General information on quantum non-destructive measurements (QND)

The third lesson introduced QND measurements of the electromagnetic field. The aim is to measure an observable of the field without disturbing it, so that the measurement can be repeated and the same result obtained in a subsequent measurement. This is the projective measurement of an observable that does not change between two successive detections as a result of Hamiltonian evolution. Field energy and photon number are observables that can be measured QND, provided that photon absorption in the detector is avoided. We have presented some simple models for QND measurements, based either on the detection of radiation pressure exerted on a mirror (opto-mechanical measurements), or on the crossed Kerr effect in a non-linear optical medium. We have analyzed the feedback effect of the measurement on the phase of the field, leading us to rigorously define a phase operator. The analysis is based either on a description of the fields in terms of state vectors (which is well suited to the case where the measurement projects the field onto a Fock state), or on a discussion in terms of photon noise, convenient when the measurement does not discriminate individual photons and the field appears as a fluctuating continuous variable. Both approaches are of course equivalent in the continuous limit.