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Communications in Theoretical Physics

Nonlinear Theory of Many Effective Two-Photon Correlated-Spontaneous-Emission Lasers

Hongbin Huang

Published Sep 15, 1996• 0 citations
Publisher

Abstract

In this paper, we transform the nonlinear density matrix equation for many effective two-photon correlated-spontaneous-emission laser field obtained recently by the author to the Fokker-Planck equation, and then discuss the inffluence of atomic coherences and the number of lower almost degenerate atomic levels on the lasing without inversion and noise reduction or phase squeezing of the field.

DOI
10.1088/0253-6102/26/2/129

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Communications in Theoretical Physics•Feb 14, 1996•0 citations
In this paper, we transform the nonlinear density matrix equation for many effective two-photon correlated-spontaneous-emission laser field obtained recently by the author to the Fokker-Planck equation, and then discuss the inffluence of atomic coherences and the number of lower almost degenerate atomic levels on the lasing without inversion and noise reduction or phase squeezing of the field.
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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.
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Both stationary and time-dependent regimes of operation, instabilities, and phase squeezing are investigated in the off-resonant two-photon correlated-spontaneous-emission laser by numerical calculation. Initial atomic coherence plays an essential role in lasing without population inversion, phase locking, and phase noise squeezing in the system. Under certain conditions, in the inverted and noninverted regimes alike, the output intensity exhibits bistable behaviors against the initial atomic coherence. Depending on the parameters, the whole or a portion of the upper or lower branch gives stable operations. In the inverted regime, even tristable behavior can be found in a narrow range of parameters. The field evolution and dynamics are studied. Furthermore, phase noise reduction near bistable areas is also investigated. In addition to the lower branch, where from previous studies, it has been known to exist, phase squeezing is also found on the upper branch both with and without population inversion, thus generating a bright source of phase noise squeezed light.
We show in this paper that phase fluctuations of active atoms in many two-photon correlated spontaneous-emission lasers will reduce field squeezings and brightness of the squeezed light. But, under certain conditions of laser operation, the fluctuations of atomic phases between lower almost degenerate atomic levels could increase the squeezings and the brightness. We also show that, even for large phase fluctuations of the active atoms, almost perfect field squeezings and substantial brightness of the squeezed light can be obtained.