Photon Number Resolution (PNR)

Figure 1. Conceptual scheme of the dynamics of superconducting nanowire single photon detectors (SNSPD) depicting absorption of (a) a single photon and (b) a pair of photons, followed by "hot spot" formation, and return to the initial state. (c) shows signal evolution over time for the 1- and 2-photon absorption cases.

Introduction to photon number resolution (PNR)

Photon number resolution (PNR) is an enabling technique used to assign the number of photons involved in a detection event precisely. This technique leverages photon-number-resolving single-photon detectors as well as sophisticated signal analysis, and it is necessary for quantum cryptography [1] and quantum communication [2].

There are several types of single-photon detectors, such as photomultiplier tubes (PMTs), single-photon avalanche diodes (SPADs), transition edge sensors (TESs), and superconducting nanowire single-photon detectors (SNSPDs). In comparison with the other types, SNSPDs have better sensitivity at telecom wavelengths, low dark counts, and can reach picosecond time resolution, making SNSPDs a key tool in quantum research. Indeed, the development of SNSPD has led to outstanding results in quantum technology [3,4].

Despite advancements in detector development, detecting and recognizing more than one photon acquired from the same pulse is a challenging quest. Typically, multiple single-photon detectors are coupled in parallel to spatially distinguish a different number of photons collected at each event [5]. The problem with this pseudo-PNR configuration is a high cost, as well as a non-zero probability that two photons are absorbed by the same pixel at the same time.

The analysis of the signal recorded from the SNSPD helps to overcome this problem.

The SNSPD signal's shape depends on the number of photons absorbed, as shown in Figure 1. The rising slope of the signal increases with a higher number of photons [6,7]. It is feasible to ascertain the number of absorbed photons employing temporal correlation analysis between the electrical pulses from the detector and the laser source, thereby accentuating disparities in slopes of the SNSPD signal's rising edge. Additionally, the falling edges of SNSPD signals shed light on the origins of the signals as well as the fluctuations inherently present in the experiment [6,8].

The possibility of simultaneously measuring different signals and their corresponding rising and falling edges are game-changing factors in PNR measurements, and this is where the power of the Swabian Instruments' Time Tagger comes into play.

Unlike conventional time tagging devices, which can typically only detect one edge, Swabian Instruments’ Time Taggers can simultaneously acquire rising and falling edges to capture a wide variety of signal profiles. The ability to capture both edges of the signal is a crucial factor not only in PNR measurements but also in experiments in which a constant fraction discriminator approach is required due to variations of amplitudes and widths of the detector pulses (e.g., PMTs).

Timing electronics required for photon number resolution (PNR) experiment

Figure 2. Representation of a typical setup built for PNR experiments. The scheme includes a photon source, a variable optical attenuator (VOA), a polarization controller (Pol. C), and superconducting nanowire single photon detectors (SNSPDs). The Time Tagger collects, combines, and streams to the PC all of the important timing information from the devices, where Swabian Instrument's software architecture takes over the signal analysis.

Photon number resolution (PNR) experiments require precise and reliable information on the timing of the acquired events. Time-to-digital converters must perform fast operations and achieve sufficient time resolution for distinguishing the number of photons. In its turns, power sources and detectors must be stable and low-noise.

A setup for a PNR experiment is shown in Figure 2. This setup includes a photon source, light modulators, superconducting nanowire single photon detectors (SNSPDs), and a time-to-digital converter. For demonstrative purposes, a laser is used as the photon source from where the emitted photons are adapted and shined onto the SNSPDs. The photons impinging on the detector lead to the formation of a "hot spot", and as a result, the SNSPD loses its superconductivity characteristics and generates a signal, which indicates the detection event - a click. The time-to-digital converter Time Tagger allows the precise and simultaneous determination of the clicks’ arrival time as well as the emission time of the photons emitted by the photon source. When the trigger signal from the laser is not directly available, the timing information of the incoming photons can be acquired with a dedicated photodiode, which collects part of the light from the photon source.

The critical hardware characteristics of a time-to-digital converter required for PNR experiments:

Timing jitter. The lower the timing jitter of the timing electronics is, the better the resolution and precision of the measurement will be. One has to take into account the jitter from SNSPDs, which is of the order of 4 ps (RMS jitter), and try to keep the timing jitter from the electronics below this value.
Dead time. Minimizing dead time is imperative to prevent data loss, especially when dealing with high photon count rates. Currently, the minimum dead time of SNSPDs is of the order of 10 ns. Swabian Instruments Time Taggers feature deadtimes below the conventional SNSPDs in the market, preventing data loss in your most advanced experiments.
Data transfer rate. Higher data transfer rates allow the capture of more photon events in a shorter time window, thereby increasing the statistical significance of measurements. Insufficient data transfer leads to overflow and data loss unless data filtering methods exist to control data acquisition before being transferred to the PC. The successful data filtering method will utilize the total sum of the count rates for each of the channels (including laser, detector, controllers, signal triggers, etc) to determine the clicks that must be transferred.

