Photon statistics of a cavity Q.E.D. laser: A comment on the laser phase-transition analogy

Perry Rice and H. J. Carmichael (U. Oregon) - Physical Review A 50, 4318 (1994)

We develop a birth-death model for a cavity Q.E.D. laser and analyze the dependence of laser threshold on the fraction, b, of spontaneous emission directed into the laser mode. We define threshold in terms of the ratio of the photon number variance to the photon number mean. We emphasize the role of b as a parameter characterizing the system size'' and show that the concept of laser threshold is well-defined in the thermodynamic'' limit, b->0, while an ideal cavity Q.E.D. laser operates far outside this limit, essentially as a one-particle device. Thus, in contrast to a conventional laser, the ideal cavity Q.E.D. laser is not a threshold device and the standard phase transition analogy does not apply. We discuss how this difference influences the noise properties of the device.