Photon Number Resolution Research Articles

Realistic photon-number resolution in Gaussian boson sampling

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

Photon number distribution of squeezed light from a silicon nitride microresonator measured without photon number resolving detectors

The measurement of the photon number distribution (PND) allows one to extract metrics of non-classicality of fundamental and technological relevance, but in principle it requires the use of detectors with photon number resolving (PNR) capabilities. In this work we reconstruct the PND of two-mode pulsed squeezed light generated from a silicon nitride microresonator using threshold detectors and variable optical attenuations. The PNDs are characterized up to ∼1.2 photons per pulse, through which we extracted an on-chip squeezing level of 6.2(2) dB and a noise reduction factor of −3.8(2) dB. The PNDs are successfully reconstructed up to a Hilbert space dimension of 6 × 6. The analysis performed on the photon number basis allows us to characterize the influence of a spurious thermal background field that spoils the photon number correlations. We evaluate the impact of self- and cross-phase modulation on the generation efficiency in case of a pulsed pump, and validate the results through numerical simulations of the master equation of the system.

Electrical trace analysis of superconducting nanowire photon-number-resolving detectors

We apply principal component analysis (PCA) to a set of electrical output signals from a commercially available superconducting nanowire single-photon detector (SNSPD) to investigate their photon-number-resolving capability. We find that the rising edge as well as the amplitude of the electrical signal have the most dependence on photon number. Accurately measuring the rising edge while simultaneously measuring the voltage of the pulse amplitude maximizes the photon-number resolution of SNSPDs. Using an optimal basis of principal components, we show unambiguous discrimination between one- and two-photon events, as well as partial resolution up to five photons. This expands the use case of SNSPDs to photon-counting experiments, without the need of detector multiplexing architectures. Published by the American Physical Society 2024

Photon discerner: adaptive quantum optical sensing near the shot noise limit

Photon statistics of an optical field can be used for quantum optical sensing in low light level scenarios free of bulky optical components. However, photon-number-resolving detection to unravel the photon statistics is challenging. Here, we propose a novel detection approach, that we call ‘photon discerning’, which uses adaptive photon thresholding for photon statistical estimation without recording exact photon numbers. Our photon discerner is motivated by the field of neural networks where tunable thresholds have proven efficient for information extraction in machine learning tasks. The photon discerner maximizes Fisher information per photon by iteratively choosing the optimal threshold in real-time to approach the shot noise limit. Our proposed scheme of adaptive photon thresholding leads to unique remote-sensing applications of quantum degree of linear polarization camera and quantum LiDAR. We investigate optimal thresholds and show that the optimal photon threshold can be counter-intuitive (not equal to 1) even for weak signals (mean photon number much less than 1), due to the photon bunching effect. We also put forth a superconducting nanowire realization of the photon discerner which can be experimentally implemented in the near-term. We show that the adaptivity of our photon discerner enables it to beat realistic photon-number-resolving detectors with limited photon-number resolution in certain applications. Our work suggests a new class of detectors for information-theory driven, compact, and learning-based quantum optical sensing.

Temporal and photon number resolution of superconducting nanowire single-photon detectors

Temporal and photon number resolution of superconducting nanowire single-photon detectors

High-performance photon number resolving detectors for 850–950 nm wavelength range

Since their first demonstration in 2001 [Gol’tsman et al., Appl. Phys. Lett. 79, 705–707 (2001)], superconducting-nanowire single-photon detectors (SNSPDs) have witnessed two decades of great developments. SNSPDs are the detector of choice in most modern quantum optics experiments and are slowly finding their way into other photon-starved fields of optics. Until now, however, in nearly all experiments, SNSPDs were used as “binary” detectors, meaning that they could only distinguish between 0 and >=1 photons, and photon number information was lost. Recent research has demonstrated proof-of-principle photon-number resolution (PNR) SNSPDs counting 2–5 photons. The photon-number-resolving capability is highly demanded in various quantum-optics experiments, including Hong–Ou–Mandel interference, photonic quantum computing, quantum communication, and non-Gaussian quantum state preparation. In particular, PNR detectors at the wavelength range of 850–950 nm are of great interest due to the availability of high-quality semiconductor quantum dots (QDs) [Heindel et al., Adv. Opt. Photonics 15, 613–738 (2023)] and high-performance cesium-based quantum memories [Ma et al., J. Opt. 19, 043001 (2017)]. In this paper, we demonstrate NbTiN-based SNSPDs with >94% system detection efficiency, sub-11 ps timing jitter for one photon, and sub-7 ps for 2 photons. More importantly, our detectors resolve up to 7 photons using conventional cryogenic electric readout circuitry. Through theoretical analysis, we show that the PNR performance of demonstrated detectors can be further improved by enhancing the signal-to-noise ratio and bandwidth of our readout circuitry. Our results are promising for the future of optical quantum computing and quantum communication.

