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Communications in Theoretical Physics

Path Integral Formalism for Nondegenerate Parametric Amplifiers in Entangled State Representation

Fan Hong‐Yi, Chao Li, Qiuyu Liu, Alfred Wünsche

Published Jun 1, 2005• 0 citations
Publisher

Abstract

We establish the path integral formalism for nondegenerate parametric amplifiers in the entangled state representations. Its advantage in obtaining the energy level gap of this system is analyzed.
DOI
10.1088/0253-6102/43/6/008

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The quantum theory of the degenerate parametric amplifier is usually treated in the parametric approximation where the pump field is treated classically. In this paper we present a fully quantized theory of this nonlinear optical device using a path-integral approach. A perturbation series, the first term of which corresponds to the parametric approximation, is employed to evaluate explicitly the coherent-state propagator. The question of the validity of the parametric approximation is considered and the conditions under which this approximation is justified are elucidated. Finally, certain correlation functions for the signal-mode operators are calculated that are needed to study squeezed states. It is shown that the quantum nature of the pump field tends to decrease the squeezing.