Photon distribution at the output of a beam splitter for imbalanced input states

TL;DR

This paper derives an analytical formula for photon distribution at a beam splitter's output when input states are imbalanced, extending understanding of quantum interference effects beyond balanced inputs.

Contribution

It introduces a new analytical formula applicable to imbalanced input states with large photon numbers, relaxing the assumption of perfect balance in quantum interference analysis.

Findings

Output distribution follows a $(1-x^2)^{-1/2}$ law for large photon numbers

The formula is valid for imbalanced inputs with large total photons

Robustness and universal features of the distribution are discussed

Abstract

In the Hong--Ou--Mandel interferometric scheme, two identical photons that illuminate a balanced beam splitter always leave through the same exit port. Similar effects have been predicted and (partially) experimentally confirmed for multi-photon Fock-number states. In the limit of large photon numbers, the output distribution follows a $(1-x^2)^{-1/2}$ law, where $x$ is the normalized imbalance in the output photon numbers at the two output ports. We derive an analytical formula that is also valid for imbalanced input photon numbers with a large total number of photons, and focus on the extent to which the hypothesis of perfect balanced input can be relaxed, discussing the robustness and universal features of the output distribution.