Phase control of a longitudinal momentum entangled photon state by a deformable membrane mirror

We propose a paradigmatic demonstration of the potentialities of a deformable mirror for closed-loop control of a two-photon momentum-entangled state, subject to phase fluctuations. A custom-made membrane mirror is used to set a relative phase shift between the arms of an interferometric apparatus. The control algorithm estimates the phase of the quantum state, by measurements of the coincidence events at the output ports of the interferometer, and uses the measurements results to provide a feedback signal to the deformable mirror. Stabilization of the coincidence rate to within 1.5 standard deviation of the Poissonian noise is demonstrated over 2000 seconds.