Quantum Theory of Two-Photon Wavepacket Interference in a Beam Splitter

TL;DR

This paper develops a comprehensive quantum theoretical framework for understanding two-photon wavepacket interference in beam splitters, highlighting the role of spectral symmetry and entanglement in interference phenomena.

Contribution

It introduces a unified Schrödinger picture theory that explicitly links spectral symmetry and entanglement to interference behavior in two-photon states.

Findings

Symmetry of the spectral amplitude spectrum determines interference type.

Entanglement can be inferred from interference patterns.

Anti-symmetric spectra lead to perfect transparency in 50/50 beam splitters.

Abstract

We study a general theory on the interference of a two-photon wavepacket in a beam splitter. The theory is carried out in the Schr\"{o}dinger picture so that the quantum nature of the two-photon interference is explicitly presented. We find that the topological symmetry of the probability-amplitude spectrum of the two-photon wavepacket dominates the manners of two-photon interference which are distinguished according to increasing and decreasing the coincidence probability for the absence of interference. However, two-photon entanglement can be witnessed by the interference manner. We demonstrate the necessary and sufficient conditions for the perfect two-photon interference. For a two-photon entangled state with an anti-symmetric spectrum, it passes a 50/50 beam splitter with the perfect transparency. The theory contributes an unified understanding to a variety of the two-photon interference effects.