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arXiv:2303.09721 · Physical Review A

Frequency-multiplexed Hong-Ou-Mandel interference

Mayuka Ichihara, Daisuke Yoshida, Feng-Lei Hong, Tomoyuki Horikiri

Published Mar 16, 2023• 7 citations
arXivHTMLPDF

Abstract

The implementation of quantum repeaters needed for long-distance quantum communication requires the generation of quantum entanglement distributed among the elementary links. These entanglements must be swapped among the quantum repeaters through Bell-state measurements. This study aims to improve the entanglement generation rate by frequency multiplexing the Bell-state measurements. As a preliminary step of the frequency-multiplexed Bell-state measurements, three frequency modes are mapped to a temporal mode by an atomic frequency comb prepared in ${\mathrm{Pr}}^{3+}$ ion-doped ${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ crystals using a weak coherent state, and Hong-Ou-Mandel interference, which is a measure of the indistinguishability of two inputs, is observed in each frequency mode by coincidence detection. The visibility for all the modes was 40%--42% (theoretically up to 50%). Furthermore, we show that a mixture of different modes is avoided. The present results are connected to frequency-selective Bell-state measurements and therefore frequency-multiplexed quantum repeaters.

DOI
10.1103/physreva.107.032608

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The implementation of quantum repeaters needed for long-distance quantum communication requires the generation of quantum entanglement distributed among the elementary links. These entanglements must be swapped among the quantum repeaters through Bell-state measurements. This study aims to improve the entanglement generation rate by frequency multiplexing the Bell-state measurements. As a preliminary step of the frequency-multiplexed Bell-state measurements, three frequency modes are mapped to a temporal mode by an atomic frequency comb prepared in Pr3+{\mathrm{Pr}}^{3+}Pr3+ ion-doped Y2SiO5{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Y2​SiO5​ crystals using a weak coherent state, and Hong-Ou-Mandel interference, which is a measure of the indistinguishability of two inputs, is observed in each frequency mode by coincidence detection. The visibility for all the modes was 40%--42% (theoretically up to 50%). Furthermore, we show that a mixture of different modes is avoided. The present results are connected to frequency-selective Bell-state measurements and therefore frequency-multiplexed quantum repeaters.
Entanglement swapping enables the distribution of quantum states over long distances. In this protocol, a Bell state measurement projects photons, which were created in separate entangled photon sources, into an entangled state when their corresponding pairs interfere at a beamsplitter. This process is optimally realized when the photons are indistinguishable in all degrees of freedom, resulting in Hong-Ou-Mandel (HOM) interference. Since its initial proposal by [1], several experimental realizations have used pulsed, synchronized pumps, as in [2] to achieve temporal indistiguishability. In the case of continuous wave (CW) pumping, the sources are not synchronized, requiring post-selection of the coincidence events after detection. This requires detectors with a temporal resolution greater than the coherence time of the photons. Previous experiments have successfully observed HOM interference using periodically poled Lithium Niobate (ppLN) waveguides and superconducting nanowire single-photon detectors (SNSPDs) [3], also with hybrid sources to improve coincidence rates and HOM visibility [4], [5].
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.
High-rate entanglement generation is essential for the realization of practical quantum repeaters. To this end, frequency multiplexing of the photons employed is an effective approach. In particular, schemes using cavity-enhanced spontaneous parametric down-conversion (cSPDC) as a photon-pair source have been proposed. In this study, toward a theoretical performance evaluation of frequency-multiplexed quantum repeaters based on cSPDC, we derive an approximate expression for the quantum state of the frequency-multiplexed photons, where each frequency mode is treated as an independent two-mode squeezed vacuum (TMSV) state. Using this expression, we calculate the heralding probability and fidelity of entanglement generation for several cases in a single-photon interference scheme using frequency multiplexing with cSPDC. Our results demonstrate that by multiplexing approximately 100 modes, the heralding probability improves to approximately 98% for an elementary link distance LEL=25kmL_\mathrm{EL}=25 \mathrm{km}LEL​=25km, even in scenarios where the fidelity exceeds 0.9 across all modes. Furthermore, for LEL=100kmL_\mathrm{EL}=100 \mathrm{km}LEL​=100km, we show that the heralding probability, which was approximately 0.7% in the single-mode case, increases to about 38% under the condition that the fidelity remains 0.9 or higher. These analytical results demonstrate the effectiveness of employing cSPDC as a photon-pair source for quantum repeaters.
We explore the suitability of a virtually imaged phased array as a spectral-to-spatial mode-mapper (SSMM) for applications in quantum communication such as a quantum repeater. To this end, we demonstrate spectrally resolved Hong-Ou-Mandel (HOM) interference with weak coherent states (WCSs). Spectral sidebands are generated on a common optical carrier, and WCSs are prepared in each spectral mode and sent to a beam splitter followed by two SSMMs and two single-photon detectors, allowing us to measure spectrally resolved HOM interference. We show that the so-called HOM dip can be observed in the coincidence detection pattern of matching spectral modes with visibilities as high as 45% (maximum 50% for WCSs). For unmatched modes, the visibility drops significantly, as expected. Due to the similarity between HOM interference and a linear-optics Bell-state measurement (BSM), this simple optical arrangement figures as a candidate for the implementation of a spectrally resolved BSM. Finally, we simulate the secret key generation rate using current and state-of-the-art parameters in a measurement-device-independent quantum key distribution scenario and explore the trade-off between rate and complexity of a spectrally multiplexed quantum communication link.
We explore the suitability of a Virtually-Imaged Phased Array (VIPA) as a Spectral-to-Spatial Mode-Mapper (SSMM) for applications in quantum communication such as a quantum repeater. To this end we demonstrate spectrally-resolved two-photon "Hong-Ou-Mandel" (HOM) interference. Spectral sidebands are generated on a common optical carrier and weak coherent pulses are prepared in each spectral mode. The pulses are subsequently sent to a beamsplitter followed by two SSMMs and two single-photon detectors, allowing us to measure spectrally-resolved HOM interference. We show that the so-called HOM dip can be observed in the coincidence detection pattern of matching spectral modes with visibilities as high as 45% (with the maximum being 50%). For unmatched modes, the visibility drops significantly, as expected. Due to the similarity between HOM interference and a linear-optics Bell-state measurement (BSM), this establishes this simple optical arrangement as a candidate for the implementation of a spectrally-resolved BSM. Finally, we simulate the secret key generation rate using current and state-of-the-art parameters in a Measurement-Device Independent Quantum Key Distribution scenario and explore the trade-off between rate and complexity in the context of a spectrally-multiplexed quantum communication link.
Quantum entanglement is a vital resource in quantum information processing. High-dimensional quantum entanglement offers advantages that classical systems cannot surpass, particularly in enhancing channel capacity, improving system noise resilience, and increasing sensitivity to external environments. The construction of multimode entanglement in the spectral domain is well-suited for fiber-optic systems. Here, we present a straightforward scheme for generating multimode frequency-bin entanglement using a semiconductor chip through a simple mode conversion. A general model for Hong–Ou–Mandel (HOM) interference with a multimode frequency-bin entangled state is presented and applied to the experiments. The multimode entangled photons we produced exhibit HOM interference with a high-visibility beating pattern, demonstrating a strong relationship with the mode number, mode spacing, and the profile of the single mode. Building on the Fisher information analysis, we explore the relationship between the features in multimode entangled state interference traces and the precision of interferometric measurements even in the presence of experimental nonidealities. This work may deepen the understanding of multimode frequency-bin entanglement and advance the application of multimode HOM interference in quantum sensing.