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Annual Meeting Optical Society of America

Quantum theory of two-mode lasing without inversion with injected atomic coherence

János A. Bergou, Pál Bogár, Mark S. Hillery

Published Jan 1, 1993• 0 citations
Publisher

Abstract

We present the quantum theory of a two-mode Lambda-type three level quantum-beat laser with injected atomic coherences. The lower two levels are coupled by an external classical field. The master equation and the Fokker–Planck equation are derived. Phases of the two modes are locked to a value depending on the phase of the external field, the phase of the injected coherence and the population of the lower two levels. Lasing without inversion and without threshold is found for both modes with and without injected coherences. Applying the appropriate initial atomic coherences one can switch intensities between the two modes, as well as bifurcation and multiple branching can be found when coherences among all levels are present. It is also possible to find phase bistability at a fixed intensity for one of the two modes, when high pump is applied. Strong intensity and phase noise reduction can be found in one of the modes at the expense of increased noises in the other one. Near Poissonian noise can be achieved. This research was supported by a grant of the Office of Naval Research.

DOI
10.1364/oam.1993.thq.4

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We present the quantum theory of a two-mode Lambda-type three level quantum-beat laser with injected atomic coherences. The lower two levels are coupled by an external classical field. The master equation and the Fokker–Planck equation are derived. Phases of the two modes are locked to a value depending on the phase of the external field, the phase of the injected coherence and the population of the lower two levels. Lasing without inversion and without threshold is found for both modes with and without injected coherences. Applying the appropriate initial atomic coherences one can switch intensities between the two modes, as well as bifurcation and multiple branching can be found when coherences among all levels are present. It is also possible to find phase bistability at a fixed intensity for one of the two modes, when high pump is applied. Strong intensity and phase noise reduction can be found in one of the modes at the expense of increased noises in the other one. Near Poissonian noise can be achieved. This research was supported by a grant of the Office of Naval Research.
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.
Noninversion lasing is investigated in \ensuremath{\Lambda}-type three-level atomic systems that are coupled to two modes of the electromagnetic field. As a result of an external field driving the transition between the lower two closely spaced levels, laser action can be achieved in both modes simultaneously at arbitrarily small initial upper-level population (lasing without inversion) provided the pumping rate exceeds a certain threshold. The relative phase of the two modes is locked to a particular value controlled by the phase of the external field. In addition, new regimes of the laser operation arise when initial coherences between various atomic levels are also injected into the resonator. Firstly, laser action can be achieved in both modes at arbitrarily small pumping (no threshold). Secondly, the injected atomic coherence can control competition between the modes, and result in a variety of multistable steady-state behavior illustrating the very sensitive dynamics of the system.
A quantum theory of a two-level single-mode laser with injected atomic coherence is developed by generalizing the Scully-Lamb laser theory to a form appropriate for the analysis of a coherently pumped laser. We assume that the active atoms are prepared initially in a coherent superposition of the upper and lower levels, and we derive the master equation for the field density operator by treating the interaction of the laser field with many active atoms simultaneously. It is shown that the photon-number distribution can be exactly Poissonian. The laser operation is analyzed in terms of the Fokker-Planck equation for the laser field. Both the intensity and phase diffusion coefficients are phase sensitive and, for stable laser operation, become much smaller than those of an ordinary laser. Consequently, the injected atomic coherence reduces both the photon-number noise and phase noise simultaneously. The intensity diffusion coefficient can vanish exactly, and at the same time the phase diffusion coefficient can become very small. This leads to spontaneous-emission noise quenching in the photon-number distribution, and the laser field can become very close to a coherent state. A scheme to generate the proper form of the initial atomic coherence necessary for the quantum noise quenching is proposed and analyzed.
In this paper, we have included the effects of initial partial coherence in the quantum theory of a non-degenerate inversionless laser. A three-level atomic system in open A-configuration is considered. The atoms are initially prepared in the partial coherent superposition of the lower two atomic levels with some incoherent population in the excited state. The master equation for the cavity field modes is derived and converted into a Fokker-Planck equation to determine the phase locking and stability conditions. The effects of initial partial coherence on the gain of two modes are studied under these conditions. The range of values of the initial partial coherence for which the action of lasing without inversion can take place are shown. Our results show that under certain conditions the two modes can amplify with equal gain below threshold.
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.
The master equation for the field in the two-mode \ensuremath{\Lambda} laser with atoms injected in a superposition of their states is presented, and lasing without population inversion is studied from this vantage. An explicit expression for the steady-state photon distribution is derived under the conditions of detailed balance and no injected coherence. We study the photon statistics, as well as the decay of off-diagonal density-matrix elements and the linewidths of the two laser modes. The effect of an injected atomic coherence on the amplification of light is examined. It is shown that the interference terms in the master equation cancel the absorption terms if the field in each mode is in a coherent state and the conditions for atomic trapping are fulfilled. Numerical calculations demonstrate the buildup of lasing without inversion from the vacuum state of the field.