Theory of the Two-Photon Laser: Cross-Correlation and Laser Thresholds

Abstract

The two—photon laser has been investigated for some time. It was an early candidate for the production of non-classical light and it is an interesting example of a phase transition in a system operating far from equilibrium. Recently, it has attracted great interest due to its experimental realisation as a micromaser and the prediction of strong squeezing under conditions of coherent pumping. Also, we have calculated the cross-correlation coefficient in the non-degenerate case. This quantity determines the extent to which the fluctuations in the two output modes are correlated — i.e. the extent to which the noise contributions in an appropriate two—photon experiment tend to cancel. We found that when the laser was operating well above threshold, near critical cross-correlation (i.e. near perfect noise suppression) was obtained. In common with most authors, we assumed an effective hamiltonian, in which the interaction is quadratic in the photon annihilation and creation operators.