Superconducting nanowire single photon detectors for high-rate quantum communication

(1)

Thesis

Reference

Superconducting nanowire single photon detectors for high-rate quantum communication

PERRENOUD, Matthieu

Abstract

The important development of quantum technologies during the past decade brought the need for efficient, fast and precise single-photon detection. Superconducting Nanowire Single-Photon Detectors (SNSPDs) are currently considered as the detection method of choice when extreme performances are required. This thesis aimed at investigating this technology, with the objective of improving existing detectors for high-rate applications in quantum communication. This document presents the work and result achieved over four years dedicated to the subject. During this thesis, single-photon detection based on superconducting nanowire has been investigated, with a particular focus on specific requirements for high speed quantum communication applications. The work achieved ranges from the design and nano-fabrication of the structures, to the characterization and the understanding of the physics, detection models and fundamental limits of the devices.

PERRENOUD, Matthieu. Superconducting nanowire single photon detectors for

high-rate quantum communication. Thèse de doctorat : Univ. Genève, 2021, no. Sc. 5574

DOI : 10.13097/archive-ouverte/unige:153779 URN : urn:nbn:ch:unige-1537795

Available at:

http://archive-ouverte.unige.ch/unige:153779

Disclaimer: layout of this document may differ from the published version.

(2)

Université de Genève Faculté des Sciences Groupe de Physique Appliquée Professeur Hugo Zbinden

Superconducting nanowire single photon detectors for high-rate

quantum communication

Thèse

présentée à la Faculté des sciences de l’Université de Genève pour obtenir le grade de Docteur ès sciences, mention Physique

par

Matthieu Perrenoud

de La Sagne (NE)

Thèse n° 5574

Genève

Centre d’impression de l’Université de Genève 2021

(3)

(4)

Dedication

To my Mom and Dad.¹

(5)

(6)

“

The trouble is, humans do have a knack of choosing precisely those things that are worst for them.

Albus Dumbledore

”

(7)

(8)

Abstract

The important development of quantum technologies during the past decade brought the need for efficient, fast and precise single-photon detection. Superconducting Nanowire Single-Photon Detectors (SNSPDs) are currently considered as the detection method of choice when extreme performances are required. This thesis aimed at investigating this technology, with the objective of improving existing detectors for high-rate applications in quantum communication. This document presents the work and result achieved over four years dedicated to the subject.

The first and second chapter cover important notions concerning single-photon detection, with a particular focus on superconducting nanowire single-photon detectors. The design, fabrication, and characterization of such detectors is presented.

The third and fourth chapter constitute the core of the thesis. The investigation of advanced detector designs aiming at maximizing the detection rate of the devices is presented. Original solutions proposed and developed during this thesis are described and the results obtained are discussed. In chapter four, work on the readout circuit of the detectors is presented.

The final chapter briefly presents various experiments conducted in our group or in the frame of international collaborations, that benefited from the detectors fabricated by our group.

During this thesis, single-photon detection based on superconducting nanowire has been investigated, with a particular focus on specific requirements for high speed quantum communication applications. The work achieved ranges from the design and nano-fabrication of the structures, to the characterization and the understanding of the physics, detection models and fundamental limits of the devices.

(9)

(10)

Résumé

L’essor important des technologies quantiques au cours de la dernière décennie s’accompagne d’un besoin grandissant pour des détecteurs de photon uniques répondant à des critères extrêmement exigeants. Efficacités proche de l’unité, taux de détections de plusieurs dizaines de mégahertz, ou encore résolution temporelle de l’ordre de dizaines de picosec- ondes, sont autant de critères requis par ces nouvelles technologies.

