The role of four-photon bunching in fourth-order correlation of thermal light in the photon counting regime

Abstract

We theoretically discuss the fourth-order spatial correlation and four-photon bunching properties of pseudo-thermal light in the photon counting regime. It is found that four-photon bunching has the maximum correlation. If they all come from the same spatial cell in phase space, then fourth-order spatial correlation can be decomposed into not only auto-correlation and cross-correlation of second- and third- order, but the pure correlations among four photons as well, which is just the four-photon bunching. In addition, we also show that the contribution from four-photon bunching leads to the enhancement of the resolution and visibility in fourth-order ghost imaging. More precisely, the contribution from four-photon bunching to fourth-order spatial correlation is equal to the sum of all contributions from two-photon bunching and three-photon bunching when three reference detectors are scanned along the identical orientation and speed. On the other hand, the sum of all contributions from two-photon bunching and three-photon bunching to fourth-order spatial correlation will exceed the contribution from four-photon bunching, when two of three reference detectors are scanned in the same orientation and the speed of one reference detector is twice that of the other; meanwhile, the other two reference detectors are moved with opposite orientation but identical speed.