amplitude vanish. Through deriving a nonlinear master equation for the CEL with injected atomic coherence in the combination modes, we show how a set of proper initial atomic conditions can keep the relative mode in its vacuum state. We obtain the Glauber P functions, the mean photon numbers, and the photon-number variances in both the combination modes and the CEL modes, and find the mode pullings of the CEL's and the natural linewidth of the sum mode. We also show a correspondence between the vacuum state of the relative mode and the vanishing of the relative-phase diffusion coefficient.
A quantum theory of a \ensuremath{\Lambda}-type three-level single-mode quantum-beat laser with injected atomic coherences and with an external microwave field, which coherently drives the lower two nearly degenerate levels, is studied. A master equation for the field-density operator and the photon statistics is derived. The laser operation is analyzed in terms of the coefficients of the Fokker-Planck equation of the laser field. Noninversion lasing is found in both cases: without and with injected atomic coherences. At the same time, in the latter case large quantum-noise reduction is found, and for particular initial parameter choices the laser field is very near to a coherent state with exactly Poissonian photon-number distribution and near-Poissonian phase distribution.