A general framework for multimode Gaussian quantum optics and photo-detection: application to Hong-Ou-Mandel interference with filtered heralded single photon sources
Oliver F. Thomas, Will McCutcheon, Dara P. S. McCutcheon
The challenging requirements of large scale quantum information processing using parametric heralded single photon sources involves maximising the interference visibility whilst maintaining an acceptable photon generation rate. By developing a general theoretical framework that allows us to include large numbers of spatial and spectral modes together with linear and non-linear optical elements, we investigate the combined effects of spectral and photon number impurity on the measured Hong--Ou--Mandel interference visibility of parametric photon sources, considering both threshold and number resolving detectors, together with the effects of spectral filtering. We find that for any degree of spectral impurity, increasing the photon generation rate necessarily decreases the interference visibility, even when using number resolving detection. While tight spectral filtering can be used to enforce spectral purity and increased interference visibility at low powers, we find that the induced photon number impurity results in a decreasing interference visibility and heralding efficiency with pump power, while the maximum generation rate is also reduced.
New methods are proposed to characterize the spectral-temporal distribution of single photons. The presented protocols take advantage of spectral filtering, frequency entanglement between two single photons the one of interest and a reference, followed by the generalized Hong, Ou and Mandel interferometer. The measurement of the coincidence probability in these different schemes reveals the chronocyclic Wigner, the pseudo-Wigner distribution and the spectrogram at the single-photon level.
The question whether two indistinguishable particles are bosons or fermions can be answered by observing the Hong-Ou-Mandel effect on a beam splitter. However, already for three particles one can consider symmetries that are neither bosonic nor fermionic. In this work, we describe a simple method of identifying them experimentally and propose a measure of a genuine multipartite indistinguishability.
We show that sub-attosecond delays and sub-Angstrom optical path differences can be measured by using Hong-Ou-Mandel interference measurements with x-rays. We propose to use a system comprising a source based on spontaneous parametric down-conversion for the generation of broadband x-ray photon pairs and a multilayer-based interferometer. The correlation time of the photon pairs and the Hong-Ou-Mandel dip are shorter than 1 attosecond, hence the precision of the measurements is expected to be better than 0.1 attosecond. We anticipate that the scheme we describe in this work will lead to the de…
Hong-Ou-Mandel interferometers are valuable tools in many Quantum Information and Quantum Optics applications that require photon indistinguishability. The theoretical limit for the Hong-Ou-Mandel visibility is 0.5 for indistinguishable weak coherent photon states, but several device imperfections may hinder achieving this value experimentally. In this work, we examine the dependence of the interference visibility on various factors, including (i) detector side imperfections due to after-pulses, (ii) mismatches in the intensities and states of polarization of the input signals, and (iii) the o…
A peak in coincidence events has been observed in a modified Hong-Ou-Mandel interferometer fed with weak coherent states inside the region of overlapping wave-packets. The inversion of the usual interference pattern represented by the HOM dip is equally observed when the wave packets are frequency displaced. The higher rate of coincidences indicates that photons are more likely to take on different output paths of the interferometer. This effect was harnessed so a detection on one of the arms could herald the presence of a photon in the other. The second order autocorrelation function at zero …
We study how the information of the beam path is related to the Hong-Ou-Mandel interference with two pulsed light sources. Through a simple model in which two photons in the form of pulses pass a beamsplitter and are observed at two detectors, we investigate how, during the measurement process, information about the paths of the two photons can be erased. There are two ways to clear the information of the beam path, the first being that from the beginning, during the physical measurement process, the time information is not obtained. The other is after measuring the information, to erase the t…
We provide a statistically robust and accurate framework to measure and track the polarisation state of light employing Hong-Ou-Mandel interference. This is achieved by combining the concepts of maximum likelihood estimation and Fisher information applied to photon detection events. Such an approach ensures that the Cramér-Rao bound is saturated and changes to the polarisation state are established in an optimal manner. Using this method, we show that changes in the linear polarisation state can be measured with 0.6 arcminute precision (0.01 degrees).
