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arXiv:2005.14696 · Physical Review A

Beyond coincidence in Hong-Ou-Mandel interferometry

Hannah Scott, Dominic Branford, Niclas Westerberg, Jonathan Leach, Erik M. Gauger

Published Sep 10, 2020• 23 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.102.033714

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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.
Quantum interference forces two indistinguishable input photons to depart a beamsplitter in the same (of two possible) spatial output modes; this is known as the Hong-Ou-Mandel (HOM) effect. It provides a quantitative way of measuring the distinguishability between two photons and also has been utilised to determine their relative temporal delays [1, 2]. HOM interferometry offers numerous advantages over its classical counterpart, most importantly it lacks any dependence on the phase of the photons and therefore can potentially provide reliable measurements in environments where the phase is unstable. To date there have been very few investigations on the precision that is achievable with HOM interferometry. Experiments with collinear geometries have yielded sensitivities as low as 0.1fs however these approaches are limited to measurements of birefringence and other polarisation dependent effects [3, 4], as the precision derives from the inherently stable shared path of the photon pairs. Typical non-shared path HOM interferometers exhibit resolution of roughly 1–3 fs (0.3–1 μm).
In this work we study the application of two-photon correlated quantum states for high-precision time estimation. To achieve this, photon pairs were fed into a Hong-Ou-Mandel polarization interferometer to generate N00N entangled states with N=2N = 2N=2. Two- and four-detector schemes were considered, and the achievable time estimation precision of each was studied, with particular emphasis on the system's Fisher information in each case. Our results reveal that using a four-detector scheme, enabling the measurement of both coincidence and photon-bunching terms, achieves the maximum precision given by the quantum Fisher information, without the need of characterizing system losses. We also show that correlations between repetitions arise due to systematic errors, limiting the precision enhancement that can be obtained by increasing the number of repetitions. Taking these correlations into account, we show that the four-detector scheme outperforms the two-detector scheme in the precision of time-delay estimation. With the experimentally determined calibration uncertainties, the four-detector scheme improves the dispersion by a factor of 2 for the repetitions performed, reaching up to a factor of 4 as both schemes approach their systematic floors.
Abstract Hong-Ou-Mandel interference, the fact that identical photons that arrive simultaneously on different input ports of a beam splitter bunch into a common output port, can be used to measure optical delays between different paths. It is generally assumed that great precision in the measurement requires that photons contain many frequencies, i.e., a large bandwidth. Here we challenge this “well-known” assumption and show that the use of two well-separated frequencies embedded in a quantum entangled state (discrete color entanglement) suffices to achieve great precision. We determine optimum working points using a Fisher Information analysis and demonstrate the experimental feasibility of this approach by detecting thermally-induced delays in an optical fiber. These results may significantly facilitate the use of quantum interference for quantum sensing, by avoiding some stringent conditions such as the requirement for large bandwidth signals.
Hong-Ou-Mandel interference, the fact that identical photons that arrive simultaneously on different input ports of a beam splitter bunch into a common output port, can be used to measure optical delays between different paths. It is generally assumed that great precision in the measurement requires that photons contain many frequencies, i.e., a large bandwidth. Here we challenge this “well-known” assumption and show that the use of two well-separated frequencies embedded in a quantum entangled state (discrete color entanglement) suffices to achieve great precision. We determine optimum working points using a Fisher Information analysis and demonstrate the experimental feasibility of this approach by detecting thermally-induced delays in an optical fiber. These results may significantly facilitate the use of quantum interference for quantum sensing, by avoiding some stringent conditions such as the requirement for large bandwidth signals.
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 limit of precision is bounded by a value set by the state and its dynamics. Theoretical results have revealed that in interference measurements with two possible outcomes, this limit can be reached under ideal conditions of perfect visibility and zero losses. However, in practice, these conditions cannot be achieved, so precision never reaches the quantum limit. But how do experimental setups approach precision limits under realistic circumstances? In this Letter, we provide a model for precision limits in two-photon Hong-Ou-Mandel interferometry using coincidence statistics for nonperfect visibility and temporally unresolved measurements. We show that the scaling of precision with visibility depends on the effective area in time-frequency phase space occupied by the state used as a probe, and we find that an optimal scaling exists. We demonstrate our results experimentally for different states in a setup where the visibility can be controlled and reaches up to 99.5%. In the optimal scenario, a ratio of 0.97 is observed between the experimental precision and the quantum limit, establishing a new benchmark in the field.