Theory of cross-correlation of signal and idler in parametric oscillators

Matthias Scholz, Lars Koch, Oliver J. Benson

Sotirios Baskoutas, A. D. Jannussis, R. Mignani

T.A.B. Kennedy, S. Swain

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.

Damian T. Pope, P. D. Drummond, W. J. Munro

P. N. Keating

The problem of the threshold and growth of parametric oscillation in a lossy optical cavity is treated quantum theoretically. It is shown that during the growth of oscillation each of the generated modes is statistically as chaotic as those observed previously in the lossless case, and is so chaotic that the additional uncertainty introduced by the loss processes has no further effect on the single-mode photon distributions. However, there is considerable cross correlation between the idler and signal modes. The cross correlation in the numbers of idler and signal quanta is essentially complete for large numbers, but is shown to be reduced when the numbers are smaller, because of noise due to loss. Correlations in phase are also investigated and it is shown that, under certain statistical conditions necessary for phase to be a relevant concept, the phase correlation is also essentially complete.

Robert Graham

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.