The uses of a silicon-pixel camera with very good time resolution ($\sim$nanosecond) for detecting multiple, bunched optical photons is explored. We present characteristics of the camera and describe experiments proving its counting capabilities. We use a spontaneous parametric down-conversion source to generate correlated photon pairs, and exploit the Hong-Ou-Mandel interference effect in a fiber-coupled beam splitter to bunch the pair onto the same output fiber. It is shown that the time and spatial resolution of the camera enables independent detection of two photons emerging simultaneously…
We extensively discuss the Hong-Ou-Mandel experiment taking an original phase-space-based perspective. For this, we analyze time and frequency variables as quantum continuous variables in perfect analogy with position and momentum of massive particles or with the electromagnetic field's quadratures. We discuss how this experiment can be used to directly measure the time-frequency Wigner function and implement logical gates in these variables. We also briefly discuss the quantum/classical aspects of this experiment providing a general expression for intensity correlations that explicit the diff…
We consider realistic photodetection in a generalization of the Hong-Ou-Mandel experiment to the multimode case. The basic layout of this experiment underlies boson sampling -- a promising model of nonuniversal quantum computations. Peculiarities of photocounting probabilities in such an experiment witness important nonclassical properties of electromagnetic field related to indistinguishability of boson particles. In practice, these probabilities are changed from their theoretical values due to the imperfect ability of realistic detectors to distinguish numbers of bunched photons. We derive a…
We apply the theory of semiparametric estimation to a Hong-Ou-Mandel interference experiment with a spectrally entangled two-photon state generated by spontaneous parametric downconversion. Thanks to the semiparametric approach we can evaluate the Cramér-Rao bound and find an optimal estimator for a particular parameter of interest without assuming perfect knowledge of the two-photon wave function, formally treated as an infinity of nuisance parameters. In particular, we focus on the estimation of the Hermite-Gauss components of the marginal symmetrised wavefunction, whose Fourier transform go…
Over the last several decades, quantum entanglement has been intensively studied for potential applications in quantum information science. The Hong-Ou-Mandel (HOM) dip is the most important test tool for direct proof of entanglement between paired photons, whose coincidence detection results in anticorrelation due to photon bunching on a beam splitter. Although anticorrelation is due to destructive quantum interference between paired photons, a wavelength-sensitive interference fringe has never been observed in any HOM-type experiments. Here, a typical HOM dip is investigated for entangled ph…
We report on the observation of a high visibility Hong-Ou-Mandel interference of two heralded photons emitted from a spontaneous parametric down conversion~(SPDC) pumped by continuous-wave~(cw) light. A non-degenerate photon pair at 1541~nm and 1580~nm is generated by cw-pumped SPDC through a periodically poled lithium niobate waveguide. The heralded single photon at 1541~nm is prepared by the detection of the photon at 1580~nm. We performed the experiment of the Hong-Ou-Mandel interference between heralded single photons in separated time bins and observed a high visibility interference. All …
We develop a fully spatio-temporal numerical model, based on stochastic simulations, simulating the generation of spatio-temporal multimode spontaneous parametric down conversion, the propagation of the signal and idler beams through a Hong-Ou-Mandel interferometer and the detection of the outgoing beams with two separate detectors arrays. Spatial and temporal properties of the two-photon interference are investigated by measuring the spatial distribution of the momenta coincidence counts between the time integrated outgoing far-field images and a full spatio-temporal HOM dip is exhibited. Num…
We investigate the relation between indistinguishability and quantum entanglement in Hong- Ou-Mandel-interference experiments theoretically and relate these quantum mechanical principles to the theorem of entanglement monogamy. Employing Glaubers theory of quantum coherence we compute the detection statistics in HOM-interference of frequency entangled photons, and find a new additional term in the coincidence detection probability, which is related to the spectral indistinguishability of the considered photons that arises from finite bandwidth effects, and therefore is relevant in the limit of…
