Hanbury-Brown and Twiss effect without quantum interference in photon counting regime

Usually HBT effect can be interpreted by classical (intensity fluctuation correlation) and quantum (interference of two-photon probability amplitudes) theories properly at the same time. In this manuscript, we report a deliberately designed experiment in which two chaotic light beams has the same intensity fluctuation but mutual-orthogonal polarizations to each other so there will be no interference of two-photon probability amplitudes. Classical and quantum theory give different predictions on if there should be HBT (photon bunching) effect or not in the experiment. The experiment results are used to test the two different predictions. At the end, both the temporal and spatial HBT effects are observed.