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arXiv:2005.10177 · Photonics Research

Spectrally resolved Hong–Ou–Mandel interferometry for quantum-optical coherence tomography

Pablo Yepiz-Graciano, Alí Angulo, Dorilian Lopez-Mago, Hector Cruz-Ramirez, Alfred B. U’Ren

Published Mar 26, 2020• 44 citations
arXivHTMLPDF

Abstract

In this paper, we revisit the well-known Hong–Ou–Mandel (HOM) effect in which two photons, which meet at a beamsplitter, can interfere destructively, leading to null in coincidence counts. In a standard HOM measurement, the coincidence counts across the two output ports of the beamsplitter are monitored as the temporal delay between the two photons prior to the beamsplitter is varied, resulting in the well-known HOM dip. We show, both theoretically and experimentally, that by leaving the delay fixed at a particular value while relying on spectrally resolved coincidence photon counting, we can reconstruct the HOM dip, which would have been obtained through a standard delay-scanning, non-spectrally resolved HOM measurement. We show that our numerical reconstruction procedure exhibits a novel dispersion cancellation effect, to all orders. We discuss how our present work can lead to a drastic reduction in the time required to acquire a HOM interferogram, and specifically discuss how this could be of particular importance for the implementation of efficient quantum-optical coherence tomography devices.

