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Quantum Information and Measurement (QIM)

A modified Hong-Ou-Mandel interferometer for two-parameter sensing

Yu Yang, Luping Xu, Vittorio Giovannetti

Published Jan 1, 2019• 0 citations
Publisher

Abstract

A modification of the standard Hong-Ou-Mandel interferometer is proposed to recover two independent parameters via the coincidences counts. Whether in the ideal or the parameter fluctuating case, estimating the parameters with the bi-photon states performs well than with the semiclassical states.
DOI
10.1364/qim.2019.f5a.83

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A modification of the standard Hong-Ou-Mandel interferometer is proposed which allows one to replicate the celebrated coincidence dip in the case of two-independent delay parameters. In the ideal case where such delays are sufficiently stable with respect to the mean wavelength of the pump source, properly symmetrized input bi-photon states allow one to pinpoint their values through the identification of a zero in the coincidence counts, a feature that cannot be simulated by semiclassical inputs having the same spectral properties. Besides, in the presence of fluctuating parameters the zero in the coincidences is washed away: still the bi-photon state permits to recover the values of parameters with a visibility which is higher than the one allowed by semiclassical sources. The detrimental role of loss and dispersion is also analyzed and an application in the context of quantum positioning is presented.
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 kkk 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=1,2k=1,2k=1,2 and k=4k=4k=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=3k=3k=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.
Hong-Ou-Mandel interferometry takes advantage of the quantum nature of two-photon interference to increase the resolution of precision measurements of time-delays. Relying on few-photon probe states, this approach is applicable also in cases of extremely sensible samples and it achieves attosecond (nanometer path length) scale resolution, which is relevant to cell biology and two-dimensional materials. Here, we theoretically analyze how the precision of Hong-Ou-Mandel interferometers can be significantly improved by engineering the spectral distribution of two-photon probe states. In particular, we assess the metrological power of different classes of biphoton states with non-Gaussian time-frequency spectral distributions, considering the estimation of both time-and frequency-shifts. We find that grid states, characterized by a periodic structure of peaks in the chronocyclic Wigner function, can outperform standard biphoton states in sensing applications. The considered states can be feasibly produced with atomic photon sources, bulk non-linear crystals and integrated photonic waveguide devices.
Hong-Ou-Mandel interferometry allows one to detect the presence of entanglement in two-photon input states. The same result holds for two-particle input states which obey fermionic statistics. In the latter case, however, antibouncing introduces qualitative differences in the interferometer response. This effect is analyzed in a gedanken experiment where the particles entering the interferometer are assumed to belong to a one-parameter family of quons which continuously interpolate between the bosonic and fermionic statistics.