Two-photon interference: the Hong-Ou-Mandel effect

Non-classicality and the effect of one photon

The quantum interference effects of mixing the most non-classical states of light, number states, with the most classical-like of pure field states, the coherent state, are investigated. We demonstrate how the non-classicality of a single photon when mixed with a coherent field can transform the statistical properties of the output and further demonstrate that the entanglement of the output is independent of the coherent state amplitude.This article is part of the theme issue 'The quantum theory of light'.

Enhanced Control of Single-Molecule Emission Frequency and Spectral Diffusion

The Stark effect provides a powerful method to shift the spectra of molecules, atoms, and electronic transitions in general, becoming one of the simplest and most straightforward ways to tune the frequency of quantum emitters by means of a static electric field. At the same time, in order to reduce the emitter sensitivity to charge noise, inversion symmetric systems are typically designed, providing a stable emission frequency with a quadratic-only dependence on the applied field. However, such nonlinear behavior might be reflected in correlations between the tuning ability and unwanted spectral fluctuations. Here, we provide experimental evidence of this trend using molecular quantum emitters in the solid state cooled down to liquid helium temperatures. We finally combine the electric field generated by electrodes, which is parallel to the molecule's induced dipole, with optically excite long-lived charge states acting in the perpendicular direction. Based on the anisotropy of the molecule's polarizability, our two-dimensional control of the local electric field allows us not only to tune the emitter's frequency but also to sensibly suppress the spectral instabilities associated with field fluctuations.

Entanglement-induced collective many-body interference

Entanglement and interference are both hallmark effects of quantum physics. Particularly rich dynamics arise when multiple (at least partially) indistinguishable particles are subjected to either of these phenomena. By combining both entanglement and many-particle interference, we propose an interferometric setting through which N-particle interference can be observed, while any interference of lower orders is strictly suppressed. We experimentally demonstrate this effect in a four-photon interferometer, where the interference is nonlocal, in principle, as only pairs of photons interfere at two separate and independent beam splitters. A joint detection of all four photons identifies a high-visibility interference pattern varying as a function of their collective four-particle phase, a genuine four-body property.

Tunable single-photon emitters in 2D materials

Single-photon emitters (SPEs) hold the key to many quantum technologies including quantum computing. In particular, developing a scalable array of identical SPEs can play an important role in preparing single photons - crucial resources for computation - at a high rate, allowing to improve the computational capacity. Recently, different types of SPEs have been found in various 2D materials. Towards realizing scalable SPE arrays in 2D materials for quantum computation, it is required to develop tunable SPEs that can produce identical photons by precisely controlling emission properties. Here, we present a brief review of the recent progress on various tuning methods in different 2D materials. Firstly, we discuss the operation principle of different 2D SPEs along with their unique characteristics. Secondly, we introduce various dynamic strain engineering methods for tuning the emission wavelengths in 2D SPEs. We also present several electric field-induced wavelength tuning methods for 2D SPEs. Lastly, we discuss the outlook of dynamically tunable 2D SPEs towards scalable 2D SPE arrays for realizing practical quantum photonics applications.

Cavity-enhanced photon indistinguishability at room temperature and telecom wavelengths

Indistinguishable single photons in the telecom-bandwidth of optical fibers are indispensable for long-distance quantum communication. Solid-state single photon emitters have achieved excellent performance in key benchmarks, however, the demonstration of indistinguishability at room-temperature remains a major challenge. Here, we report room-temperature photon indistinguishability at telecom wavelengths from individual nanotube defects in a fiber-based microcavity operated in the regime of incoherent good cavity-coupling. The efficiency of the coupled system outperforms spectral or temporal filtering, and the photon indistinguishability is increased by more than two orders of magnitude compared to the free-space limit. Our results highlight a promising strategy to attain optimized non-classical light sources.

Estimation with Ultimate Quantum Precision of the Transverse Displacement between Two Photons via Two-Photon Interference Sampling Measurements

We present a quantum sensing scheme achieving the ultimate quantum sensitivity in the estimation of the transverse displacement between two photons interfering at a balanced beam splitter, based on transverse-momentum sampling measurements at the output. This scheme can possibly lead to enhanced high-precision nanoscopic techniques, such as superresolved single-molecule localization microscopy with quantum dots, by circumventing the requirements in standard direct imaging of camera resolution at the diffraction limit, and of highly magnifying objectives. Interestingly, we show that our interferometric technique achieves the ultimate spatial precision in nature irrespectively of the overlap of the two displaced photonic wave packets, while its precision is only reduced of a constant factor for photons differing in any nonspatial degrees of freedom. This opens a new research paradigm based on the interface between spatially resolved quantum interference and quantum-enhanced spatial sensitivity.

