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

Ryo Okamoto; Holger F. Hofmann; Tomohisa Nagata; Jeremy L. O'Brien; Keiji Sasaki; Shigeki Takeuchi

doi:10.1088/1367-2630/10/7/073033

paper

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

arXiv:0804.0087 · doi:10.1088/1367-2630/10/7/073033

Abstract

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 complex 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 $V = 82 \pm 6$ % (an extension of our previous work [Science \textbf{316}, 726 (2007)]) 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.

submitted for publication Oct 2007, 5pages, 3figures

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

Abstract

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