Measurement of the quantum phase by photon counting

Abstract

We address the problem of identifying the dynamical variables representing the phase of a quantum field by analyzing what is measured in two simple homodyne experiments. This leads us to identify operators C${\mathrm{^}}_{\mathit{M}}$,S${\mathrm{^}}_{\mathit{M}}$ corresponding to the measured cosine and sine of the phase difference. The predictions of the theory are tested in an experiment in which the input fields are derived from a highly stable He:Ne laser. Photon-counting measurements extending from mean photon numbers 30 down to ${10}^{\mathrm{\ensuremath{-}}2}$ show good agreement between theory and experiment. The implications for identifying the ``correct'' phase operator are briefly discussed.