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Acta Physica Sinica

THE OPERATION IN THE STEADY STATE AND SQUEEZING OF QUANTUM NOISE IN TWO-MODE TWO-PHOTON CORRELATED-SPONTANEOUS-EMISSION LASERS

Xiangming Hu, PENG JIN-SHENG, (1)华中师范大学物理系; (2)华中师范大学应用物理研究所

Published Jan 1, 1997• 3 citations
Publisher

Abstract

Operation in the steady state and squeezing of quantum noise in two-mode two-photon correlated-spontaneous-emission lasers(CEL) are studied via nonliner quantum theory.It is shown that the two-mode two-photon CEL exhibits lasing without inversion and two-mode hysteresis even without triggering.The features of squeezing of quantum noise in the relative amplitude and the average phase are given.

DOI
10.7498/aps.46.255

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Operation in the steady state and squeezing of quantum noise in two-mode two-photon correlated-spontaneous-emission lasers(CEL) are studied via nonliner quantum theory.It is shown that the two-mode two-photon CEL exhibits lasing without inversion and two-mode hysteresis even without triggering.The features of squeezing of quantum noise in the relative amplitude and the average phase are given.
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.
An analytical steady-state distribution for the phase difference \ensuremath{\psi} in a correlated spontaneous-emission laser (CEL) is derived based on the amplitude and phase equations of a CEL. This distribution is shown to be an excellent approximation to that obtained from a numerical simulation of the complete set of CEL equations. In particular, the effects of amplitude noise on CEL operation are considered and it is shown that fluctuations in the relative amplitude are also noise quenched.