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Quantum 2.0 Conference and Exhibition

Quantum Limits in Precision Hong-Ou-Mandel Interferometry

Kyle M. Jordan, Raphael A. Abrahão, Jeff S. Lundeen

Published Jan 1, 2022• 0 citations
Publisher

Abstract

We examine the precision limits of Hong-Ou-Mandel interferometry-based timing measurements using the Cramér-Rao bounds. We show how to adapt the method for realistic sources of photon pairs involving unequal mode bandwidths and nonmaximal frequency correlations.
DOI
10.1364/quantum.2022.qtu2a.12

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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 tradeoff between high interference visibility and strong frequency anticorrelations, with the optimal precision occurring when the photons share nonmaximal 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.
In quantum mechanics, the precision achieved in parameter estimation using a quantum state as a probe is determined by the measurement strategy employed. The quantum precision limit, a fundamental boundary, is defined by the intrinsic characteristics of the state and its dynamics. Theoretical results have revealed that in interference measurements with two possible outcomes, like the Hong Ou-Mandel interference, this limit can be reached under ideal conditions of perfect visibility and zero losses. However, in practice, this cannot be achieved, so precision never reaches the quantum limit. But how do experimental setups approach precision limits under realistic circumstances? In this work, we provide a general model for precision limits in two-photon Hong-Ou-Mandel interferometry for non-perfect visibility and validate it experimentally using different quantum states. A remarkable ratio of 0.97 between the experimental precision and the quantum limit is observed, establishing a new benchmark in the field.
The Hong-Ou-Mandel effect provides a mechanism to determine the distinguishability of a photon pair by measuring the bunching rates of two photons interfering at a beam splitter. Of particular interest is the distinguishability in time, which can be used to probe a time delay. Photon detectors themselves give some timing information, however, while that resolution may dwarf that of an interferometric technique, typical analyses reduce the interference to a binary event, neglecting temporal information in the detector. By modeling detectors with number and temporal resolution we demonstrate a greater precision than coincidence rates or temporal data alone afford. Moreover, the additional information can allow simultaneous estimation of a time delay alongside calibration parameters, opening up the possibility of calibration-free protocols and approaching the precision of the quantum Cram\'er-Rao bound.
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