We demonstrate deterministic generation of two distinct collective excitations in one atomic ensemble, and we realize the Hong-Ou-Mandel interference between them. Using Rydberg blockade we create single collective excitations in two different Zeeman levels, and we use stimulated Raman transitions to perform a beam-splitter operation between the excited atomic modes. By converting the atomic excitations into photons, the two-excitation interference is measured by photon coincidence detection with a visibility of 0.89(6). The Hong-Ou-Mandel interference witnesses an entangled NOON state of the …
Quantum technologies based on the particle nature of a photon has been progressed over the last several decades, where the fundamental quantum feature of entanglement has been tested by Hong-Ou-Mandel (HOM) type anticorrelation as well as Bell-type nonlocal correlation. Mutually exclusive quantum natures of the wave-particle duality of a single photon have been intensively investigated to understand the fundamental physics of mysterious quantum nature. Here, we revisit the HOM-type quantum correlation to answer the question whether the HOM-type anticorrelation can be a test tool for quantum en…
Hong-Ou-Mandel interference is a cornerstone of optical quantum technologies. We explore both theoretically and experimentally how the nature of unwanted multi-photon components of single photon sources affect the interference visibility. We apply our approach to quantum dot single photon sources in order to access the mean wavepacket overlap of the single-photon component - an important metric to understand the limitations of current sources. We find that the impact of multi-photon events has thus far been underestimated, and that the effect of pure dephasing is even milder than previously ex…
Sources of entanglement are an enabling resource in quantum technology, and pushing the limits of generation rate and quality of entanglement is a necessary pre-requisite towards practical applications. Here, we present an ultra-bright source of polarization-entangled photon pairs based on time-reversed Hong-Ou-Mandel interference. By superimposing four pair-creation possibilities on a polarization beam splitter, pairs of identical photons are separated into two spatial modes without the usual requirement for wavelength distinguishability or non-collinear emission angles. Our source yields hig…
Quantum coupling between mechanical oscillators and atomic gases generating entanglement has been recently experimentally demonstrated using their subsequent interaction with light. The next step is to build a hybrid atom-mechanical quantum gate showing bosonic interference effects of single quanta in the atoms and oscillators. We propose an experimental test of Hong-Ou-Mandel interference between single phononic excitation and single collective excitation of atoms using the optical connection between them. A single optical pulse is sufficient to build a hybrid quantum-nondemolition gate to ob…
The well-known Hong-Ou-Mandel effect is revisited. Two physical reasons are discussed for the effect to be less pronounced or even to disappear: differing polarizations of photons coming to the beamsplitter and delay time of photons in one of two channels. For the latter we use the concepts of biphoton frequency and temporal wave functions depending, correspondingly, on two frequency continuous variables of photons and on two time variables $t_1$ and $t_2$ interpreted as the arrival times of photons to the beamsplitter. Explicit expressions are found for the probability densities and total pro…
Heralded single photons (HSPs) generated by spontaneous parametric down-conversion (SPDC) are useful resource to achieve various photonic quantum information processing. Given a large-scale experiment which needs multiple HSPs, increasing the generation rate with suppressing higher-order pair creation is desirable. One of the promising ways is to use a pump laser with a GHz-order repetition rate. In such a high repetition rate regime, however, single-photon detectors can only partially identify the pulses. Hence, we develop a simple model to consider that effect on the spectral purity, and exp…
A generalized multi-parameter Hong-Ou-Mandel interferometer is presented which extends the conventional "Mandel dip" configuration to the case where a symmetric biphoton source is used to monitor the contemporary presence of k independent time-delays. Our construction results in a two-input/two-output setup, obtained by concatenating 50:50 beam splitters with a collection of adjustable achromatic wave-plates. For k=1,2 and k=4 explicit examples can be exhibited that prove the possibility of uniquely linking the zero value of the coincidence counts registered at the output of the interferometer…
Two-photon intensity correlation of the Hong-Ou-Mandel (HOM) effect has been intensively studied over the last several decades for one of the most interesting quantum features. According to the particle nature of quantum mechanics, indistinguishable photon characteristics interacting on a beam splitter are the prerequisite of the photon bunching phenomenon. Here, a coherence approach based on the wave nature of a photon is used to interpret HOM effect based on entangled photon pairs. As a result, a complete solution of the HOM effect is derived from the coherence approach for the indistinguish…