Les détecteurs à nanofil supraconducteur (SNSPDs) constituent une technologie à la pointe de la détection de photon unique, capable d’atteindre les spécifications demandées par les applications les plus complexes. Ce travail de thèse s’intéresse à cette technologie, de son principe de fonctionnement à l’élaboration et à la caractérisation de solutions innovantes, en passant par le design et la fabrication des détecteurs eux-mêmes. Une attention particulière a été dédiée à la recherche de nouvelles solutions permettant de dépasser les limites actuelles de cette technologie en terme de taux de détection et temps de récupération, tout en conservant les excellentes performances obtenues en terme d’efficacité et de résolution temporelle.

Les deux premiers chapitres de ce document présentent la technologie des détecteurs de photon unique à nanofil supraconducteur, et décrivent brièvement les étapes de leur fabrication ainsi que les setups de mesure nécessaires à leur caractérisation.

Les chapitres trois et quatre constituent le cœur de ce travail. Plusieurs solutions pouvant mener à l’amélioration du taux de détection maximal des détecteurs ont été investiguées. En particulier, des designs innovants visant à s’affranchir des limitations observées sont proposés, tant concernant le détecteur lui-même que son circuit de lecture.

Les performances finales obtenues avec des détecteurs présentant des taux de détection de plusieurs centaines de mégaherzt sont présentées.

Finalement, le chapitre cinq présente brièvement certaines expériences conduites au groupe de physique appliquée ainsi que dans le cadre de collaborations internationales, et mettant à profits les qualités des détecteurs produits dans le cadre de cette thèse.

(11)

(12)

1 Introduction

Superconducting nanowire single photon detectors (SNSPDs) are a key tool for many modern quantum experiments and applications. This thesis focuses on the development of SNSPDs for quantum key distribution and quantum communication experiments, which are the main activity of the Quantum Technology group at the university of Geneva. This first chapter presents the context of this work as well as a review of the existing single photon detection solutions (section 1.1). Section 1.2 presents the detection mechanism of SNSPDs, with a discussion on the state of the art and limitations that are addressed in this work. Finally, the outline of the thesis is presented.

(15)

1.1 Quantum technologies and single-photon detection

From a new and revolutionary theory in the beginning of the 20^th century, quantum physics has made its path to experimental and applied fields [1]. New technologies are therefore needed to enable the use of this theory in practical applications.

Applied quantum mechanics might bring drastic changes in the way we send, process, and compute information. In particular, Quantum Key Distribution is a new technology using quantum properties in order to secure communications beyond the limitations of current cryptography systems. Quantum state can be encoded in many different physical systems, such as atoms, electrons, or photons. Photons are a system of choice when it comes to transferring a state to long distances and is therefore widely used for applications in quantum communications and cryptography. The ability to detect single photons efficiently is therefore a crucial point to build such technologies [2].

The past decade has seen an increase in interest in single-photon detector technologies.

A major cause of this trend has been the push towards optical quantum information applications such as quantum key distribution. These new applications require extreme detector performances. The performances of a single-photon detector are assessed in terms of its spectral range, dead time, dark count rate, detection efficiency, timing jitter and ability to resolve photon number. The different single-photon detection technologies and their corresponding performances are listed in table 1.1.

Note that the best performances for each category are given and the values are only indicative of the technology potential, it does not mean that detectors combines the performances at the same time. In practice, performances in one category are usually optimized at the expense of others and one has to think about which technology fits the best the requirements, which depends on the application. Other specifications such as the after pulsing effect, photon number resolving capabilities, power consumption, etc.

have to be taken into account as well.

This thesis presents the work achieved on Superconducting Single Photon Detectors (SNSPDs), from design and fabrication to device characterization. New solution designed to push forward the performances of our devices are presented. The practical use of the fabricated detectors for quantum information experiments and industrial applications will also be discussed.

(16)

1.2. SNSPDs detection mechanism

Figure 1.1: Meandered shaped nanowire (colored in blue). The circle represents the 3-sigma area of the optical mode of the fiber coupled to the detector, where 99.73% of the incident photons are located.

1.2 SNSPDs detection mechanism

Superconducting Nanowire Single Photon detectors were first introduced in 2001 [3].

