Single-Shot Adaptive Measurements of the Phase of a Single Mode Field

Abstract

A standard single-shot measurement of the phase of single-mode field can be achieved by heterodyne detection (using a detuned local oscillator). This effects a joint measurement of both phase and amplitude quadratures, which introduces noise into both results. Such techniques are consequently less accurate than an ideal or canonical measurement of phase. If we assume that the phase of the field is already approximately known then homodyne detection (using a resonant local oscillator) could be used to accurately determine the phase, but this assumption is counter to the idea of a “phase measurement”. Here we suggest a new sort of phase measurement using a resonant local oscillator with an adjustable phase. This scheme is adaptive, in that the local oscillator phase is continually adjusted to be shifted by π/2 from the estimated system phase. The estimate for the system phase is made from the results so far in the single-shot measurement. We show that for states with high photon number, the adaptive scheme has an accuracy intermediate between a canonical and a standard measurement.