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Physical Review A

Phase squeezing in two-photon correlated-spontaneous-emission lasers

S. M. Dutra, L. Davidovich

Published Apr 1, 1994• 3 citations
Publisher

Abstract

We show that in a two-photon correlated-spontaneous-emission laser with a fast-decaying intermediate relay level, it is possible to obtain the same degree of phase squeezing as when all levels have comparable lifetimes, but with a much higher gain coefficient.
DOI
10.1103/physreva.49.2986

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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.
I show that, in the case of both one- and two-photon resonances, a many-cascade two-photon correlated-spontaneous-emission laser can generate light exhibiting phase and photon-number squeezings. Optimizing the mean photon number in the cavity with respect to a phase factor sin[1/2(n-1)\ensuremath{\theta}]/sin(1/2\ensuremath{\theta}), we find that the maximized mean photon number and its squeezing increase with increasing the top populations ${\mathrm{\ensuremath{\rho}}}_{\mathit{n}\mathit{n}}^{\mathit{a}}$ of the active atoms. However, the photon-number squeezing may decrease, increase, or not change when increasing the number n-1 of lower, almost degenerate atomic levels, depending on the relative phase \ensuremath{\theta} of lower atomic states determined by the optimization conditions. The phase squeezing has a maximum value with increasing n-1 and ${\mathrm{\ensuremath{\rho}}}_{\mathit{n}\mathit{n}}^{\mathit{a}}$.