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

TL;DR

This paper develops a theory for phase sensitivity in N-photon interferometers, showing how detection efficiency and fringe visibility influence quantum-enhanced measurement sensitivity, and experimentally demonstrates surpassing the standard quantum limit.

Contribution

The paper introduces a comprehensive theory linking phase sensitivity to detection efficiency and fringe visibility, and experimentally confirms quantum advantage in phase measurement.

Findings

Phase sensitivity depends on detection efficiency and fringe visibility.

Maximum sensitivity phase differs from maximum fringe slope phase.

Experiment achieves 1.3 times sensitivity beyond the standard quantum limit.

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 $\eta$ 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 $\eta=3/4$ and $V=82\pm6$% (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.