A two-step optimized measurement for the phase shift

A two-step detection strategy is suggested for the precise measurement of the optical phase shift. In the first step an unsharp, but unbiased, joint measurement of the phase and photon number is performed by heterodyning the signal field. Information coming from this step is then used for appropriate squeezing of the probe made to obtain a sharp phase distribution. Application to squeezed states leads to a phase sensitivity scaling as Delta phi similar or equal to N-1 relative to the total number of photons impinged onto the apparatus. Numerical simulations of the whole detection strategy are also presented.