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Journal of the Optical Society of America B

Output properties of parametric amplifiers in cavities

Matthew J. Collett, R. Loudon

Published Oct 1, 1987• 71 citations
Publisher

Abstract

The theory of a parametric amplifier in a cavity is given for both the degenerate and the nondegenerate modes of operation. Previous work on the degenerate case is extended to include the effects of a coherent input and to derive the degrees of coherence and photodetection statistics of the output. Analogous calculations are performed for the nondegenerate parametric amplifier, and particular attention is given to the effects of correlations between the light beams formed from the two frequency components. These are contrasted with the analogous effects for the parametric media in free space often used in experimental studies.

DOI
10.1364/josab.4.001525

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The theory of a parametric amplifier in a cavity is given for both the degenerate and the nondegenerate modes of operation. Previous work on the degenerate case is extended to include the effects of a coherent input and to derive the degrees of coherence and photodetection statistics of the output. Analogous calculations are performed for the nondegenerate parametric amplifier, and particular attention is given to the effects of correlations between the light beams formed from the two frequency components. These are contrasted with the analogous effects for the parametric media in free space often used in experimental studies.
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In this paper, we have studied the squeezing and statistical properties of the light produced by a three-level laser whose cavity contains a parametric amplifier, and with the cavity mode driven by coherent light and coupled to a vacuum reservoir. We obtain stochastic differential equations associated with the normal ordering using the pertinent master equation. By making use of the solutions to the resulting differential equations, we calculate the quadrature variances. We also determine the mean and variance of the photon number for the cavity mode by employing the Q function. It is found that the parametric amplifier increases the degree of squeezing, while the driving coherent light does not have any effect on the squeezing. Moreover, the mean photon number increases considerably due to the driving coherent light and the parametric amplifier.
The theory of a two-mode nondegenerate parametric amplifier in a cavity is reformulated in terms of quadrature-phase-amplitude variables. The corrrespondence with a genuine classical stochastic linear process is found (non-negative-definite diffusion matrices) for the case of a cavity device immersed in thermal or ordinary (nonsqueezed) vacuum sources. A special kind of squeezing, i.e., quadrature squeezing [B. L. Schumaker, Phys. Rep. 135, 318 (1986)], is found to be characteristic of the internal steady state for the case of a cavity model subjected to an additional phase-sensitive noise source coupled to one of the two internal modes. Finally, the usual squeezing spectrum of the output field is calculated in both cases by means of an input-output formalism based upon a symmetric ordering scheme of noncommuting operators, well adapted for the quadrature-phase description of the fields involved in the interaction.
In the framework of Hamiltonian formalism the quantum statistical properties of an optical field propagating inside a directional coupler operating by nondegenerate parametric amplification are studied. We investigate the effect of switching between the input modes and the outgoing fields from the coupler. Particular attention is paid to two-mode squeezing, the second-order correlation function, quasiprobability distribution functions, and photon-number distribution. Incident number and coherent states are considered. It has been shown that when one of the modes enters the coupler in the Fock state |1 and the other modes are in vacuum states, the coupler can serve as a generator of a coherent state. Furthermore, regimes for the generation and transmission of squeezed and/or sub-Poissonian light are found.
Applying stochastic differential equations, we study the squeezing and statistical properties of the cavity and output modes of a degenerate three-level laser whose cavity contains a parametric amplifier and coupled to a squeezed vacuum reservoir. We consider the case in which the top and bottom levels of the three-level cascade atoms injected into the cavity are coupled by the pump mode emerging from the parametric amplifier. It turns out that the presence of the squeezed vacuum reservoir and the parametric amplifier contribute considerably to the mean photon number and the degree of squeezing of the cavity and output modes. It appears that almost perfect squeezing can be achieved at steady state and at threshold for a suitable choice of parameters.