Two-Photon Counting Statistics for Laser and Chaotic Radiation

The relation between the two-quantum photocounting distribution p(n, T) and the intensity fluctuations of the radiation incident on the detector is obtained and compared with the one-quantum results. The actual statistics are evaluated for several cases of interest, including a chaotic source, an amplitude-stabilized wave, and the output of a single-mode laser (Van der Pol oscillator). The two-quantum count rate 〈n〉/T is found to depend on the mean-square intensity of the radiation, in contrast to the one-quantum count rate which is proportional to the mean intensity. The effects of photon correlations in the radiation beam become apparent since the two-quantum distributions manifest a distinctly more positive second derivative than the corresponding one-quantum distributions. Both the low-and the high-count probabilities are therefore increased at the expense of counts near the mean. The quantum-theoretical treatment is found to be equivalent to the semiclassical treatment for density operators possessing a positive-definite weight function in the P-representation. Some possible experiments to verify the theory are discussed and shown to be feasible.