Measurement of Quantum Phase Distribution by Projection Synthesis

Stephen Mark Barnett, David Thomas Pegg

Experimental determination of the canonical quantum optical phase probability distribution has, until now, required sufficient measurements to determine the complete state of the field. In this Letter we present a more direct means for measuring this distribution which involves synthesizing the projection onto a phase state. Projection synthesis may be applied more generally to measure the probability distribution associated with other observables.

Jaewoo Noh

David Thomas Pegg

David Thomas Pegg, Stephen Mark Barnett, Lee S. Phillips

We show how the recently-introduced method of projection synthesis can be applied to find the phase probability distribution for a single-mode field. The realization of such a measurement scheme requires the production of reciprocal-binomial states of light or suitable alternative states. We describe how such states might be produced in the laboratory.

K. L. Pregnell, David Thomas Pegg

Methods proposed so far for measuring the canonical phase probability distribution of light are very difficult to implement. In particular the method of projection synthesis, which synthesizes a phase state projector, involves the use of a beam splitter and a specially engineered reference state. Here we extend this method by use of an additional beam splitter to synthesize phase sine and cosine operators. This allows the measurement of all the moments needed to construct the phase distribution. The reference state required for operator synthesis is, remarkably, just an easily prepared coherent state.

Z. Hradil