Binomial states and the phase distribution measurement of weak optical fields

Abstract

We show that the eight-port interferometer used by Noh, Foug\`eres, and Mandel [Phys. Rev. Lett. 71, 2579 (1993)] to measure their operational phase distribution of light can also be used to measure the canonical phase distribution of weak optical fields, where canonical phase is defined as the complement of photon number. A binomial reference state is required for this purpose, which we show can be obtained to an excellent degree of approximation from a suitably squeezed state. The proposed method requires only photodetectors that can distinguish among zero photons, one photon, and more than one photon and is not particularly sensitive to photodetector imperfections.