Detecting single photons is not always necessary to evidence interference of photon probability amplitudes

Abstract

Subtracting accidental coincidences is a common practice in quantum optics experiments. For zero mean Gaussian states, such as a squeezed vacuum, we show that if one removes accidental coincidences, the measurement results are quantitatively the same for both photon coincidences at very low flux and intensity covariances. Consequently, pure quantum effects at the photon level, like interference of photon wave functions or photon bunching, are reproduced in the correlation of fluctuations of macroscopic beams issued from spontaneous down-conversion. This is true both in experiment if the detection resolution is smaller than the coherence cell (size of the mode) and in stochastic simulations based on sampling the Wigner function. We also discuss the limitations of this correspondence, such as Bell inequalities (for which one cannot subtract accidental coincidences), highly multimode situations such as quantum imaging, and higher-order correlations.