Hong-Ou-Mandel interference on a lattice: symmetries and interactions

TL;DR

This paper explores Hong-Ou-Mandel interference on a lattice, revealing how symmetries and interactions influence two-particle quantum interference, with implications for quantum simulation and photonic systems.

Contribution

It introduces a symmetry-based reformulation of two-particle interference on a lattice and extends the analysis to interacting particles, supported by analytical and numerical comparisons.

Findings

Symmetries enable reformulation of interference as wave interference.

Interactions modify the bunching probability in predictable ways.

Analytical predictions align well with numerical simulations.

Abstract

We describe the Hong-Ou-Mandel interference of two identical particles evolving on a one-dimensional tight-binding lattice where a potential barrier plays the role of a beam splitter. Careful consideration of the symmetries underlying the two-particle interference effect allows us to reformulate the problem in terms of ordinary wave interference in a Michelson interferometer. This approach is easily generalized to the case where the particles interact, and we compare the resulting analytical predictions for the bunching probability to numerical simulations of the two-particle dynamics.