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Physical Review Letters

General Correlation Identity for Parametric Processes

Robert Graham

Published Jan 9, 1984• 57 citations
Publisher

Abstract

A new connection between autocorrelation and cross correlation functions of the intensities of signal and idler in parametric oscillators is derived, with the same origin and generality as the Manley-Rowe relations and with inserting experimental implications in the quantum domain.
DOI
10.1103/physrevlett.52.117

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Using the quantum theory of a non-degenerate parametric amplifier, we discuss the phase correlations between signal and idler modes well above threshold. Particular attention is paid to the influence which fluctuation of the driving laser has on these correlations. We point out that the signal and idler mode phase correlation may be tuned by control of the driving laser field intensity and linewidth. For coherent driving, the mode phases are negatively cross-correlated. We stress the qualitative importance of these mode correlations for a class of two-photon resonant excitation experiments in atoms. In particular, the non-degenerate parametric oscillator represents a concrete model of a source with negatively cross-correlated phase fluctuations.
We develop the quantum theory of a driven, damped intracavity parametric oscillator in the case of nondegenerate signal and idler modes. An analysis of the results of different types of local-oscillator measurements on the outgoing modes is presented. The frequency-domain squeezing is calculated below threshold including the effect of detunings and nonequal decay rates. We also calculate a nonclassical correlation in the quadrature amplitudes of the output beams. The existence of an Einstein-Podolsky-Rosen paradox is demonstrated through violations of the inferred Heisenberg uncertainty principle at causally unrelated locations in the output field. This provides a way of maintaining the commutation relations of the measured operators in the exact form envisaged originally by Einstein, Podolsky, and Rosen.