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Bulletin of the South Ural State University series Mathematics Mechanics Physics

ON SELECTING OPTIMAL PARAMETERS FOR DELAY TIME MEASUREMENT USING THE HONG–OU–MANDEL EFFECT

Dmitry Kuts, Mikhail S. Podoshvedov, А. Г. Воронцов, S. P. Kulik, Sergey A. Podoshvedov

Published Jan 1, 2025• 0 citations

Abstract

The paper deals with the measurement error of the delay time between the arrivals at the beam splitter of two photons traveling through different channels in an optical system based on a HongOu-Mandel (HOM) interferometer. We consider the source of two-photon light to be the radiation of spontaneous parametric scattering (SPS) of light of the second type. The photon delay in one of the HOM interferometer channels can be induced by a change in the optical path length due to various factors: mechanical displacement of interferometer parts, changes in the refractive index of the medium caused by temperature variations, electric fields, etc. In the scheme, the outputs of the beam splitter are connected to single-photon detectors, which send signals to a coincidence counter upon photon detection. The coincidence counter data determine the delay time. The authors determine the absolute error in estimating the delay time in terms of the biphoton spectral width, the visibility, calculated from the maximum and minimum values of the coincidence counter signal, and the estimated delay time value itself. The derived expression facilitates finding the estimated delay time value. The study reveals that for a fixed biphoton field width, the delay time corresponding to the minimum absolute error value approaches the inflection point of the coincidence-time curve with decreasing visibility. This should be taken into account when designing measuring devices based on the Hong-Ou-Mandel interferometer.

DOI: 10.14529/mmph250306

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The paper deals with the measurement error of the delay time between the arrivals at the beam splitter of two photons traveling through different channels in an optical system based on a HongOu-Mandel (HOM) interferometer. We consider the source of two-photon light to be the radiation of spontaneous parametric scattering (SPS) of light of the second type. The photon delay in one of the HOM interferometer channels can be induced by a change in the optical path length due to various factors: mechanical displacement of interferometer parts, changes in the refractive index of the medium caused by temperature variations, electric fields, etc. In the scheme, the outputs of the beam splitter are connected to single-photon detectors, which send signals to a coincidence counter upon photon detection. The coincidence counter data determine the delay time. The authors determine the absolute error in estimating the delay time in terms of the biphoton spectral width, the visibility, calculated from the maximum and minimum values of the coincidence counter signal, and the estimated delay time value itself. The derived expression facilitates finding the estimated delay time value. The study reveals that for a fixed biphoton field width, the delay time corresponding to the minimum absolute error value approaches the inflection point of the coincidence-time curve with decreasing visibility. This should be taken into account when designing measuring devices based on the Hong-Ou-Mandel interferometer.

Abstract An analysis of the precision of temporal delay estimation in a Hong–Ou–Mandel (HOM) interferometer is carried out via the error propagation formula and the classical Fisher information. The study finds delay times characterized by a minimum precision, where precision is defined as the standard deviation of the estimated delay, and those for which this precision is a minimal fraction of the delay time itself. The temporal delay is measured in units set by the location of the inflection point on the HOM coincidence dip, with the corresponding delay time in the considered models depending solely on the biphoton spectrum width. The paper also discusses the estimation of photon loss probability in an interferometer, which is based on the temporal delay estimate that possesses minimum variance.

The paper addresses the issue of selecting the optimal operating point for a sensor based on a Hong–Ou–Mandel (HOM) interferometer with collinear degenerate type-II phase-matching. Experimental data on coincidence counting rates from single-photon detectors are compared to a model constructed using an approximation where the spectral amplitude of the biphoton field is modeled by a double-Gaussian function. Errors in determining the delay time in the HOM interferometer are estimated based on the Cramér–Rao bound. The delay times corresponding to the minimum absolute and minimum relative errors are calculated for the interferometer model. The authors have found that these delay times occur in the regions where the discrepancy between the model and the experimentally measured coincidence counting rate is approximately 2–3 %. Therefore, when selecting the operating point of the sensor, the deviation between the modeled and experimentally observed coincidence count function should be additionally taken into account.

We theoretically extend the original Hong–Ou–Mandel (HOM) interferometer to three parameters by concatenating 50:50 beam splitters with three independent and adjustable time delays. The coincidence probability of such an interferometer is obtained based on the linear transformation of the beam splitter matrix. We present a comprehensive analysis of the interference characteristics of the interferometer at different time delays with various types of frequency-correlated resources and input states. It is found that by properly setting the time delays, one can obtain typical interferograms that include multiple sub-interferograms associated with one- and two-parameter HOM interferometers, revealing richer and more complicated two-photon interference phenomena. In particular, additional enhancements of the interference signal at a specific delay can be achieved, and the symmetry of the interferograms on both sides can also be changed. This work provides comprehensive insights into the interference characteristics of the three-parameter HOM interferometer and enables the simultaneous optimal estimation of multiple time-delay parameters within a single interferometer, which holds potential for applications in multiparameter estimation and quantum metrology.

A generalized multiparameter Hong-Ou-Mandel interferometer is presented which extends the conventional ``Mandel dip'' configuration to the case where a symmetric biphoton source is used to monitor the contemporary absence of

k

independent time delays. Our construction results in a two-input/two-output setup, obtained by concatenating 50:50 beam splitters with a collection of adjustable achromatic wave plates. For

k=1,2

and

k=4

explicit examples can be exhibited that prove the possibility of uniquely linking the zero value of the coincidence counts registered at the output of the interferometer with the contemporary absence of all the time delays. Interestingly enough the same result cannot be extended to

k=3

. Besides, the sensitivity of the interferometer is analyzed when the time delays are affected by strong fluctuations, i.e., the fluctuations over timescales that are larger than the inverse of the frequency of the pump used to generate the biphoton state.

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.