DOI
10.1364/prj.388693

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In this paper, we revisit the well-known Hong–Ou–Mandel (HOM) effect in which two photons, which meet at a beamsplitter, can interfere destructively, leading to null in coincidence counts. In a standard HOM measurement, the coincidence counts across the two output ports of the beamsplitter are monitored as the temporal delay between the two photons prior to the beamsplitter is varied, resulting in the well-known HOM dip. We show, both theoretically and experimentally, that by leaving the delay fixed at a particular value while relying on spectrally resolved coincidence photon counting, we can reconstruct the HOM dip, which would have been obtained through a standard delay-scanning, non-spectrally resolved HOM measurement. We show that our numerical reconstruction procedure exhibits a novel dispersion cancellation effect, to all orders. We discuss how our present work can lead to a drastic reduction in the time required to acquire a HOM interferogram, and specifically discuss how this could be of particular importance for the implementation of efficient quantum-optical coherence tomography devices.
In recent works we have explored a multi-photon extension of the celebrated two-photon Hong-Ou-Mandel (HOM) effect in which the quantum amplitudes for a two-photon input to a lossless, balanced 50:50 beamsplitter (BS) undergoes complete destructive interference. In the extended Hong-Ou-Mandel (eHOM) effect the multi-photon scattering of photons from the two input ports to the two output ports of the BS for Fock number basis input states (FS) ∣n,m⟩12|n,m\rangle_{12}∣n,m⟩12​ exhibit complete destructive interference pairwise within the quantum amplitudes containing many scattering components, generalizing the two-photon HOM effect. This has profound implications for arbitrary bipartite photonic input states constructed from such basis states: if the input state to one input port of the BS is of odd parity, i.e. constructed from only of odd numbers of photons, then regardless of the input state to the second 50:50 BS port, there will be a central nodal line (CNL) of zeros in the joint output probability distribution along the main diagonal for coincidence detection. The first goal of this present work is to show diagrammatically how the extended HOM effect can be seen as a succession of multi-photon HOM effects when the latter is viewed as a pairwise cancellation of mirror image scattering amplitudes. The second goal of this work is to explore considerations for the experimental realization of the extended Hong-Ou-Mandel effect. We examine the case of a single photon interfering with a coherent state (an idealized laser) on a balanced 50:50 beamsplitter and consider prospects for experimental detection of the output destructive interference by including additional effects such as imperfect detection efficiency, spatio-temporal mode functions, and time delay between the detected output photons.
Hong-Ou-Mandel (HOM) interferometry enables delay estimation at the quantum precision limit but is traditionally constrained to path differences within the coherence time of the interfering photons. Here, we demonstrate single-measurement path-delay sensing at the measurement Cramer-Rao bound using spectrally resolved HOM interference, thereby removing the conventional dynamic-range limitation imposed by the photon coherence window, with no scanning required for calibration. By extracting delay information from the spectral interference fringes of spectrally entangled photon pairs, we retain near-optimal sensitivity over an operational range exceeding the photon coherence time by over two orders of magnitude. Using one million detected photon pairs, we achieve a time-delay precision of 20 attosecond (6 nm), while real-time operation (at 1 Hz) yields 330 attosecond (100 nm) precision. Because the estimator relies on fringe periodicity rather than absolute coincidence rates, the method is intrinsically robust to photon losses and variations in interference visibility, eliminating the need for recalibration. As a practical demonstration, we measure the thickness of a 300 um transmissive target with nanometer-scale precision. These results mark a significant step towards deploying quantum-limited measurements in real-world sensing applications using HOM interferometry.
The Hong-Ou-Mandel (HOM) effect ranks among the most notable quantum interference phenomena, and is central to many applications in quantum technologies. The fundamental effect appears when two independent and indistinguishable photons are superimposed on a beam splitter, which achieves a complete suppression of coincidences between the two output ports. Much less studied, however, is when the fields share coherence (continuous-wave lasers) or mode envelope properties (pulsed lasers). In this case, we expect the existence of two distinct and concurrent HOM interference regimes: the traditional HOM dip on the coherence length time scale, and a structured HOM interference pattern on the pulse length scale. We develop a theoretical framework that describes HOM interference for laser fields having arbitrary temporal waveforms and only partial overlap in time. We observe structured HOM interference from a continuous-wave laser via fast polarization modulation and time-resolved single photon detection fast enough to resolve these structured HOM dips.
Hong-Ou-Mandel (HOM) interferometry is a powerful quantum metrology technique to reconstruct the surface-depth profile of transparent samples with complementary benefits of measurement precision and experimental robustness. It is generally assumed that a trade-off exists between the standard HOM interferometry sensitivity and its ambiguity-free dynamic range. Here we challenge this ``well-known'' assumption through the implementation of spectrally resolved HOM interferometry with discrete color entanglement, and show that the well-separated frequencies embedded in a quantum state suffices to achieve great advantages in enhancing the temporal resolution but without limiting its ambiguity-free dynamic range. Backed by the Fisher-information analysis, spectrally resolved coincidence detection is an optimal measurement strategy as it enables us to recover the quantum Cram\'er-Rao bound. These results may significantly facilitate the use of spectrally resolved quantum interference for real-time quantum information processing, such as ultrafast phase transition and spectral-temporal photography.
The dispersion cancellation observed in Hong-Ou-Mandel (HOM) interference between frequency-entangled photon pairs has been the basis of quantum optical coherence tomography and quantum clock synchronization. Here we explore the effect of phase dispersion on ultranarrow HOM dips. We show that the higher-order dispersion, the linewidth of the pump laser, and the spectral shape of the parametric fluorescence have a strong effect on the dispersion cancellation in the high-resolution regime with several experimental verifications. Perfect dispersion cancellation with a linewidth of 3 $\ensuremath{\mu}$m is also demonstrated through 25 mm of water.
Hong–Ou–Mandel (HOM) interference is a quantum optics laboratory experiment that has recently become more accessible to undergraduate students. The experiment consists of two identical photons simultaneously entering a nonpolarizing beamsplitter, where the photon wavefunctions interfere. As a result, the photon pair exits from the same beamsplitter output, whereas classically, the two photons are equally likely to exit from the two different outputs. This effect is demonstrated by observation of a dip in coincidence counts measured between the two beamsplitter outputs. Due to the precision needed to achieve photon indistinguishability, the setup and alignment of this experiment is often considered to be too difficult and time consuming to be appropriate for the undergraduate instructional laboratory. Here, we present an alternative optical-fiber-based apparatus that gives a consistently reproducible experiment. In our approach, quantum interference occurs within a fused-fiber coupler, instead of within a traditional beamsplitter. We use a commercially available fiber-coupled biphoton source that requires minimal alignment and increases the interference coherence length. In addition, our biphoton source provides direct temperature-based control of the frequency degeneracy of the photon pairs, allowing students to investigate physical properties of HOM interference such as coherence length and interference visibility. Through use of standard optomechanical parts, combined with the commercially available fiber-integrated biphoton source, our apparatus is positioned midway between a completely built-from-scratch and a pre-aligned setup, making it ideal for the advanced instructional laboratory.