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 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.
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.
A high visibility Hong-Ou-Mandel (HOM) interference between two independently prepared photons plays an important role in various photonic quantum information processing. In a standard HOM experiment using photons generated by pulse-pumped spontaneous parametric down conversion (SPDC), larger detection time windows than the coherence time of photons have been employed for measuring the HOM visibility and/or drawing the HOM dip. If large amounts of stray photons continuously exist within the detection time windows, employing small detection time windows is favorable for reducing the effect of background noises. Especially, such a setup is helpful for the HOM experiment using continuous wave (cw)-pumped SPDC and the time-resolved coincidence measurement. Here we argue that the method for determining the HOM visibility used in the previous cw experiments tends to suffer from distortion arising from biased contribution of the background noises. We then present a new method with unbiased treatment of the cw backgrounds. By using this method, we experimentally demonstrate a high visibility HOM interference of two heralded telecom photons independently generated by SPDC with employing cw pump light. An observed HOM visibility is 0.87 ± 0.04, which is as high as those observed by using pulse-pumped SPDC photons.
Hong-Ou-Mandel interference between independent photon sources (HOMI-IPS) plays an important role in quantum information processing. A variety of HOMI-IPS experiments have been demonstrated at near-infrared wavelengths or telecom wavelengths [1]. In all the previous HOMI-IPS experiments, the HOM dips are obtained by recording the four-fold coincidence counts as a function of the temporal delay. However, the spectral correlation during the interference is omitted, partially due to technical difficulties, e.g., the acquisition time is too long for measuring a joint spectral distribution. Spectral information, as the conjugate of the temporal information in the Fourier transformation, is definitely of great importance and should be investigated. Very recently, a new technique of spectral correlation measurement in a HOM interference has been developed by Gerrits, et al [2]. This technique has the merits of high speed and high resolution, therefore, has been used as a powerful tool to analyse the spectral correlation in a HOM interference between signal and idler photons from one spontaneous parametric down conversion (SPDC) source. In this work, we measure the joint spectral distribution in HOMI-IPS using the new technique developed in [2]. The experimental setup is shown in Fig. 1 (Left). The two independent sources are based on SPDC from two 30-mm-long periodically poled KTiOPO4 (PPKTP) crystals pumped by picosecond laser pulses (76 MHz, 792 nm, temporal duration ~ 2 ps). In Fig. 1 (Left), the dispersion compensation fiber model (DCFMs), the superconducting nanowire single-photon detectors (SNSPDs) [3,4,5] and the time interval analyzer (TIA) constitute a fiber spectral analyzer [6]. Fig. 1(Right: (a)) is the measured four-fold HOM interference between signal1 and signal2, with idler1 and idler2 as heralders. Without subtraction of any background counts, the raw visibility of the HOM dip is 69.9±3.2%, which is consistent with our previous results in [1,7,8]. Fig. 1(Right: (b)-(g)) are the measured joint spectral intensities at different delay positions. The splitting phenomenon in the joint spectral distribution is clearly observed. The experimental results agree well with our theoretical simulations. This experiment not only can deepen our understanding of HOMI-IPS from the viewpoint of spectral domain, but also can be used to improve the visibility of HOMI-IPS by temporal filtering.
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 (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 Hong-Ou-Mandel (HOM) effect is a quintessential process in various quantum information technologies and quantum optics applications. In this work, we investigate multi-photon interference, developing a model for the simultaneous characterization of polarization and spectro-temporal mode mismatch on the coincidence probabilities including the effects of realistic imperfections of devices used in HOM experiments. We also study the coincidence probability for coherent states as a function of source intensity, as well as spectro-temporal and polarization mismatch of the incident beams. We apply our model to the case of multi-photon interference from independent sources and analyze the consequences of mode mismatch in various instances that occur in quantum networking including entanglement swapping, quantum key distribution, quantum sensing, quantum optical classification, and photonic quantum computing.