Scheme for proving the bosonic commutation relation using single-photon interference

TL;DR

This paper proposes an experiment using single-photon interference to directly demonstrate the bosonic commutation relation, leveraging recent advances in photon addition and subtraction, and assesses its experimental feasibility.

Contribution

It introduces a novel interferometric scheme to directly prove the bosonic commutation relation using single-photon operations, which is experimentally feasible.

Findings

The scheme can directly verify the bosonic commutation relation.

Experimental imperfections are manageable and do not hinder realization.

The method can produce highly nonclassical states.

Abstract

We propose an experiment to directly prove the commutation relation between bosonic annihilation and creation operators, based on the recent experimental success in single-photon subtraction and addition. We devise a single-photon interferometer to realize coherent superpositions of two sequences of photon addition and subtraction. Depending on the interference outcome, the commutation relation is directly proven or a highly nonclassical state is produced. Experimental imperfections are assessed to show that the realization of the scheme is highly feasible.