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Physical Review A

Two-mode Λ laser with atoms injected in a superposition of their states

Fam Le Kien, Georg M. Meyer, Ulrich W. Rathe, Marlan O. Scully, HERBERT WALTHER, Shi-Yao Zhu

Published Oct 1, 1995• 7 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.52.3279

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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.
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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.
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.
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We discuss a generalized version of the Scully-Lamb laser master equation for a collection of driven multilevel atoms in a lambda-type configuration. We are especially interested in the effect of the external driving field on the laser process with or without a population inversion between the lasing levels. We provide an exact solution of the photon probability distribution in steady state and discuss regimes of operation that can lead to sub-Poissonian statistics, as measured by the ratio between the variance and the average photon number. We solve the field master equation in the transient regime and analyze the effects of the external driving field on the linewidth of the emitted radiation. The largest reduction of the photon variance relative to the mean number corresponds to the injection into the cavity of atoms prepared in the nonlasing level. Injection of atoms in an incoherent mixture of the three energy states normally leads to super-Poissonian statistics.
The LWI operation condition for an open Λ-type three level atomic system is obtained by solving the steady-state density-matrix equation with the system being driven by a strong coherent field while the inherent pumping rate and decay rate being arbitrary.It is shown that the inversions of inherent pumping rate and spontaneous decay rate replace the inversion of population,and together help to realize lasing without population inversion.Furthermore,the LWI can be realized if just either one of the two inversions is fulfilled.A schrodinger equation of three-level atomic system with appropriate conditions is analytically solved to explain the quantum interference process that leads to LWI.