Analytic expressions for conditional and unconditional wait-time distributions for the n-th photo-detection are derived for the light from a degenerate parametric oscillator and subthreshold laser, in the small photon number regime where quantum effects dominate.
Statistics of photons emitted by a nondegenerate parametric oscillator (NDPO) operating below threshold are discussed. Analytical expressions for the generating function are obtained when two nondegenerate modes of the NDPO are mixed on a photocathode or when the intensities of the two modes are added. From the generating function, photon-counting distributions and waiting-time distributions as measured by a detector placed outside the cavity are derived. Similarities and differences between the distributions for the NDPO, the degenerate parametric oscillator, degenerate four-wave mixing, nondegenerate four-wave mixing, and thermal light are also discussed.
Nonclassical light beams generated by the degenerate optical parametric oscillator operating below threshold are analyzed in terms of photoelectron-counting sequences. The positive-P representation is used to calculate the generating function for photoelectron statistics in a closed form. This generating function is used to derive expressions for the photoelectron-counting and waiting-time distributions. The dependence of these distributions on mean photon number inside the cavity and efficiency of detection is studied. The relationship between photoelectron-counting sequence and the photon emission sequence is used to present a simple physical picture of light beams produced by the degenerate parametric oscillator.
Wait-time distributions for the nth photodetection at a detector illuminated by a stationary light beam are studied. Both unconditional measurements, initiated at an arbitrary instant, and conditional measurements, initiated upon a photodetection, are considered. Simple analytic expressions are presented for several classical and quantum sources of light and are used to quantify and compare photon sequences generated by them. These distributions can be measured in photon-counting experiments and are useful in characterizing and generating photon sequences with prescribed statistics. The effects of nonunit detection efficiency are also discussed, and curves are presented to illustrate the behavior.