Characterization of Two-Particle Interference by Complementarity

TL;DR

This paper develops a duality relation linking particle distinguishability and two-particle interference visibility, unifying the understanding of HOM and HBT effects as manifestations of a single quantum interference phenomenon.

Contribution

It introduces a quantitative duality relation for two-particle interference, establishing a bound on interference sharpness based on particle distinguishability, and unifies HOM and HBT effects.

Findings

Derived a duality relation between distinguishability and interference visibility.

Showed that particle internal states limit two-particle interference sharpness.

Concluded HOM and HBT effects are fundamentally equivalent phenomena.

Abstract

Bohr's Complementarity Principle is quantitatively formulated in terms of the distinguishability of various paths a quanton can take, and the measure of the interference it produces. This phenomenon results from the interference of single-quanton amplitudes for various paths. The distinguishability of paths puts a bound on the sharpness of the interference the quanton can produce. However there exist other kinds of quantum phenomena where interference of two-particle amplitudes results in a two-particle interference, if the particles are indistinguishable. The Hong-Ou-Mandel (HOM) effect and the Hanbury-Brown-Twiss (HBT) effect are two well known examples. However, two-particle interference is not as easy to define as its single particle counterpart, and the realization that it involves interference of two-particle amplitudes, came much later. In this work, a duality relation, between the particle distinguishability and the visibility of two-particle interference, is derived. The distinguishability of the two particles, arising from some internal degree of freedom, puts a bound on the sharpness of the two-particle interference they can produce, in a HOM or HBT kind of experiment. It is argued that the existence of this kind of complementarity can be used to characterize two-particle interference, which in turn leads one to the conclusion that the HOM and the HBT effects are equivalent in essence, and may be treated as a single two-particle interference phenonmenon.