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Physical Review Letters

Spectral Hong-Ou-Mandel Effect between a Heralded Single-Photon State and a Thermal Field: Multiphoton Contamination and the Nonclassicality Threshold

Anahita Khodadad Kashi, Lucia Caspani, Michael Kues

Published Dec 4, 2023• 7 citations
Publisher

Abstract

The Hong-Ou-Mandel (HOM) effect is crucial for quantum information processing, and its visibility determines the system's quantum-classical characteristics. In an experimental and theoretical study of the spectral HOM effect between a thermal field and a heralded single-photon state, we demonstrate that the HOM visibility varies dependent on the relative photon statistics of the interacting fields. Our findings reveal that multiphoton components in a heralded state get engaged in quantum interference with a thermal field, resulting in improved visibilities at certain mean photon numbers. We derive a theoretical relationship for the HOM visibility as a function of the mean photon number of the thermal field and the thermal part of the heralded state. We show that the nonclassicality degree of a heralded state is reflected in its HOM visibility with a thermal field; our results establish a lower bound of 41.42% for the peak visibility, indicating the minimum assignable degree of nonclassicality to the heralded state. This research enhances our understanding of the HOM effect and its application to high-speed remote secret key sharing, addressing security concerns due to multiphoton contamination in heralded states.

DOI
10.1103/physrevlett.131.233601

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The Hong-Ou-Mandel (HOM) effect is crucial for quantum information processing, and its visibility determines the system's quantum-classical characteristics. In an experimental and theoretical study of the spectral HOM effect between a thermal field and a heralded single-photon state, we demonstrate that the HOM visibility varies dependent on the relative photon statistics of the interacting fields. Our findings reveal that multiphoton components in a heralded state get engaged in quantum interference with a thermal field, resulting in improved visibilities at certain mean photon numbers. We derive a theoretical relationship for the HOM visibility as a function of the mean photon number of the thermal field and the thermal part of the heralded state. We show that the nonclassicality degree of a heralded state is reflected in its HOM visibility with a thermal field; our results establish a lower bound of 41.42% for the peak visibility, indicating the minimum assignable degree of nonclassicality to the heralded state. This research enhances our understanding of the HOM effect and its application to high-speed remote secret key sharing, addressing security concerns due to multiphoton contamination in heralded states.
The heralding technique has been widely deployed as a statistical approach to approximate deterministic single-photon states from the spontaneous parametric down-conversion (SPDC) process. As necessary for the two-photon Hong-Ou-Mandel (HOM) effect, the single frequency mode preparation of heralded single-photon states – which can be achieved by removing frequency correlations – introduces thermal characteristics to the heralded state, whose impact on the HOM visibility has not been explicitly studied so far.
Spectral Hong-Ou-Mandel effect is experimentally revealed between a thermal field and a heralded state. We demonstrate that multi-photon components in heralded state get engaged in quantum interference which is manifested in improved visibilities for certain mean photon numbers of the thermal field. A theoretical relationship is derived for the visibility, showing its compound dependency on the mean photon number per pulse period within the thermal field and the thermal part of the heralded state. Relying on pulsed excitation, we demonstrate an experimental approach for time-efficient acquisition of visibility. The results of this research are of potential application to high-speed remote secret key-sharing and combating the security gaps arising from multi-photon contamination.
Hong–Ou–Mandel (HOM) interference is a standard method for characterizing photon indistinguishability. However, in practical systems, the measured interference visibility is not solely determined by intrinsic spectral–temporal mismatch but can also be affected by photon-number statistics, multiphoton background, and technical noise. Here, we establish an observable-level framework for HOM interference in practical sources. Within this framework, under stationary-field and fixed-detection conditions, the measured coincidence rate is decomposed into a delay-dependent interference term and a stationary background term that is independent of the HOM interference. The former is described by an effective spectral overlap function G(τ), while the latter mainly originates from source statistics and additive imperfections. This separation shows that the dip profile and intrinsic depth are governed by overlap-limited interference, whereas the observed visibility can be further degraded by statistical and external backgrounds. For single-photon and weak coherent-state inputs, G(τ) represents the effective temporal–spectral mode overlap. For the stationary thermal field, its delay-dependent envelope can be related to the first-order temporal coherence function g(1)(τ), whereas photon bunching contributes separately through g2(0). We further clarify that post-selection suppresses background and reveals intrinsic interference more directly but cannot improve the intrinsic spectral–temporal overlap. This framework provides a unified basis for distinguishing genuine indistinguishability loss from measurement-induced visibility degradation.
Hong-Ou-Mandel (HOM) interference between independent photon sources (HOMI-IPS) is the fundamental block for quantum information processing. All the previous HOMI-IPS experiments were carried out in time-domain, however, the spectral information during the interference was omitted. Here, we investigate the HOMI-IPS in spectral domain using the recently developed fast fiber spectrometer, and demonstrate the spectral distribution during the HOM interference between two heralded single-photon sources, and two thermal sources. This experiment not only can deepen our understanding of HOMI-IPS from the viewpoint of spectral domain, but also presents a tool to test the theoretical predictions of HOMI-IPS using spectrally engineered sources.
Hong-Ou-Mandel (HOM) interference is one of the most important experimental phenomena in quantum optics. It has drawn considerable attention with respect to quantum cryptography and quantum communication because of the advent of the measurement device independent (MDI) quantum key distribution (QKD) protocol. Here, we realize HOM interference, having a visibility of approximately 38.1%, using two independent heralded single-photon sources (HSPSs). The HOM interference between two independent HSPSs is a core technology for realizing the long-distance MDI QKD protocol, the quantum coin-tossing protocol, and other quantum cryptography protocols.
The Hong-Ou-Mandel (HOM) effect, an effective two-photon interference phenomenon, is a cornerstone of quantum optics and a key tool for linear optical quantum information processing. While the HOM effect has been extensively studied both theoretically and experimentally for various photonic quantum states, particularly in the spectral domain, detailed overviews of its behaviour for structured photons - those with complex spatial profiles - under arbitrary spatial mode measurement schemes are still lacking. This tutorial aims to fill this gap by providing a comprehensive theoretical analysis of the HOM effect for structured photons, including an arbitrary mode projection on quantum interference outcomes. The tutorial also provides analytical, closed-form expressions of the HOM visibility under different measurement conditions.