Two-Photon Correlations in Atomic Transitions

Abstract

A general formula is derived for two-photon coincidence rates. The result obtained is a function of the orientation of linear polarizers, of the solid angles subtended, and of the relative position of the photon detectors. It applies to both cascade emissions and resonance flourescence when the transitions are of electric dipole type. Allowance is made for anisotropic initial-state populations. It is shown that a single parameter describes the atomic transition when the initial states are isotropically populated. This parameter is found to have a particularly simple form, even when the nuclear spin is nonzero. It is the product of two Racah coefficients and an $E$ coefficient defined here. Tables of the required Racah and $E$ coefficients are provided so that this parameter can be easily determined when the states in the transitions have $J$ values 0, 1, 2, 3, 4, 1/2, 3/2, 5/2, 7/2, or 9/2, and when the nuclear spin is 0, 1, 1/2, 3/2, 5/2, 7/2, or 9/2. Experiments to test hidden-variable theories which are possible in view of these results are discussed. Experiments to determine the effective quantum efficiency of photon detectors using these results are described.