Quantum theory of two-photon wavepacket interference in a beamsplitter

A general theory is derived for the interference of a two-photon wavepacket in a beamsplitter. The theory is presented in the Schrodinger picture so that the quantum nature of the two-photon interference is explicitly revealed. We find that the topological symmetry of the probability-amplitude spectrum of the two-photon wavepacket dominates the nature of the two-photon interference, which may be distinguished by the increase or decrease of the coincidence probability in the absence of interference. However, two-photon entanglement can be identified by the nature of the interference. We demonstrate the necessary and sufficient conditions for perfect two-photon interference. It is shown that a two-photon entangled state with an anti-symmetric spectrum passes through a 50/50 beamsplitter with perfect transparency. The theory provides us with a unified understanding of the various two-photon interference effects.