Realistic quantum states of light with minimum phase uncertainty

Abstract

Starting from a convenient measure for the phase uncertainty delta phi , a rigorous solution to the variational problem in which ( delta phi )2 is minimized under the constraint that the mean photon number N is held fixed, was found. In an approximation valid for large values of N, closed-form expressions for both ( delta phi )2 and the variance of the photon number ( Delta n)2 were obtained. In the final result, the approximation is very similar to an approximation scheme recently discussed by Summy and Pegg Opt. Commun., vol.77, p.75, 1990. The phase uncertainty for the phase optimized states is found to decrease as (N+1)-1 with growing N.