Quantum metrology timing limits of the Hong-Ou-Mandel interferometer and of general two-photon measurements

TL;DR

This paper investigates the fundamental precision limits of Hong-Ou-Mandel interferometry and general two-photon measurements, highlighting the impact of photon bandwidths, frequency correlations, and spectral engineering on measurement accuracy.

Contribution

It provides a comprehensive analysis of the quantum limits of two-photon measurement precision, including the effects of spectral properties and generalized measurement strategies.

Findings

Optimal precision occurs with non-maximal frequency anticorrelations.

Generalized measurements share similar precision limits to HOM when insensitive to net delay.

Spectral engineering can improve measurement performance in realistic scenarios.

Abstract

We examine the precision limits of Hong-Ou-Mandel (HOM) timing measurements, as well as precision limits applying to generalized two-photon measurements. As a special case, we consider the use of two-photon measurements using photons with variable bandwidths and frequency correlations. When the photon bandwidths are not equal, maximizing the measurement precision involves a trade-off between high interference visibility and strong frequency anticorrelations, with the optimal precision occuring when the photons share non-maximal frequency anticorrelations. We show that a generalized measurement has precision limits that are qualitatively similar to those of the HOM measurement whenever the generalized measurement is insensitive to the net delay of both photons. By examining the performance of states with more general frequency distributions, our analysis allows for engineering of the joint spectral amplitude for use in realistic situations, in which both photons may not have ideal spectral properties.