Sagnac interferometry as a probe to the commutation relation of a macroscopic quantum mirror

Single photon Sagnac interferometry as a probe to macroscopic quantum mechanics is considered at the theoretical level. For a freely moving macroscopic quantum mirror susceptible to radiation pressure force inside a Sagnac interferometer, a careful analysis of the input-output relation reveals that the particle spectrum readout at the bright and dark ports encode information concerning the noncommutativity of position and momentum of the macroscopic mirror. A feasible experimental scheme to probe the commutation relation of a macroscopic quantum mirror is outlined to explore the possible frontier between classical and quantum regimes. In the Appendix, the case of Michelson interferometry as a feasible probe is also sketched.

NBRP of China [2010CB832800]

NNSF of China [10505009]

NSFC [10731080]

973 project [2006CB805905]