Precisely determining photon-number in real time

Superconducting transition-edge sensors (TES) are extremely sensitive microcalorimeters used as photon detectors with unparalleled energy resolution. They have found application from measuring astronomical spectra through to determining the quantum property of photon-number, n^=a^†a^, for energies from 0.6-2.33eV. However, achieving optimal energy resolution requires considerable data acquisition – on the order of 1GB/min – followed by post-processing, which does not allow access to energy information in real time. Here we use a custom hardware processor to process TES pulses while new detections are still being registered, allowing photon-number to be measured in real time as well as reducing data requirements by orders-of-magnitude. We resolve photon number up to n=16 – achieving up to parts-per-billion discrimination for low photon numbers on the fly – providing transformational capacity for applications of TES detectors from astronomy through to quantum technology.

Improving photon number resolvability of a superconducting nanowire single-photon detector array using a level comparator circuit

Photon number resolving (PNR) capability is very important in many optical applications, including quantum information processing, fluorescence detection, and few-photon-level ranging and imaging. Superconducting nanowire single-photon detectors (SNSPDs) with a multipixel interleaved architecture give the array an excellent spatial PNR capability. However, the signal-to-noise ratio (SNR) of the PNR (SNRPNR) of the array will be degraded with increasing the element number due to the electronic noise in the readout circuit, which limits the PNR resolution as well as the maximum PNR number. In this study, a 16-element interleaved SNSPD array was fabricated, and the PNR capability of the array was investigated and analyzed. By introducing a level comparator circuit (LCC), the SNRPNR of the detector array was improved over a factor of four. In addition, we performed a statistical analysis of the photon number on this SNSPD array with LCC, showing that the LCC method effectively enhances the PNR resolution. Besides, the system timing jitter of the detector was reduced from 90 ps to 72 ps due to the improved electrical SNR.

Superconducting single photon detector with speed of 5 GHz and photon number resolution of 61

Superconducting single photon detector with speed of 5 GHz and photon number resolution of 61

Number-state reconstruction with a single single-photon avalanche detector

Single-photon avalanche detectors (SPADs) are crucial sensors of light for many fields and applications. However, they are not able to resolve photon number, so typically more complex and more expensive experimental setups or devices must be used to measure the number of photons in a pulse. Here, we present a methodology for performing photon number-state reconstruction with only one SPAD. The methodology, which is cost-effective and easy to implement, uses maximum-likelihood techniques with a detector model whose parameters are measurable. We achieve excellent agreement between known input pulses and their reconstructions for coherent states with up to ≈10 photons and peak input photon rates up to several Mcounts/s. When detector imperfections are small, we maintain good agreement for coherent pulses with peak input photon rates of over 40 Mcounts/s, greater than one photon per detector dead time. For anti-bunched light, the reconstructed and independently measured pulse-averaged values of g(2)(0) are also consistent with one another. Our algorithm is applicable to light pulses whose pulse width and correlation time scales are both at least a few detector dead times. These results, achieved with single commercially available SPADs, provide an inexpensive number-state reconstruction method and expand the capabilities of single-photon detectors.

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.

Detection scheme using a beam splitter and on-off detectors for non-Gaussian state-based quantum illumination with attenuation

Quantum illumination is an entanglement-based protocol for target detection. The use of a two-mode squeezed vacuum (TMSV) state as a type of Gaussian state has been widely discussed. In our previous study, we found that the quasi-Bell state, which is a non-Gaussian state, outperforms the TMSV state in the quantum illumination protocol with attenuation. In this paper, we construct a detection scheme using practical elements and demonstrate that it can outperform the TMSV state without using the photon-number resolution.