Photon Phase Delay Sensing with Sub-Attosecond Uncertainty

The application of statistical estimation theory to Hong-Ou-Mandel interferometry led to enticing results in terms of the detection limit for photon reciprocal delay and polarisation measurement. In the following paper, a fully fibre-coupled setup operating in the telecom wavelength region proves to achieve, for the first time, in common-path Hong-Ou-Mandel-based interferometry, a detection limit for photon phase delay at the zeptosecond scale. The experimental results are then framed in a theoretical model by calculating the Cramer-Rao bound (CRB) and, after comparison with the obtained experimental results, it is shown that our setup attains the optimal measurement, nearly saturating CRB.

Accessing the spectrum of a single-photon by the Hong-Ou-Mandel interference

We present and experimentally demonstrate a method for determining the spectral characterization of a single-photon state. This technique is based on the Hong-Ou-Mandel interference between a well-defined weak coherent state and a measured single-photon state. We estimate the spectrum of the single-photon state by fitting the measured interference dip with proposed model and least square method. Our method is particularly useful for characterising spectral property the single-photon state. It opens a way for robust and efficient on-line monitoring the single-photon emitters.

Fast simulation for multi-photon, atomic-ensemble quantum model of linear optical systems addressing the curse of dimensionality

Photons are elementary particles of light in quantum mechanics, whose dynamics can be difficult to gain detailed insights, especially in complex systems. Simulation is a promising tool to resolve this issue, but it must address the curse of dimensionality, namely, that the number of bases increases exponentially in the number of photons. Here we mitigate this dimensionality scaling by focusing on optical systems composed of linear optical objects, modeled as an ensemble of two-level atoms. We decompose the time evolutionary operator on multiple photons into a group of time evolution operators acting on a single photon. Since the dimension of a single-photon time evolution operator is exponentially smaller than that of a multi-photon one in the number of photons, the decomposition enables the multi-photon simulations to be performed at a much lower computational cost. We apply this method to basic single- and multi-photon phenomena, such as Hong-Ou-Mandel interference and violation of the Bell-CHSH inequality, and confirm that the calculated properties are quantitatively comparable to the experimental results. Furthermore, our method visualizes the spatial propagation of photons hence provides insights that aid experiment designs for quantum-enabled technologies.

Towards quantum telescopes: demonstration of a two-photon interferometer for precision astrometry

Classical optical interferometry requires maintaining live, phase-stable links between telescope stations. This requirement greatly adds to the cost of extending to long baseline separations and limits on baselines will in turn limit the achievable angular resolution. Here we describe a novel type of two-photon interferometer for astrometry, which uses photons from two separate sky sources and does not require an optical link between stations. Such techniques may make large increases in interferometric baselines practical, even by orders of magnitude, with a corresponding improvement in astrometric precision benefiting numerous fields in astrophysics. We tested a benchtop analogue version of the two-source interferometer and unambiguously observe correlated behavior in detections of photon pairs from two thermal light sources, in agreement with theoretical predictions. This work opens new possibilities in future astronomical measurements.

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

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.

Comparison of multi-mode Hong-Ou-Mandel interference and multi-slit interference

Hong-Ou-Mandel (HOM) interference of multi-mode frequency entangled states plays a crucial role in quantum metrology. However, as the number of modes increases, the HOM interference pattern becomes increasingly complex, making it challenging to comprehend intuitively. To overcome this problem, we present the theory and simulation of multi-mode-HOM interference (MM-HOMI) and compare it to multi-slit interference (MSI). We find that these two interferences have a strong mapping relationship and are determined by two factors: the envelope factor and the details factor. The envelope factor is contributed by the single-mode HOM interference (single-slit diffraction) for MM-HOMI (MSI). The details factor is given by sin (Nx)/sin (x) ([sin (Nv)/sin (v)]2) for MM-HOMI (MSI), where N is the mode (slit) number and x (v) is the phase spacing of two adjacent spectral modes (slits). As a potential application, we demonstrate that the square root of the maximal Fisher information in MM-HOMI increases linearly with the number of modes, indicating that MM-HOMI is a powerful tool for enhancing precision in time estimation. We also discuss multi-mode Mach-Zehnder interference, multi-mode NOON-state interference, and the extended Wiener-Khinchin theorem. This work may provide an intuitive understanding of MM-HOMI patterns and promote the application of MM-HOMI in quantum metrology.

