Cavity-QED-based scheme for verification of the photon commutation relation

We propose an experimental scheme to prove the photon commutation relation, [a, a(dagger)] = 1. The scheme exploits interaction between a single-mode cavity field and three two-level atoms, two of which are prepared in an entangled state. The success of the scheme is subject to observation of the atoms in predetermined states after the interaction. We show, in particular, that a reasonably high success probability can be obtained with our scheme by preparing the cavity field in a superposition of two Fock states and choosing the interaction times appropriately.