Swabian Instruments’ Time Taggers - an advanced solution for precise photon number resolution (PNR) measurements

High-Performing & Scalable Hardware

Timing electronics are crucial components in performing photon number resolution (PNR) measurements. Our TIme Tagger can scale with your scientific needs by featuring the latest upgrades and increasing the total number of input channels. Time Tagger X provides you with the specs necessary for ground-breaking PNR research:

Timing jitter down to 1.3 ps.
Dead time down to 1.5 ns.
Data transfer rate up to 80 M tags/s. Swabian Instruments' Data Filtering feature overcomes overflow problems for experiments with high counts by removing time tags unnecessary for the experiment on the hardware level.

Versatile & Intuitive Software Engine

Along with the outstanding performances of the Time Tagger , our powerful software engine enables you to simultaneously carry out multiple measurements on-the-fly just by using a few lines of code in your favorite programming language (Python, Matlab, LabVIEW, C#/C++, Mathematica, .NET…) or by using a few clicks in our GUI TimeTaggerLab. Run, visualize, and analyze your experiments like never before!

Endless capabilities for photon counting are made easy with Time Tagger

Swabian Instruments' Time Tagger provide the new standard in time-correlated single photon counting. The unique data-streaming architecture and intuitive software sets us apart from our competitors. We help researchers drastically improve their work efficiency and expedite their research timelines. A recent publication shows how the integration of Time Tagger helps to perform cutting-edge PNR experiments [6].

Results demonstrated by Swabian Instruments’ Time Tagger in precise photon number resolution (PNR)

Figure 3. A) A two-dimensional histogram of the time difference between the trigger of a pulsed laser and the rising and falling edges of electrical pulses generated from detection events. The histogram shows well-distinguishable modes that can be related to the photon numbers. B) Projections of the histogram to the rising edge (blue) and for optimal mode distinction (red, along mode separation boundaries in Figure 3 A). Also, considering the falling edge results in substantially better distinguishability of photon-number modes. Figure adapted from [6].

Swabian Instruments' Time Taggers are powerful tools used to gain precise knowledge of the photons' arrival time. Therefore, their implementation is a key factor in precise photon number resolution (PNR) measurements. In a recent publication by G.Sauer et al. [6], a Time Tagger X was employed to read the signal from superconducting nanowire single-photon detectors (SNSPDs).

The approach of PNR experiments with SNPDSs is well established. However, conventional PNR measurements are carried out with several SNSPDs in parallel.

The cost-efficiency and precision of this pseudo-PNR method pose limitations. Here, the authors demonstrate how, with just a single SNSPD, it is possible to extract accurate PNR information from the detected signal. As shown in Figure 3, there is a clear distinguishability of photon modes with up to 5 photons. Thanks to Time Tagger X , it is now possible to measure the number of photons precisely using a single SNSPD, and with this method, the measurements can be precisely calibrated.

References

[1] A. Gaidash, et al. „Revealing beam-splitting attack in a quantum cryptography system with a photon-number resolving detector.", JOSA B, 33:1451–5 (2016)

[2] F.E. Becerra, et al., „Photon number resolution enables quantum receiver for realistic coherent optical communications.", Nat Photonics, 9:48 (2015)

[3] K. Nicolich, et al., "Universal Model for the Turn-on Dynamics of Superconducting Nanowire Single-Photon Detectors.", Phys. Rev. Applied, 12, 034020 (2019)

[4] C.R. Fitzpatrick, et al., „A superconducting nanowire single-photon detector system for single-photon source characterization.", Proceedings of SPIE, 7681, 768105 (2010)

[5] F. Marsili, et al., “Superconducting parallel nanowire detector with photon number resolving functionality.”, Journal of Modern Optics, 56:2-3, 334-344, DOI: 10.1080/09500340802220729 (2009)

[6] G. Sauer, et al., "Resolving Photon Numbers Using Ultra-High-Resolution Timing of a Single Low-Jitter Superconducting Nanowire Detector.", arXiv:2310.12472 [quant-ph] (2023)

[7] Mamoru Endo, et al., "Quantum detector tomography of a superconducting nanostrip photon-number-resolving detector.", Opt. Express 29, 11728-11738 (2021)

[8] T. Schapeler. Et al., “How well can superconducting nanowire single-photon detectors resolve photon number?”, arXiv:2310.12471 [quant-ph] (2023)