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Europhysics Letters (EPL)

Two-Photon Population Inversion by Squeezed Light in a Fabry-Perot Microcavity

Z. Ficek, P. D. Drummond

Published Nov 20, 1993• 28 citations
Publisher

Abstract

A three-level atom interacting with a squeezed-vacuum field is driven into a coherent superposition of the ground state and upper excited state, which can lead to a two-photon population inversion. We describe a possible technique for testing this prediction, using a microcavity Fabry-Perot interferometer. This could provide a useful technique for pumping a two-photon laser.

DOI
10.1209/0295-5075/24/6/005

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A three-level atom interacting with a squeezed-vacuum field is driven into a coherent superposition of the ground state and upper excited state, which can lead to a two-photon population inversion. We describe a possible technique for testing this prediction, using a microcavity Fabry-Perot interferometer. This could provide a useful technique for pumping a two-photon laser.
It has been suggested that phased atomic decay in a squeezed vacuum could be detected in the fluorescence spectrum emitted from a driven two-level atom in a cavity. Recently, the existence of other very distinctive features in the fluorescence spectra arising from the nonclassical features of the squeezed vacuum has been reported. In this paper, we investigate the possibility of experimental observation of these spectra. The main obstacle to the experimentalist is ensuring an effective squeezed-vacuum-atom coupling. To overcome this problem we propose the use of a Fabry-P\'erot microcavity. The analysis involves a consideration of the three-dimensional nature of the electromagnetic field, and the possibility of a mismatch between the squeezed and cavity modes. The problem of squeezing bandwidths is also addressed. We show that under experimentally realistic circumstances many of the spectral anomalies predicted in free space also occur in this environment. In addition, we report large population inversions in the dressed states of the two-level atom.
We propose a theory that makes it possible to examine both laser and micromaser two-photon light generation. The theory is based on the Lamb-Scully model, in which two-level atoms have initial coherence. Such an initial state allows for light generation involving atoms without inversion or even atoms with negative population inversion in the transition. We analyze the conditions needed for the emergence of squeezed states of the light field. We also show that the photon statistics in lasing is always classical but that there appears a state of the field squeezed in the phase with maximum photodetection shot-noise suppression. For a micromaser we find a regime where sub-Poisson light with a shot-noise suppression level of 60% is realized in an inversionless transition. In another regime, a squeezed state that produces 75% suppression of noise can be generated.
A quantum theory of two-photon correlated-spontaneous-emission lasers (CEL's) is developed, starting from the exact atom-field interaction Hamiltonian for cascade three-level atoms interacting with a single-mode radiation field. We consider the situation where the active atoms are prepared initially in a coherent superposition of three atomic levels and derive a master equation for the field-density operator by using a quantum theory for coherently pumped lasers. The master equation is transformed into a Fokker-Planck equation for the antinormal-ordering Q function. The drift coefficients of the Fokker-Planck equation enable us to study the steady-state operation of the two-photon CEL's analytically. We have studied both resonant two-photon CEL for which there is no threshold, and off-resonant two-photon CEL for which there exists a threshold. In both cases the initial atomic coherences provide phase locking, and squeezing in the phase quadrature of the field is found. The off-resonant two-photon CEL can build up from a vacuum when its linear gain is larger than the cavity loss (even without population inversion). Maximum squeezing is found in the no-population-inversion region with the laser intensities far below saturation in both cases, which are more than 90% for the resonant two-photon CEL and nearly 50% for the off-resonant one. Approximate steady-state Q functions are obtained for the resonant two-photon CEL and, in certain circumstances, for the off-resonant one.
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.