Photon Number Resolving Detectors Research Articles

Photon number resolving detection with a single-photon detector and adaptive storage loop

Photon number resolving (PNR) measurements are beneficial or even necessary for many applications in quantum optics. Unfortunately, PNR detectors are usually large, slow, expensive, and difficult to operate. However, if the input signal is multiplexed, photon ‘click’ detectors, that lack an intrinsic PNR capability, can still be used to realize photon number resolution. Here, we investigate the operation of a single click detector, together with a storage line with tunable outcoupling. Using adaptive feedback to adjust the storage outcoupling rate, the dynamic range of the detector can in certain situations be extended by up to an order of magnitude relative to a purely passive setup. An adaptive approach can thus allow for photon number variance below the quantum shot noise limit under a wider range of conditions than using a passive multiplexing approach. This can enable applications in quantum enhanced metrology and quantum computing.

Reduction of g2(0) value in heralded spontaneous parametric down-conversion sources using photon number resolving detectors

Single Photon Sources (SPSs) play a pivotal role in fields such as quantum communication and quantum cryptography by generating information in a secure manner. However, realizing the ideal emission of single photons with high efficiency is still a theoretical model. This leads to the presence of multiphoton components in SPSs, which could potentially compromise security. This study focuses on enhancing the purity of a class of sources by characterizing their photon number distribution and mitigating the impact of the multiphoton components. We propose the use of Photon Number Resolving Detectors (PNRD) as a technique to exclude multiphoton contributions, particularly in sources like Spontaneous Parametric Down Conversion sources, where emitted photons can be represented as Two-Mode Squeezed Vacuum states. By analyzing the second-order cross-correlation function, g2(0), using either PNRD or Single Photon Detectors, we can quantify the reduction in multiphoton contributions.

A Quadratic Speedup in the Optimization of Noisy Quantum Optical Circuits

Linear optical quantum circuits with photon number resolving (PNR) detectors are used for both Gaussian Boson Sampling (GBS) and for the preparation of non-Gaussian states such as Gottesman-Kitaev-Preskill (GKP), cat and NOON states. They are crucial in many schemes of quantum computing and quantum metrology. Classically optimizing circuits with PNR detectors is challenging due to their exponentially large Hilbert space, and quadratically more challenging in the presence of decoherence as state vectors are replaced by density matrices. To tackle this problem, we introduce a family of algorithms that calculate detection probabilities, conditional states (as well as their gradients with respect to circuit parametrizations) with a complexity that is comparable to the noiseless case. As a consequence we can simulate and optimize circuits with twice the number of modes as we could before, using the same resources. More precisely, for an M-mode noisy circuit with detected modes D and undetected modes U, the complexity of our algorithm is O(M2∏i∈UCi2∏i∈DCi), rather than O(M2∏i∈D∪UCi2), where Ci is the Fock cutoff of mode i. As a particular case, our approach offers a full quadratic speedup for calculating detection probabilities, as in that case all modes are detected. Finally, these algorithms are implemented and ready to use in the open-source photonic optimization library MrMustard.

Fast High-Efficiency Photon-Number-Resolving Parallel Superconducting Nanowire Single-Photon Detector

Photon-number-resolving (PNR) single-photon detectors are an enabling technology in many areas, such as photonic quantum computing, nonclassical light-source characterization, and quantum imaging. Here, we demonstrate high-efficiency PNR detectors using a parallel superconducting nanowire single-photon-detector (P-SNSPD) architecture that does not suffer from crosstalk between the pixels and that is free of latching. The behavior of the detector is modeled and used to predict the possible outcomes given a certain number of incoming photons. We apply our model to a four-pixel P-SNSPD with a system detection efficiency of 92.5%. We also demonstrate how this detector allows reconstructing the photon-number statistics of a coherent source of light, which paves the way towards the characterization of the photon statistics of other types of light source using a single detector.

