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Physical Review A

Bistability and intensity-noise quenching in the single-atom two-photon laser without inversion

Yi Mu

Published Jun 1, 1994• 0 citations
Publisher

Abstract

Based on a master equation method, a two-photon laser is modeled as a single noninverted three-level atom interacting via a two-photon transition with a single resonant-cavity field mode. The laser exhibits the bistability switching between vacuum and lasing states in the high pump power without injected signal. Such a feature is accompanied by intensity-noise quenching and lasing without inversion. The bistability is forbidden in a similar ordinary laser---a Raman laser.

DOI
10.1103/physreva.49.5142

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Based on a master equation method, a two-photon laser is modeled as a single noninverted three-level atom interacting via a two-photon transition with a single resonant-cavity field mode. The laser exhibits the bistability switching between vacuum and lasing states in the high pump power without injected signal. Such a feature is accompanied by intensity-noise quenching and lasing without inversion. The bistability is forbidden in a similar ordinary laser---a Raman laser.
A two-photon laser is modeled as NNN two-level atoms interacting via a two-photon transition with a single resonant-cavity field mode. The quadratic form of this interaction makes such a system a candidate to exhibit reduced quantum fluctuations (squeezing) in one quadrature of the output field. A Fokker-Planck equation containing all leading quantum noise terms is derived following the method of Haken. A linearized fluctuation analysis reveals that there is no squeezing in a two-photon laser with injected signal. A small amount of squeezing may be present in two-photon optical bistability. Our calculations confirm the results of Lugiato and Strini, who adopted a factorization of moment equations.
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.
The quantum mechanical master equation for a single two-level atom in a single-mode optical cavity is numerically solved in both the quantum and the semiclassical limits. The quantum limit of few cavity photons shows semiclassically forbidden behaviour such as steady state two-level population inversion. Qualitatively new fluorescent spectra, having sidebands broadened by the cavity interaction, also occur. The quantum theory of the single-atom laser with injected signal is presented. At the interface between its quantum and semiclassical dynamics we elucidate the signature of semiclassical limit cycles.
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.
We develop a nonlinear theory of a two-photon correlated-spontaneous-emission laser (CEL) by using an effective interaction Hamiltonian for a two-level system coupled by a two-photon transition. Assuming that the active atoms are prepared initially in a coherent superposition of two atomic levels involved in the two-photon transition, we derive a master equation for the field-density operator by using our quantum theory for coherently pumped lasers. The steady-state properties of the two-photon CEL are studied by converting the field master equation into a Fokker-Planck equation for the antinormal-ordering Q representation of the field-density operator. Because of the injected atomic coherence, the drift and diffusion coefficients become phase sensitive. This leads to laser phase locking and an extra two-photon CEL gain. The laser field can build up from a vacuum in the no-population-inversion region, in contrast to an ordinary two-photon laser for which triggering is needed. We find an approximate steady-state solution of the Q representation for the laser field, which consists of two identical peaks of elliptical type. We calculate the phase variance and, for any given mean photon number, obtain the minimum variance in the phase quadrature as a function of the initial atomic variables. Squeezing of the quantum noise in the phase quadrature is found and it exhibits the following features: (1) it is possible only when the laser intensity is smaller than a certain value; (2) it becomes most significant for small mean photon number, which is achievable in the no-population-inversion region; and (3) a maximum of 50% squeezing can be asymptotically approached in the small laser intensity limit. As a by-product we also study the ordinary two-photon laser and find, e.g., photon-number variance and laser linewidth.