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Physical Review A

Correlated-emission laser: Theory of the quantum-beat micromaser

János A. Bergou, Miguel Orszag

Published Jul 1, 1988• 14 citations
Publisher

Abstract

We show that if we inject three-level atoms, at a low rate, through a double cavity, with the two upper levels strongly coupled, and if, in the theoretical analysis, one makes the rotating-wave approximation, this problem is formally equivalent to the ordinary two-level micromaser. We also obtain the relevant master equation and the photon statistics.

DOI
10.1103/physreva.38.763

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We show that if we inject three-level atoms, at a low rate, through a double cavity, with the two upper levels strongly coupled, and if, in the theoretical analysis, one makes the rotating-wave approximation, this problem is formally equivalent to the ordinary two-level micromaser. We also obtain the relevant master equation and the photon statistics.
We derive the master equations for the fields in the one-mode \ensuremath{\Lambda}-type micromaser and laser with injected atoms in a superposition of their states. In terms of effective parameters, these equations are equivalent to those for a two-level micromaser and laser. The interference terms in the master equations may cancel the absorption terms independent of statistical properties of the field. Due to the atomic coherence between the two degenerate lower levels, the generation of field states with sub-Poissonian photon statistics is possible in the micromaser without the need for a population inversion. If an equivalent level system is used in a laser operating without population inversion it can produce field states with Poisson distributions of the photon number.
We derive the dressed states for the interaction of a cascade three-level atom with a quantum cavity field, suggest using ultra-cold cascade three-level atoms in micromasers, put forward the idea of the two-photon mazer, establish its general quantum theory and study its emission probability and photon statistics. We examine the effects of the atomic centre-of-mass momentum, the atom-field detuning, the photon number in thermal equilibrium, the ratio of the atomic injection rate to the cavity decay rate and the interaction length on the emission probability and the photon statistics.
The realization of the micromaser prompted theoretical interest in the fundamental problems of laser physics. In particular, it has been shown that the usual quantum theory of the laser can be recovered from the micromaser theory if a Poissonian average with respect to the time intervals between subsequent injections is taken. The problem of general injection statistics has not been fully resolved but, instead, has been circumvented in the following ways. Instead of the time period between successive injections, the number of injected atoms during a fixed time interval was considered as a stochastic variable and was averaged with respect to a general sub-Poissonian distribution. This led to a closed-form master equa tion, but correction terms arise when the effect of cavity damping is significant. In another approach a stroboscopic theory has been developed: The system is observed when a full cycle of pumping, firing, and decay is completed. This assumes observation of the system on a nonuniform time scale. Here we carry out the averaging over the time interval between subsequent injections with sub-Poissonian distribution, suggest a new compact master equation, and exploit some of its consequences. We show that this approach reproduces the previous ones if the cavity damping is negligible. The surprising result of our approach is that altering the pump statistics affects both the gain and the loss part of the laser dynamics.
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.
Quantum interference effects are theoretically investigated in the steady-state photon statistics of single-mode Λ- and V-type micromasers with injected three-level atoms in a superposition of their internal states. The two lower (upper) levels are nondegenerate and coherent in a general case. For the Λ-type case, we have discussed how detunings affect the photon statistics of the noninversion micromaser. Under the proper conditions strongly sub-Poissonian field states with a large number of photons can be easily produced in this novel micromaser even if there exists no coherence between the two lower levels. For the V-type case, we have analysed how the photon statistics changes with the increase of the ground-state population. Although the generation of the strongly sub-Poissonian states is always possible in the micromaser under the noninversion case, their photon intensities become very weak compared to the Λ-type case. Our results indicate that it is perfectly possible to experimentally realize a noninversion micromaser with strongly sub-Poissonian statistics in the Λ-type system.
We develop a quantum theory of a correlated-emission laser (CEL) with injected atomic coherence for arbitrary initial atomic conditions and arbitrary atomic decay rates. The effect of initial atomic coherence on the CEL is studied. It is shown that, with a proper form of the initial atomic coherence and equal atomic decay rates between the two upper levels of V-type three-level lasing atoms, the diffusion coefficients for the relative phase and the relative amplitude of two laser modes can vanish under certain conditions. These conditions, plus equal cavity-loss rates, lead to the vanishing of the normally ordered variances (quantum-noise quenching) of Hermitian operators corresponding to the relative phase and the relative amplitude.