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Journal of the Optical Society of America B

Effect of fluctuation coupling on the spectrum of squeezing

Ning Lu

Published May 1, 1991• 0 citations
Publisher

Abstract

Using a two-photon correlated-spontaneous-emission laser (CEL) as an example, I show that a non-Lorentzian spectrum of squeezing is the result of fluctuation coupling and that the narrow peak at the center of the spectrum is a reflection of the fluctuations in the conjugate quadrature. More than 90% extracavity phase squeezing can be generated by the two-photon CEL near threshold with large one-photon detunings.

DOI
10.1364/josab.8.001135

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Using a two-photon correlated-spontaneous-emission laser (CEL) as an example, I show that a non-Lorentzian spectrum of squeezing is the result of fluctuation coupling and that the narrow peak at the center of the spectrum is a reflection of the fluctuations in the conjugate quadrature. More than 90% extracavity phase squeezing can be generated by the two-photon CEL near threshold with large one-photon detunings.
In the preceding paper we developed a formalism based on the true modes of the universe containing a leaky cavity to analyze the relationship of quantum noise inside that cavity to that outside. We illustrate this formalism here by studying several active systems. We analyze both an ordinary laser and a laser operating in the phase-locked regime. We calculate the extracavity quadrature variances for the phase-locked laser and find that the spectrum of noise reduction in the squeezed quadrature is Lorentzian. Our formalism is also applied to a two-photon correlated-spontaneous-emission laser. We find the familiar result that with 50% squeezing in the phase quadrature of the field inside the cavity, one has nearly 100% phase squeezing outside the cavity. However, under different conditions the phase quadrature of the intracavity field is nearly perfectly squeezed, but the extracavity field shows almost no squeezing in its phase quadrature. We also analyze the effect of finiteness of measurement time on the extracavity quadrature variances.
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.