Adaptive phase measurements for narrowband squeezed beams

We have previously [Phys. Rev. A 65, 043803 (2002)] analyzed adaptive measurements for estimating the continuously varying phase of a coherent beam, and a broadband squeezed beam. A real squeezed beam must have finite photon flux N and hence can be significantly squeezed only over a limited frequency range. In this paper we analyze adaptive phase measurements of this type for a realistic model of a squeezed beam. We show that, provided it is possible to suitably choose the parameters of the beam, a mean-square phase uncertainty scaling as (N∕κ)^-5∕8 is possible, where κ is the linewidth of the beam resulting from the fluctuating phase. This is an improvement over the (N∕κ)^-1∕2 scaling found previously for coherent beams. In the experimentally realistic case where there is a limit on the maximum squeezing possible, the variance will be reduced below that for coherent beams, though the scaling is unchanged.