Influence of decorrelation on Heisenberg-limited interferometry with quantum correlated photons

The feasibility of a Heisenberg-limited phase measurement using a Mach-Zehnder interferometer fed with twin photon correlated light is investigated theoretically. To take advantage of the Heisenberg limit, 1/N, for the phase sensitivity, one wants the number of correlated photons, N, to be high. This favors the use of parametric oscillation rather than the weaker but better correlated source given by parametric down-conversion. In real systems, decorrelation arising from photon absorption, mode mismatch, and nonideal detectors must be considered. In this paper we address the problem of detection when correlated photons are used as the input. We study the influence of photon statistics and of imperfect quantum correlation of the input light, and show that it is still possible to break the classical 1/sqrt[N] phase sensitivity limit in nonideal experimental conditions. All the results are valid in the general case of quantum correlated bosons.