Ontological indistinguishability as a central tenet of quantum theory

Quantum indistinguishability directly relates to the philosophical debate on the notions of identity and individuality. They are crucial for our understanding of multipartite quantum systems. Furthermore, the correct interpretation of this feature of quantum theory has implications that transcend fundamental science and philosophy, given that quantum indistinguishability is a resource in quantum information theory. Most of the conceptual analysis of quantum indistinguishability is restricted to studying the permutational invariance of quantum states, the concomitant quantum statistics and their entanglement. Here, we analyse the role of indistinguishability and non-individuality in other areas of quantum theory. We start by analysing how a very peculiar use of indistinguishability underlies Feynman's rules for summing amplitudes in interference phenomena. Next, we study how quantum indistinguishability is underestimated in several topics of debate in the quantum physics literature, such as the Einstein-Podolsky-Rosen argument, Bell's inequalities and the Bell-Kochen-Specker theorem. Finally, we argue that an ontology of truly indistinguishable entities can serve as a basis for a quantum ontology that can give interesting answers to the interpretational problems of quantum mechanics. We claim that, in addition to superposition, contextuality and entanglement, indistinguishability (understood in a robust ontological sense) is one of the central features of quantum physics. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.

Attosecond-Level Delay Sensing via Temporal Quantum Erasing

Traditional Hong-Ou-Mandel (HOM) interferometry, insensitive to photons phase mismatch, proved to be a rugged single-photon interferometric technique. By introducing a post-beam splitter polarization-dependent delay, it is possible to recover phase-sensitive fringes, obtaining a temporal quantum eraser that maintains the ruggedness of the original HOM with enhanced sensitivity. This setup shows promising applications in biological sensing and optical metrology, where high sensitivity requirements are coupled with the necessity to keep light intensity as low as possible to avoid power-induced degradation. In this paper, we developed a highly sensitive single photon birefringence-induced delay sensor operating in the telecom range (1550 nm). By using a temporal quantum eraser based on common path Hongr-Ou-Mandel Interferometry, we were able to achieve a sensitivity of 4 as for an integration time of 2·104 s.

Time-Resolved Line Shapes of Single Quantum Emitters via Machine Learned Photon Correlations

Solid-state single-photon emitters (SPEs) are quantum light sources that combine atomlike optical properties with solid-state integration and fabrication capabilities. SPEs are hindered by spectral diffusion, where the emitter's surrounding environment induces random energy fluctuations. Timescales of spectral diffusion span nanoseconds to minutes and require probing single emitters to remove ensemble averaging. Photon correlation Fourier spectroscopy (PCFS) can be used to measure time-resolved single emitter line shapes, but is hindered by poor signal-to-noise ratio in the measured correlation functions at early times due to low photon counts. Here, we develop a framework to simulate PCFS correlation functions directly from diffusing spectra that match well with experimental data for single colloidal quantum dots. We use these simulated datasets to train a deep ensemble autoencoder machine learning model that outputs accurate, noiseless, and probabilistic reconstructions of the noisy correlations. Using this model, we obtain reconstructed time-resolved single dot emission line shapes at timescales as low as 10 ns, which are otherwise completely obscured by noise. This enables PCFS to extract optical coherence times on the same timescales as Hong-Ou-Mandel two-photon interference, but with the advantage of providing spectral information in addition to estimates of photon indistinguishability. Our machine learning approach is broadly applicable to different photon correlation spectroscopy techniques and SPE systems, offering an enhanced tool for probing single emitter line shapes on previously inaccessible timescales.

Two electrons interacting at a mesoscopic beam splitter

The nonlinear response of a beam splitter to the coincident arrival of interacting particles enables numerous applications in quantum engineering and metrology. Yet, it poses considerable challenges to control interactions on the individual particle level. Here, we probe the coincidence correlations at a mesoscopic constriction between individual ballistic electrons in a system with unscreened Coulomb interactions and introduce concepts to quantify the associated parametric nonlinearity. The full counting statistics of joint detection allows us to explore the interaction-mediated energy exchange. We observe an increase from 50% up to 70% in coincidence counts between statistically indistinguishable on-demand sources and a correlation signature consistent with the independent tomography of the electron emission. Analytical modelling and numerical simulations underpin the consistency of the experimental results with Coulomb interactions between two electrons counterpropagating in a quadratic saddle potential. Coulomb repulsion energy and beam splitter dispersion define a figure of merit, which in this experiment is demonstrated to be sufficiently large to enable future applications, such as single-shot in-flight detection and quantum logic gates.

