Comparative study of photon antibunching on non-stationary fields

Two standard criteria of the photon antibunching for non-stationary fields are compared. A new criterion, obtained by direct application of the Cauchy-Schwarz inequality, is proposed. All three definitions, based on the two-time correlation functions, are equivalent for stationary fields. However, the photon antibunching in the non-stationary regime is demonstrated to be not uniquely defined, since different criteria can lead to self-contradictory predictions. As an example, photon correlations of the signal mode in the parametric frequency converter are analysed analytically.