Algorithm of quantum engineering of large-amplitude high-fidelity Schrödinger cat states

We present an algorithm of quantum engineering of large-amplitude ge 5 high-fidelity ge 0.99 even/odd Schrödinger cat states (SCSs) using a single mode squeezed vacuum (SMSV) state as resource. Set of k beam splitters (BSs) with arbitrary transmittance and reflectance coefficients sequentially following each other acts as a hub that redirects a multiphoton state into the measuring modes simultaneously measured by photon number resolving (PNR) detectors. We show that the multiphoton state splitting guarantees significant increase of the success probability of the SCSs generator compared to its implementation in a single PNR detector version and imposes less requirements on ideal PNR detectors. We prove that the fidelity of the output SCSs and its success probability are in conflict with each other (which can be quantified) in a scheme with ineffective PNR detectors, especially when subtracting large (say, 100) number of photons, i.e., increasing the fidelity to perfect values leads to a sharp decrease in the success probability. In general, the strategy of subtracting up to 20 photons from initial SMSV in setup with two BSs is acceptable for achieving sufficiently high values of the fidelity and success probability at the output of the generator of the SCSs of amplitude le 3 with two inefficient PNR detectors.

Optimal transmission estimation with dark counts

Transmission measurements are essential from fibre optics to spectroscopy. Quantum theory dictates that the ultimate precision in estimating transmission or loss is achieved using probe states with definite photon number and photon-number-resolving detectors (PNRDs). Can the quantum advantage relative to classical probe light still be maintained when the detectors fire due to dark counts and other spurious events? We demonstrate that the answer to this question is affirmative and show in detail how the quantum advantage depends on dark counts and increases with Fock-state-probe strength. These results are especially pertinent as the present capabilities of PNRDs are being dramatically improved.

Realistic conversion of single-mode squeezed vacuum state to large-amplitude high-fidelity Schrödinger cat states by inefficient photon number resolving detection

We theoretically propose an efficient way to generate optical analogs of both even and odd Schrӧdinger cat states (SCSs) of large amplitude with high fidelity and reasonable generation rate. The resources consumed are a single-mode squeezed vacuum state (SMSV) and possibly a single photon or nothing. We report the generation of even (odd) SCS with amplitude fidelity higher than with success probability a little more than by subtraction of photons from SMSV by ideal photon number detection. In order to reduce the requirements for the sensitivity of photon number resolving (PNR) detector, we show the implementation of even/odd SCSs with the same characteristics with two PNR detectors resolving only photons each instead of In the case of inefficient detector, SCS’s size and its fidelity can be kept close to perfect by using highly transmitting beam splitter, but at the cost of very dramatic reduction of the success probability. In order to have certain harmony between the characteristics (large amplitude, high fidelity and acceptable success probability) in the case of imperfect detection, highly transmitting beam splitters should not be used and number of the subtracted photons must be reduced to

Laser Ranging Bathymetry Using a Photon-Number-Resolving Detector

The sensitivity and robustness against background noise of optical measurements, and specifically range-finding, can be improved by detecting the light with photon-number-resolving detectors (PNRD). We use a PNRD to detect single pulse reflections from the seabed level in the presence of high attenuation of the sea water. Measurements are performed from above the sea level, overcoming broad daylight conditions. We demonstrate continuous measurement of the seabed depth up to around 24 m, using laser pulse energies of 10 μJ, while sailing at speed of 2.2 knots. Additionally, we use these data to extract values of the refractive index and optical attenuation in coastal seawater. The method could be used as a novel and optically-accurate bathymetry tool for coastal research and underwater sensing applications.

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

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.

Quantum non-Gaussianity certification of photon number-resolving detectors.

We report on direct experimental certification of the quantum non-Gaussian character of a photon number-resolving detector. The certification protocol is based on an adaptation of the existing quantum non-Gaussianity criteria for quantum states to quantum measurements. In our approach, it suffices to probe the detector with a vacuum state and two different thermal states to test its quantum non-Gaussianity. The certification is experimentally demonstrated for the detector formed by a spatially multiplexed array of ten single-photon avalanche photodiodes. We confirm the quantum non-Gaussianity of POVM elements Π^m associated with the m-fold coincidence counts, up to m = 7. The experimental ability to certify from the first principles the quantum non-Gaussian character of Π^m is for large m limited by low probability of the measurement outcomes, especially for vacuum input state. We find that the injection of independent Gaussian background noise into the detector can be helpful and may reduce the measurement time required for reliable confirmation of quantum non-Gaussianity. In addition, we modified and experimentally verified the quantum non-Gaussianity certification protocol employing a third thermal state instead of a vacuum to speed up the whole measurement. Our findings demonstrate the existence of efficient tools for the practical characterization of fundamental non-classical properties and benchmarking of complex optical quantum detectors.

