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.
@article{arxiv.0901.2708,
title = {Scheme for proving the bosonic commutation relation using single-photon interference},
author = {M. S. Kim and H. Jeong and A. Zavatta and V. Parigi and M. Bellini},
journal= {arXiv preprint arXiv:0901.2708},
year = {2009}
}