Temporal Distinguishability of an N-Photon State and Its Characterization by Quantum Interference

TL;DR

This paper develops a multi-mode model to analyze the temporal distinguishability of N-photon states, linking it to quantum interference visibility and providing a quantitative measure of photon indistinguishability.

Contribution

It introduces a comprehensive model connecting photon temporal distribution, indistinguishability, and interference visibility, extending understanding of multi-photon quantum interference.

Findings

Maximum interference visibility occurs with indistinguishable photons.

Visibility decreases as photons become temporally distinguishable.

The model offers a measurable way to quantify photon indistinguishability.

Abstract

We present a multi-mode model to describe an arbitrary N-photon state with a wide spectral range and some arbitrary temporal distribution. In general, some of the $N$ photons are spread out in time while other may overlap and become indistinguishable. From this model, we find that the temporal (in)distinguishability of photons is related to the exchange symmetry of the multi-photon wave function. We find that simple multi-photon detection scheme gives rise to a more general photon bunching effect with the famous two-photon effect as a special case. We then send this N-photon state into a recently discovered multi-photon interference scheme. We calculate the visibility of the multi-photon interference scheme and find that it is related to the temporal distinguishability of the $N$ photons. Maximum visibility of one is achieved for the indistinguishable N-photon state whereas the visibility degrades when some of the photons are separated and become distinguishable. Thus we can identify an experimentally measurable quantity that may quantitatively define the degree of indistinguishability of an N-photon state. This presents a quantitative demonstration of the complementary principle of quantum interference.