Superconducting Nanowire Photon-Number-Resolving Detectors Integrated with Current Reservoirs

Photon-number-resolving detectors (PNRDs) play pivotal roles in many quantum-photonic applications; and intrinsic and multiplexed PNRDs have been reported previously. However, for intrinsic PNRDs, the maximum resolvable photon number is limited to a few photons; for the multiplexed PNRDs, the fidelity generally decreases when the to-be-resolved photon number becomes large. Here, to resolve more photons with high fidelity, we report on combined PNRDs, based on a spatial multiplexing configuration of multiple elements, each capable of resolving a few photons. After setting up a model and calculating the fidelity, we propose a possible physical system to realize the combined PNRDs. The proposed detectors are based on the superconducting nanowire multiphoton detectors integrated with current reservoirs that we recently reported, but are designed and configured into PNRDs. Specifically, information about the detected photon numbers is stored in the format of the supercurrent in the current reservoir and then readout by an integrated yTron. We present in detail the operating principle and show a design that can resolve up to 11 photons with high fidelity.

Thresholded Quantum LIDAR: Exploiting Photon-Number-Resolving Detection.

We present a technique that improves the signal-to-noise-ratio (SNR) of range-finding, sensing, and other light-detection applications. The technique filters out low photon numbers using photon-number-resolving detectors. This technique has no classical analog and cannot be done with classical detectors. We investigate the properties of our technique and show under what conditions the scheme surpasses the classical SNR. Finally, we simulate the operation of a rangefinder, showing improvement with a low number of signal samplings and confirming the theory with a high number of signal samplings.

Evaluating the performance of photon-number-resolving detectors

We analyze the performance of photon-number-resolving (PNR) detectors and introduce a figure of merit for the accuracy of such detectors. This figure of merit is the (worst-case) probability that the photon-number-resolving detector correctly predicts the input photon number. Simulations of various PNR detectors based on multiplexed single-photon `click detectors' is performed. We conclude that the required quantum efficiency is very high in order to achieve even moderate (up to a handful) photon resolution, we derive the required quantum efficiency as a function of the the maximal photon number one wants to resolve, and we show that the number of click detectors required grows quadratically with the maximal number of photons resolvable.

Hybrid quantum key distribution using coherent states and photon-number-resolving detectors

We put forward a hybrid quantum key distribution protocol based on coherent states, Gaussian modulation, and photon-number-resolving (PNR) detectors, and show that it may enhance the secret key generation rate (KGR) compared to homodyne-based schemes. Improvement in the KGR may be traced back to the dependence of the two-dimensional discrete output variable on both the input quadratures, thus overcoming the limitations of the original protocol. When reverse reconciliation is considered, the scheme based on PNR detectors outperforms the homodyne one both for individual and collective attacks. In the presence of direct reconciliation, the PNR strategy is still the best one against individual attacks, but for the collective ones the homodyne-based scheme is still to be preferred as the channel transmissivity decreases.

Security of six-state quantum key distribution protocol with threshold detectors.

The security of quantum key distribution (QKD) is established by a security proof, and the security proof puts some assumptions on the devices consisting of a QKD system. Among such assumptions, security proofs of the six-state protocol assume the use of photon number resolving (PNR) detector, and as a result the bit error rate threshold for secure key generation for the six-state protocol is higher than that for the BB84 protocol. Unfortunately, however, this type of detector is demanding in terms of technological level compared to the standard threshold detector, and removing the necessity of such a detector enhances the feasibility of the implementation of the six-state protocol. Here, we develop the security proof for the six-state protocol and show that we can use the threshold detector for the six-state protocol. Importantly, the bit error rate threshold for the key generation for the six-state protocol (12.611%) remains almost the same as the one (12.619%) that is derived from the existing security proofs assuming the use of PNR detectors. This clearly demonstrates feasibility of the six-state protocol with practical devices.

Interferometric superlocalization of two incoherent optical point sources.