Quality of individual photons and their ability to interfere is traditionally tested by measuring the Hong-Ou-Mandel photon bunching effect. However, this phase insensitive measurement only tests the particle aspect of the quantum interference. Motivated by these limitations, we formulate a witness capable of recognizing both the quality and the coherence of two photons from a single set of measurements. We exploit the conditional nonclassical squeezing which is sensitive to both the quality of the single photons and their indistinguishability and we show that it can be used to irectly reveal …
The Hong-Ou-Mandel effect lies at the heart of quantum interferometry, having multiple applications in the field of quantum information processing and no classical counterpart. Despite its popularity, only a few works have considered polarization-frequency interaction within the interferometer. In this paper, we fill this gap. Our system of interest is a general biphoton polarization state that experiences effective dephasing noise by becoming entangled with the same photons' frequency state, as the photons propagate through birefringent media. The photons then meet at a beam splitter, where e…
Entanglement is not only fundamental for understanding multipartite quantum systems but also generally useful for quantum information applications. Despite much effort devoted so far, little is known about minimal resources for detecting entanglement and also comparisons to tomography which reveals the full characterization. Here, we show that all entangled states can in general be detected in an experimental scheme that estimates the fidelity of two pure quantum states. An experimental proposal is presented with a single Hong-Ou-Mandel interferometry in which only two detectors are applied re…
We propose a method to perform the quantum state tomography (QST) of an $\mathit{n}$-partite qudit state embedded in single photons using the Hong-Ou-Mandel (HOM) interference between the target state and probe state. This method requires only passive beam splitters for the HOM interference and removes all active optical devices in the target modes to control the measurement bases needed in conventional QST. Hence, it is applicable to various degree of freedom of the target state without altering the measurement setup. Moreover, a faithful estimation is realized even with classical probe light…
We expand the two-photon Hong-Ou-Mandel (HOM) effect onto a higher-dimensional set of spatial modes and introduce an effect that allows controllable redistribution of quantum states over these modes using directionally unbiased linear-optical four-ports without post-selection. The original HOM effect only allows photon pairs to exit in two directions in space. But when accompanied by beam splitters and phase shifters, the result is a directionally controllable two-photon HOM effect in four spatial modes, with direction controlled by changing the phases in the system. This controllable quantum …
The Hong-Ou-Mandel effect provides a mechanism to determine the distinguishability of a photon pair by measuring the bunching rates of two photons interfering at a beam splitter. Of particular interest is the distinguishability in time, which can be used to probe a time delay. Photon detectors themselves give some timing information, however--while that resolution may dwarf that of an interferometric technique--typical analyses reduce the interference to a binary event, neglecting temporal information in the detector. By modelling detectors with number and temporal resolution we demonstrate a …
A modification of the standard Hong-Ou-Mandel interferometer is proposed which allows one to replicate the celebrated coincidence dip in the case of two-independent delay parameters. In the ideal case where such delays are sufficiently stable with respect to the mean wavelength of the pump source, properly symmetrized input bi-photon states allow one to pinpoint their values through the identification of a zero in the coincidence counts, a feature that cannot be simulated by semiclassical inputs having the same spectral properties. Besides, in the presence of fluctuating parameters the zero in…
Side-channel attacks on practical quantum key distribution systems compromise its security. Although some of these attacks can be taken into account, the general recipe of how to eliminate all side-channel flaws is still missing. In this work, we propose a method for estimation of the total passive side-channel information leakage from the Alice's light source. The method relies on Hong-Ou-Mandel interference between different signals emitted by Alice, which reveals their overall mode mismatch without the necessity to measure all individual degrees of freedom independently. We include experime…