Characterization of two-photon interference between a weak coherent state and a heralded single photon state

We experimentally investigate two-photon interference between a weak coherent state and a heralded single-photon state, producing from a spontaneous parametric down conversion. Both the unequal spectrum linewidth and average photon number ratio in a given time interval are considered in our model. We obtained excellent agreement between our experimental data and prediction from our model. Furthermore, the range of observing high visibility two-photon interference is significantly extended by isolating coincidence events from two-photon contributions in the weak coherent state. These results may throw some new light on quantum information technology when the two-photon interference with independent sources is required.

Hong-Ou-Mandel interference of longitudinal spatially coherent beams

The Hong-Ou-Mandel (HOM) interference of two light beams having different longitudinal spatial coherence properties is investigated theoretically and experimentally. The normalized second-order correlation function (g ⁽²⁾) is determined for the interfering photons from two sources of different angular widths using Feynman's path integral theory. We find that the difference in angular width of the sources has an explicit impact on the HOM interference pattern, which can be quantified through the visibility and full width at half maxima of the HOM dip. The effect of distinguishability of the interfering longitudinally spatially coherent beams on the HOM dip is verified experimentally and is analogous to non-classical HOM interference. The magnitude of the angular width of beams manifested through the difference in angular width has a significant impact. Along with the difference of two sources, this HOM scheme is sensitive to the angular spectrum width of each source. The enhanced sensitivity can be useful in the remote sensing of objects and beams in metrological applications. This work can play a significant role in fundamental and applied physics.

Hong-Ou-Mandel Interference between Two Hyperentangled Photons Enables Observation of Symmetric and Antisymmetric Particle Exchange Phases

Two-photon Hong-Ou-Mandel (HOM) interference is a fundamental quantum effect with no classical counterpart. The existing research on two-photon interference was mainly limited in one degree of freedom (DOF); hence, it is still a challenge to realize quantum interference in multiple DOFs. Here, we demonstrate HOM interference between two hyperentangled photons in two DOFs of polarization and orbital angular momentum (OAM) for all 16 hyperentangled Bell states. We observe hyperentangled two-photon interference with a bunching effect for ten symmetric states (nine boson-boson states and one fermion-fermion state) and an antibunching effect for six antisymmetric states (three boson-fermion states and three fermion-boson states). More interestingly, expanding the Hilbert space by introducing an extra DOF for two photons enables one to transfer the unmeasurable external phase in the initial DOF to a measurable internal phase in the expanded two DOFs. We directly measured the symmetric exchange phases being 0.012±0.002, 0.025±0.002, and 0.027±0.002 in radian for the three boson states in OAM and the antisymmetric exchange phase being 0.991π±0.002 in radian for the other fermion state, as theoretical predictions. Our Letter may not only pave the way for more wide applications of quantum interference, but also develop new technologies by expanding Hilbert space in more DOFs.

Probing ultra-fast dephasing via entangled photon pairs

We demonstrate how the Hong-Ou-Mandel (HOM) interference with polarization-entangled photons can be used to probe ultrafast dephasing. We can infer the optical properties like the real and imaginary parts of the complex susceptibility of the medium from changes in the position and the shape of the HOM dip. From the shift of the HOM dip, we are able to measure 22 fs dephasing time using a continuous-wave (CW) laser even with optical loss > 97 %, while the HOM dip visibility is maintained at 92.3 % (which can be as high as 96.7 %). The experimental observations, which are explained in terms of a rigorous theoretical model, demonstrate the utility of HOM interference in probing ultrafast dephasing.

Quantum Interference between Nonidentical Single Particles

Quantum interference between identical single particles reveals the intrinsic quantum statistic nature of particles, which could not be interpreted through classical physics. Here, we demonstrate quantum interference between nonidentical bosons using a generalized beam splitter based on a quantum memory. The Hong-Ou-Mandel type interference between single photons and single magnons with high visibility is demonstrated, and the crossover from the bosonic to fermionic quantum statistics is observed by tuning the beam splitter to be non-Hermitian. Moreover, multiparticle interference that simulates the behavior of three fermions by three input photons is realized. Our work extends the understanding of the quantum interference effects and demonstrates a versatile experimental platform for studying and engineering quantum statistics of particles.

