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Acta Physica Sinica

FULL QUANTUM THEORY OF OPTICALLY PUMPED THREE-LEVEL LASER

Guo Guang-Can, 中国科学技术大学物理系

Published Jan 1, 1984• 0 citations
Publisher

Abstract

The Langevin quantum theory has been used to treat the optically pumped three-level laser system. We derive an equation of motion for laser field in the type of Van der Pol equation when the photon number of the laser field is not too high. It includes not only both incoherent and coherent pumping, but also both strong and weak optical pumping. If an average over reservoir is taken, the equation will give all the semi-classical results. Our results show that the laser gain comes from two basic processes, i.e., a two-photon process and a two-step process. When the pumping strength is larger than some value, the dynamic Stark effect will appear. The laser linewidth is mainly contributed by the thermal noise, the vaecum fluctuation, the spontaneous emissions between the laser levels and the spontaneous Raman scattering.

DOI
10.7498/aps.33.1661

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The Langevin quantum theory has been used to treat the optically pumped three-level laser system. We derive an equation of motion for laser field in the type of Van der Pol equation when the photon number of the laser field is not too high. It includes not only both incoherent and coherent pumping, but also both strong and weak optical pumping. If an average over reservoir is taken, the equation will give all the semi-classical results. Our results show that the laser gain comes from two basic processes, i.e., a two-photon process and a two-step process. When the pumping strength is larger than some value, the dynamic Stark effect will appear. The laser linewidth is mainly contributed by the thermal noise, the vaecum fluctuation, the spontaneous emissions between the laser levels and the spontaneous Raman scattering.
The Langevin quantum theory has been used to treat the optically pumped three-level laser system. We derive an equation of motion for laser field in a type of Van der Pol equation when the photon number of the laser field is not too high. It includes not only both incoherent and coherent pumping, but also both strong and weak optical pumping. If an average over the reservoir is taken, the equation will give all the semi-classical results. Our results show that the laser gain comes from two basic processes, i.e., a two-photon process and a two-step process. When the pumping strength is larger than a certain value, the dynamic Stark effect will appear. The laser linewidth is mainly contributed by the thermal noise, the vacuum fluctuation, the spontaneous emissions between the laser levels and the spontaneous Raman scattering.
In this paper, a two-photon laser by optical pumping, with two-photon losses, is studied by means of the Langevinian theory, the langevinian equation is obtained. Then the steady-state average photon number, the frequency pulling, the linewidth and the dynamical Stark effect are obtained. From the analysis of the gain, it is shown that, for the incoherent pumping, only the two-step process of single-and two-photon gives contribution. And for the coherent pumping, in addition, the one-step process of single and two-photon also contributes. And two processes are confined by the negative-feedback and saturation. The linewidth is independent of the steady state average photon number.
In this paper we have studied the statistical and squeezing properties of the cavity light generated by a three-level laser. In this quantum optical system, N three-level atoms available in an open cavity, coupled to a two-mode vacuum reservoir, are pumped to the top level by means of electron bombardment at constant rate. We have considered the case in which the three-level atoms and the cavity modes interact with the two-mode vacuum reservoir. Applying the solutions of the equations of evolution for the expectation values of the atomic operators and the quantum Langevin equations for the cavity mode operators, we have calculated the mean and variance of the photon number as well as the quadrature squeezing for the cavity light. In addition, we have shown that the presence of the spontaneous emission process leads to a decrease in the mean and variance of the photon number. We have observed that the two-mode cavity light is in a squeezed state and the squeezing occurs in the minus quadrature. In addition, we have found that the effect of the vacuum reservoir noise is to increase the photon-number variance and to decrease the quadrature squeezing of the cavity light. However, the vacuum reservoir noise does not have any effect on the mean photon number. Moreover, the maximum quadrature squeezing of the light generated by the laser, operating far below threshold, is found to be 37.5% below the vacuum-state level. In addition, our result indicates that the quadrature squeezing is greater for γ=0 than that for γ=0.4 for 0.01 < ra < 0.35 and is smaller for γ=0 than that for γ=0.4 for 0.35 < ra < 1.
We consider a laser model consisting of a single four-level or three-level atom, an optical cavity, and an incoherent pump. Results for photon statistics for varying pump levels are obtained using a quantum trajectory algorithm. In particular, we calculate the mean photon number, Fano factor (which is the variance over the mean). We examine that the behavior of the single-atom device as \ensuremath{\beta}, the fraction of spontaneous emission into the lasing mode, is varied. Typical values considered for \ensuremath{\beta} are $0.01<\ensuremath{\beta}<1.0.$ We find that for large enough \ensuremath{\beta}, lasing action, with properties similar to those predicted by semiclassical theories that factorize atom-field correlations and use a small-noise approximation, can occur. Squeezing can occur as \ensuremath{\beta} is increased. There is no evidence of a sharp phase transition from weakly excited thermal light to coherent light at a particular pump power. This is consistent with work on many-atom lasers with \ensuremath{\beta} values in the range considered here. As \ensuremath{\beta} is increased, the output goes from quasithermal light to coherent and finally to squeezed light, progressing into a fully quantum-mechanical regime. We also consider the effects of cavity damping and spontaneous emission rates on these results.
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.