GHz photon-number resolving detection with high detection efficiency and low noise by ultra-narrowband interference circuits

We demonstrate the photon-number resolution (PNR) capability of a 1.25 GHz gated InGaAs single-photon avalanche photodiode (APD) that is equipped with a simple, low-distortion ultra-narrowband interference circuit for the rejection of its background capacitive response. Through discriminating the avalanche current amplitude, we are able to resolve up to four detected photons in a single detection gate with a detection efficiency as high as 45%. The PNR capability is limited by the avalanche current saturation, and can be increased to five photons at a lower detection efficiency of 34%. The PNR capability, combined with high efficiency and low noise, will find applications in quantum information processing technique based on photonic qubits.

Gaussian boson sampling with click-counting detectors

Gaussian boson sampling constitutes a prime candidate for an experimental demonstration of quantum advantage within reach with current technological capabilities. The original proposal employs photon-number-resolving detectors, however, these are not widely available. Nevertheless, inexpensive threshold detectors can be combined into a single click-counting detector to achieve approximate photon-number resolution. We investigate the problem of sampling from a general multimode Gaussian state using click-counting detectors and show that the probability of obtaining a given outcome is related to a matrix function which is dubbed as the Kensingtonian. We show how the Kensingtonian relates to the Torontonian and the Hafnian, thus bridging the gap between known Gaussian boson sampling variants. We then prove that, under standard complexity-theoretical conjectures, the model cannot be simulated efficiently. Published by the American Physical Society 2024

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.

Photon-number resolution with microwave Josephson photomultipliers

Photon-number resolution with microwave Josephson photomultipliers

Bound for Gaussian-state quantum illumination using a direct photon measurement.

It is important to find feasible measurement bounds for quantum information protocols. We present analytic bounds for quantum illumination with Gaussian states when using an on-off detection or a photon number resolving (PNR) detection, where its performance is evaluated with signal-to-noise ratio. First, for coincidence counting measurement, the best performance is given by the two-mode squeezed vacuum (TMSV) state which outperforms the coherent state and the classically correlated thermal (CCT) state. However, the coherent state can beat the TMSV state with increasing signal mean photon number in the case of the on-off detection. Second, the performance is enhanced by taking Fisher information approach with all counting probabilities including non-detection events. In the Fisher information approach, the TMSV state still presents the best performance but the CCT state can beat the TMSV state with increasing signal mean photon number in the case of the on-off detection. Furthermore, we show that it is useful to take the PNR detection on the signal mode and the on-off detection on the idler mode, which reaches similar performance of using PNR detection on both modes.

An Unbiased Quantum Random Number Generator Based on Boson Sampling

AbstractIt is proven that Boson sampling is a much promising model of optical quantum computation, which is applied to designing quantum computer successfully, such as “Jiuzhang”. However, the meaningful randomness of Boson sampling results has not been utilized or exploited. In this research, Boson sampling is applied to design a quantum random number generator (QRNG) by fully exploiting the randomness of Boson sampling results, and its prototype system is constructed with the programmable silicon photonic processor, which can generate unbiased random sequences and overcome the shortcomings of the existing discrete QRNGs such as source‐restricted, high demand for the photon number resolution capability of detector and slow self‐detection generator speed. Boson sampling is implemented as a random entropy source, and random bit strings with satisfactory randomness and uniformity can be obtained after post‐processing the sampling results. It is the first approach for applying the randomness of Boson sampling results to develop a practical prototype system for actual tasks, and the experiment results demonstrate that the designed Boson sampling‐based QRNG prototype system passes 15 tests of the NIST SP 800‐22 statistical test component, which proves that Boson sampling has great potential for practical applications with desirable performance besides quantum advantage.

Quantum Random Number Generation Based on Multi-photon Detection.

We demonstrate quantum random number generation based on a photon-number detection scheme with the use of a silicon photomultiplier. We implement a time integral with detector response signals for resolving photon numbers, which are subsequently digitized into a stream of 4-bit sequences with a generation rate of 13.6 Mbit/s. Our generated random bits pass the statistical randomness validation according to the U.S. National Institute of Standards and Technology (NIST) Special Publication 800-22. This scheme is implementable with inexpensive components, and the system can be miniaturized to the size of a plug-and-play portable cryptographic device.

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.