A novel interferometric method - SLIVER (Super Localization by Image inVERsion interferometry) - is proposed for estimating the separation of two incoherent point sources with a mean squared error that does not deteriorate as the sources are brought closer. The essential component of the interferometer is an image inversion device that inverts the field in the transverse plane about the optical axis, assumed to pass through the centroid of the sources. The performance of the device is analyzed using the Cramér-Rao bound applied to the statistics of spatially-unresolved photon counting using photon number-resolving and on-off detectors. The analysis is supported by Monte-Carlo simulations of the maximum likelihood estimator for the source separation, demonstrating the superlocalization effect for separations well below that set by the Rayleigh criterion. Simulations indicating the robustness of SLIVER to mismatch between the optical axis and the centroid are also presented. The results are valid for any imaging system with a circularly symmetric point-spread function.

Measurement of photon correlations with multipixel photon counters

Development of reliable photon number resolving detectors (PNRD), devices which are capable to distinguish 1,2,3.. photons, is of a great importance for quantum optics and its applications. A new class of affordable PNRD is based on multipixel photon counters (MPPC). Here we review results of experiments on using MPPCs for direct characterization of squeezed vacuum (SV) states, generated via parametric downconversion (PDC). We use MPPCs to measure the second order normalized intensity correlation function (g^(2)) and directly detect the two-mode squeezing of SV states. We also present a method of calibration of crosstalk probability in MPPCs based on g^(2) measurements of coherent states.

Highly Sensitive, Photon Number Resolving Detectors Mediated by Phonons Using δ-Doped GaAs Transistors

We report a photon number resolving detector using two-dimensional electron gas (2DEG) based transistors. When the photon pulses impinge on the absorption region, the generated phonons dissipate ballistically in the 2DEG toward the trench isolated nanowire transistors near the surface. The phonon-electron interaction induces a positive conductance in the transistors, resulting in a current increase. With this principle, we obtain an internal quantum efficiency for this type of detector of up to 85%.

Physics and application of photon number resolving detectors based on superconducting parallel nanowires

The parallel nanowire detector (PND) is a photon number resolving (PNR) detector that uses spatial multiplexing on a subwavelength scale to provide a single electrical output proportional to the photon number. The basic structure of the PND is the parallel connection of several NbN superconducting nanowires (≈100 nm wide, a few nm thick), folded in a meander pattern. PNDs were fabricated on 3–4 nm thick NbN films grown on MgO (TS = 400 °C) substrates by reactive magnetron sputtering in an Ar/N2 gas mixture. The device performance was characterized in terms of speed and sensitivity. PNDs showed a counting rate of 80 MHz and a pulse duration as low as 660 ps full-width at half-maximum (FWHM). Building the histograms of the photoresponse peak, no multiplication noise buildup is observable. Electrical and optical equivalent models of the device were developed in order to study its working principle, define design guidelines and develop an algorithm to estimate the photon number statistics of an unknown light. In particular, the modeling provides novel insight into the physical limit to the detection efficiency and to the reset time of these detectors. The PND significantly outperforms existing PNR detectors in terms of simplicity, sensitivity, speed and multiplication noise.

Tuning of Tungsten Thin Film Superconducting Transition Temperature for Fabrication of Photon Number Resolving Detectors

Tungsten thin films can form in one of two crystal structures: alpha (bcc), with a superconducting transition temperature (T/sub c/) of 15 mK, and beta (A15), with a T/sub c/ between 1 and 4 K. Films with intermediate T/sub c/s are composed of both alpha and beta phases. We have investigated how to tune the film T/sub c/ in order to obtain certain values (T/sub c/ /spl sim/ 100 mK) suitable for the fabrication of photon number resolving transition-edge sensor (TES) and arrays of TES detectors for astronomical and quantum information applications. Variation of deposition conditions, and also the choice of the underlayer/coating for equal deposition conditions, affect the T/sub c/s of tungsten films. We have used x-ray diffraction to determine the structure of tungsten thin films and film stress. The results indicates that the film stress state depends on the underlying substrate and coating. To understand the variation of T/sub c/ values and to allow precise tuning of these values, we have investigated substrates and coatings for tungsten film multilayer stacks and determined tungsten film stress by x-ray diffraction at both room temperature and 8 K.