Beating the standard quantum limit: phase super- sensitivity of N-photon interferometers

Quantum metrology promises greater sensitivity for optical phase measurements than could ever be achieved classically. Here, we present a theory of the phase sensitivity for the general case where the detection probability is given by an N photon interference fringe. We find that the phase sensitivity has a complicated dependence on both the intrinsic efficiency of detection η and the interference fringe visibility V . Most importantly, the phase that gives maximum phase sensitivity is in general not the same as the phase at which the slope of the interference fringe is a maximum, as has previously been assumed.We determine the parameter range where quantum enhanced sensitivity can be achieved. In order to illustrate these theoretical results, we perform a four-photon experiment with η = 3/4 and V = 82± 6% (an extension of our previous work (Nagata et al 2007 Science 316 726)) and find a phase sensitivity 1.3 times greater than the standard quantum limit at a phase different to that which gives maximum slope of the interference fringe. 5 Author to whom any correspondence should be addressed. New Journal of Physics 10 (2008) 073033 1367-2630/08/073033+9$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft