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arXiv:2206.11387 · Physical Review A

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

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

Published Dec 22, 2022• 22 citations
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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 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.

DOI
10.1103/physreva.106.063715

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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.
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-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 [1].
The Hong-Ou-Mandel interferometer is a versatile tool for analyzing the joint properties of photon pairs, relying on a truly quantum interference effect between two-photon probability amplitudes. While the theory behind this form of two-photon interferometry is well established, the development of advanced photon sources and exotic two-photon states has highlighted the importance of quantifying precisely what information can and cannot be inferred from features in a Hong-Ou-Mandel interference trace. Here we examine Hong-Ou-Mandel interference with regard to a particular class of states, so-called quantum frequency combs, and place special emphasis on the role spectral phase plays in these measurements. We find that this form of two-photon interferometry is insensitive to the relative phase between different comb line pairs. This is true even when different comb line pairs are mutually coherent at the input of a Hong-Ou-Mandel interferometer and the fringe patterns display sharp temporal features. Consequently, Hong-Ou-Mandel interference cannot speak to the presence of high-dimensional frequency-bin entanglement in two-photon quantum frequency combs.
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.
Biphoton frequency comb (BFC), which encompasses multiple discrete frequency modes and represents high-dimensional frequency entanglement, is crucial in quantum information processing due to its high information capacity and error resilience. It also holds significant potential for enhancing timing precision in quantum metrology. Here, we examine quantum metrology timing limits using the BFC as a probe state and derive a quantum Cramér-Rao bound (QCRB) that depends on the mode number, mode spacing, frequency detuning, and single-mode bandwidth. Our results coincide with previous findings that considered only the latter two factors. Under ideal conditions (zero loss and perfect visibility), this bound can be saturated by both spectrally non-resolved Hong-Ou-Mandel (HOM) interferometry at zero delay and spectrally resolved HOM interferometry at arbitrary delays. In practical scenarios, the Fisher information is below the QCRB but can approach its maximum by increasing the mode number and mode spacing for a fixed delay point, suggesting an optimal strategy for improving the precision of HOM-based sensing in practice. Furthermore, compared to spectrally non-resolved measurement, spectrally resolved measurement is a superior strategy due to its higher Fisher information, shorter measurement times, and ambiguity-free dynamic range.
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.