Generalized approach to quantum interference in lossy N-port devices via a singular value decomposition

Modeling quantum interference in the presence of dissipation is a critical aspect of quantum technologies. Including dissipation into the model of a linear device enables for assessing the detrimental impact of photon loss, as well as for studying dissipation-driven quantum state transformations. However, establishing the input-output relations characterizing quantum interference at a general lossy N-port network poses important theoretical challenges. Here, we propose a general procedure based on the singular value decomposition (SVD), which allows for the efficient calculation of the input-output relations for any arbitrary lossy linear device. In addition, we show how the SVD provides an intuitive description of the principle of operation of linear optical devices. We illustrate the applicability of our method by evaluating the input-output relations of popular reciprocal and nonreciprocal lossy linear devices, including devices with singular and nilpotent scattering matrices. Our method also enables the analysis of quantum interference in large lossy networks, as we exemplify with the study of an N-port epsilon-near-zero (ENZ) hub. We expect that our procedure will motivate future research on quantum interference in complex devices, as well as the realistic modelling of photon loss in linear lossy devices.

High-speed imaging of spatiotemporal correlations in Hong-Ou-Mandel interference

The Hong-Ou-Mandel interference effect lies at the heart of many emerging quantum technologies whose performance can be significantly enhanced with increasing numbers of entangled modes one could measure and thus utilize. Photon pairs generated through the process of spontaneous parametric down conversion are known to be entangled in a vast number of modes in the various degrees of freedom (DOF) the photons possess such as time, energy, and momentum, etc. Due to limitations in detection technology and techniques, often only one such DOFs can be effectively measured at a time, resulting in much lost potential. Here, we experimentally demonstrate, with the aid of a time tagging camera, high speed measurement and characterization of two-photon interference. With a data acquisition time of only a few seconds, we observe a bi-photon interference and coalescence visibility of ∼64% with potentially up to ∼2 × 10³ spatial modes. These results open up a route for practical applications of using the high dimensionality of spatiotemporal DOF in two-photon interference, and in particular, for quantum sensing and communication.

Two-photon interferences of weak coherent lights

Multiphoton interference is an important phenomenon in modern quantum mechanics and experimental quantum optics, and it is fundamental for the development of quantum information science and technologies. Over the last three decades, several theoretical and experimental studies have been performed to understand the essential principles underlying such interference and to explore potential applications. Recently, the two-photon interference (TPI) of phase-randomized weak coherent states has played a key role in the realization of long-distance quantum communication based on the use of classical light sources. In this context, we investigated TPI experiments with weak coherent pulses at the single-photon level and quantitatively analyzed the results in terms of the single- and coincidence-counting rates and one- and two-photon interference-fringe shapes. We experimentally examined the Hong–Ou–Mandel-type TPI of phase-randomized weak coherent pulses to compare the TPI effect with that of correlated photons. Further experiments were also performed with two temporally- and spatially separated weak coherent pulses. Although the observed interference results, including the results of visibility and fringe shape, can be suitably explained by classical intensity correlation, the physics underlying the TPI effect needs to be interpreted as the interference between the two-photon states at the single-photon level within the utilized interferometer. The results of this study can provide a more comprehensive understanding of the TPI of coherent light at the single-photon level.

High speed imaging of spectral-temporal correlations in Hong-Ou-Mandel interference

In this work we demonstrate spectral-temporal correlation measurements of the Hong-Ou-Mandel (HOM) interference effect with the use of a spectrometer based on a photon-counting camera. This setup allows us to take, within seconds, spectral temporal correlation measurements on entangled photon sources with sub-nanometer spectral resolution and nanosecond timing resolution. Through post processing, we can observe the HOM behaviour for any number of spectral filters of any shape and width at any wavelength over the observable spectral range. Our setup also offers great versatility in that it is capable of operating at a wide spectral range from the visible to the near infrared and does not require a pulsed pump laser for timing purposes. This work offers the ability to gain large amounts of spectral and temporal information from a HOM interferometer quickly and efficiently and will be a very useful tool for many quantum technology applications and fundamental quantum optics research.