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

Z. C. Wang, Hermann Haken

S. Swain

We consider the theory of the two-photon laser using the Scully–Lamb theory developed for ordinary single-photon lasers, concentrating on the calculation of the linewidths and the cross-correlation coefficient. In a previous publication we have shown that the quantum-mechanical noise in the modes of a two-mode laser may be highly correlated. Here we show that the same situation appertains to the two-photon laser, that is the two modes are strongly positively cross-correlated when the laser is operating well above threshold. The two-photon laser has the advantage of tunability over the two-mode or quantum-beat laser. The point of using modes whose noise properties are strongly correlated is that in an appropriate two-photon experiment the noises may effectively ‘cancel out’ leaving a very low noise signal. We present a brief development of the two-photon laser theory and show the connection between our work and that of other approaches.

Z. C. Wang, Hermann Haken

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.

Dai Zu-cheng, Xiang You-Lin, Mei Dong-Cheng

An inhomogeneously broadened two-mode laser system with cross-correlations between the real and imaginary parts of quantum noise is considered. The Fokker–Planck equation of the system is derived by the phase-locking method. The steady-state probability distribution, the mean light intensity, the normalization autocorrelation function, and cross correlation function are calculated. The results indicate that: (i) The cross-correlation between the real and imaginary parts of quantum noise can cause the stationary probability distribution from one peak structure to two extrema structure when the laser system is operated above threshold; (ii) The cross-correlation between the real and imaginary parts of quantum noise enhance the light intensity fluctuation and decrease the laser output when the laser system is operated below or near threshold; (iii) The effect of the cross-correlation between the real and imaginary parts of quantum noise is very weak on the stationary properties when the laser system is operated far above threshold.

Wang Zhi Cheng, Hermann Haken