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arXiv:2112.07028 · Physica Scripta

Realistic photon-number resolution in generalized Hong-Ou-Mandel experiment

V Ye Len, M M Byelova, V. A. Uzunova, А. А. Семенов

Published Sep 8, 2022• 4 citations
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Abstract

Abstract 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 analytical expressions for photocounting distributions in the generalized Hong-Ou-Mandel experiment for the case of realistic photon-number resolving (PNR) detectors. It is shown that probabilities of properly postselected events are proportional to probabilities obtained for perfect PNR detectors. Our results are illustrated with examples of arrays of on/off detectors and detectors affected by a finite dead time.

DOI
10.1088/1402-4896/ac9095

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Abstract 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 analytical expressions for photocounting distributions in the generalized Hong-Ou-Mandel experiment for the case of realistic photon-number resolving (PNR) detectors. It is shown that probabilities of properly postselected events are proportional to probabilities obtained for perfect PNR detectors. Our results are illustrated with examples of arrays of on/off detectors and detectors affected by a finite dead time.
Gaussian boson sampling (GBS) is a model of nonuniversal quantum computation that claims to demonstrate quantum supremacy with current technologies. This model entails sampling photocounting events from a multimode Gaussian state at the outputs of a linear interferometer. In this scheme, collision events—those with more than one photon for each mode—are infrequent. However, they are still used for validation purposes. Therefore, the limitation of realistic detectors to perfectly resolve adjacent photon numbers becomes pivotal. We derive a photocounting probability distribution in GBS schemes which is applicable for use with general detectors and photocounting techniques. This probability distribution is expressed in terms of functionals of the field-quadrature covariance matrix, e.g., Hafnian and Torontonian in the well-known special cases of photon-number-resolving and on-off detectors, respectively. Based on our results, we consider a GBS validation technique involving detectors with realistic photon-number resolution. Published by the American Physical Society 2024
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 modeling detectors with number and temporal resolution we demonstrate a greater precision than coincidence rates or temporal data alone afford. Moreover, the additional information can allow simultaneous estimation of a time delay alongside calibration parameters, opening up the possibility of calibration-free protocols and approaching the precision of the quantum Cram\'er-Rao bound.
Abstract We extensively discuss the Hong–Ou–Mandel experiment by 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 make explicit the differences between a classical Hong–Ou–Mandel-like dip and a quantum one. Throughout the manuscript, we will often focus and refer to a particular system based on AlGaAs waveguides emitting photon pairs via spontaneous parametric down conversion, but our results can be extended to other analogous experimental systems and to various degrees of freedom. Graphical Abstract The Hong–Ou–Mandel experiment is a landmark in quantum optics, showing the bunching of indistinguishable bunch. In the present contribution, we give another perspective to this experiment based on a phase space representation of the continuous degrees of freedom of the single photons sent into the input arms of such interferometer. We show that the coincidence detection in the output ports of an Hong– Ou–Mandel interferometer is a direct measurement of the Wigner function of the produced photons in a given region of space, and we discuss how continuous degrees of freedom of single photons can be used in continuous variables quantum protocols, as quantum error correction and metrology. Our results open the perspective of broadening even more the applications of single photon-based quantum information-related protocols.
We test ideas put forward, e.g., by \ifmmode \dot{Z}\else \.{Z}\fi{}ukowski et al. [M. \ifmmode \dot{Z}\else \.{Z}\fi{}ukowski et al., Phys. Rev. A 95, 042113 (2017)], which suggest that using rates in quantum optics can lead to better indicators of nonclassicality for states of quantum optical fields with undefined photon numbers. By rate we mean the ratio of registered photons in a given detector to the total number of detected photons in all detectors in a run of the experiment. For the Hong-Ou-Mandel effect for parametric down-conversion fields, we show that by using two detector correlation functions, which are defined in terms of averages of products of measured rates, rather than usual intensities, one can observe nonclassical visibilities beyond 1/21/21/2 for significantly higher pump rates. At such rates we already have the partially stimulated emission, which leads to significant amplitudes for multiple pairs production, still the approach allows us to clearly see the nonclassical dip. We consider both the perfect and imperfect detection efficiency.
The Hong–Ou–Mandel (HOM) dip has played an important role in recent linear optics experiments. It is crucial for quantum computing with photons and can be used to characterize the quality of single photon sources and linear optics setups. In this paper, we consider generalized HOM experiments with N bosons or fermions passing simultaneously, i.e. within their coherence time, through a symmetric Bell multiport beam splitter. It is shown that for an even number of bosons, the HOM dip occurs naturally in the coincidence detection in the output ports. In contrast, fermions always leave the setup separately, exhibiting perfect coincidence detection. Our results can be used to verify or employ the quantum statistics of particles experimentally.
In the context of Fock states, demonstrating multiphoton quantum interference, e.g., the generalized Hong-Ou-Mandel (HOM) interference, is at the core of many applications of quantum technologies. However, it is difficult to demonstrate high-visibility quantum interference for a large number of photons. Here, we introduce an experimentally feasible proposal to achieve this goal using phase-randomized weak coherent states and practical photon-number-resolving detectors. Our method can be used to obtain analytically tight bounds of the generalized HOM dip in a beam splitter, and it is robust against practical errors. The simulation shows that for an ideal detector that can resolve any number of photons without an upper bound, the proposed method can bound the generalize HOM interference for a large number of photons, e.g., 100 photons; for a practical detector that can resolve up to 29 photons, the proposed method can bound the generalized HOM interference for 56 photons with visibility 99.499.4%99.4. Our proposal is a general approach for multiphoton quantum interference in optical networks with multiple inputs and outputs.