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 r
ealize 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.
Annihilating and creating a photon in a travelling light field are useful building blocks for quantum-state engineering to generate a photonic state at will. In this paper, we review the relevance of these operations to some of the fundamental aspect
s of quantum physics and recent advances in this research.