This new type of detectors offers unprecedented quantum efficiencies [4, 5, 6] which have been pushed up to near unity very recently [7, 8]. Sub-Hertz dark count rates [9] can be obtained and a wide range of wavelength from X-Ray to mid-infrared can be detected.

SNSPD have a high temporal resolution, with timing jitter values typically under 100 ps and intrinsic jitter values below 10 ps have been demonstrated [10]. Detection rates of hundred of MHz can be obtained. However not all of these parameters can be obtained with the exact same device, and SNSPDs are typically designed to favor one or several characteristics above the others. Nevertheless SNSPDs currently offer the best combined performances among other existing single-photon detectors [11].

An SNSPD structure is fairly simple and the working principle of SNSPDs can be described in an intuitive manner. The detector consists, as the name suggest, in a thin superconducting film (typically few nm) of type-II superconductor, patterned into a long wire with a typical width of ∼100 nm. This nanowire is usually shaped as a meander which aims at covering a given surface area, usually much larger than the nanowire width itself, as shown on figure 1.1.

The meander area is usually chosen to match the optical mode diameter of an optical

(17)

is essential to reach high detection efficiencies. The percentage of the detection area effectively covered by the nanowires depends on the nanowire width and of the spacing between each meander line. This value is often referred to as the fill factor of the detector (FF) with :

F F = w

w+d (1.1)

withwthe nanowire width, and dthe distance separating two lines of the meander.

The nanowire is biased with aμA electronic currentI_b(represented on fig. 1.1). Absorption of a single photon into the superconducting film will make the superconducting nanowire switch to a resistive state, which will create a resistance of ∼1 kΩ, and will redirect the bias current to the readout circuit. Although the exact detection mechanism is not fully understood, the photo absorption process is usually described with the six consecutive steps shown on fig. 1.2 (see for example ref [3, 12, 13, 11]). However this is not the only description that has been done of the detection mechanism, and in particular the points (iii) and (iv) of fig. 1.2 are subject to discussion. Recent fundamental achievements on understanding the detection mechanisms can be found in ref. [14], but answering this question goes far beyond the scope of this thesis. The next paragraphs briefly presents important notions and definitions which will be used along this document.

(i)

(ii)

(iii) (iv)

(v)

t ≈ 6 nm w ≈ 150 nm

(vi)

I

b

Figure 1.2: Basic operation principle of an SNSPD (see [3, 12, 13, 11]) (i) A thin superconducting nanowire is biased near its critical current. (ii) An incoming photon is absorbed into the nanowire. (iii) The energy diffusion creates a cloud of excited electrons and phonons, so-called hotspot. (iv) This cloud then obstructs the current flow, leading to a non-superconducting cross-section in the nanowire that grows under the influence of Joule heating. (v) Because of the large resistive section (∼1 kΩ), the current is redirected in the readout electrics, producing a voltage pulse. (vi) The nanowire cools down and becomes superconducting again, ready to detect another photon.

(18)

Superconductivity

The superconducting absorptive film is at the core of the detector. Important properties of superconductors such as the penetration length [15], the coherence length [16] and the bandgap [17] were described in the early 1950s. The properties of type I superconductors were modeled by John Bardeen, Leon Cooper, and Robert Schrieffer in 1957 in what is commonly called the BCS theory of superconductivity [18, 19]. The theory goes far beyond the scope of this work, but a few key principles are of interest to us. Superconductors carry pairs of electrons, called Cooper pairs, which travel without interacting with the superconductor’s lattice and hence move resistance-free. This phenomenon is related to the bandgap of the material : the charge carriers energy is quantized, so that they do not have any available energy levels withing reach of the energies of interaction with the lattice.

Increasing the temperature will bring energy to the particles and get carriers across the gap and break the superconductivity. This temperature is called the critical temperature T_c of the material, and is directly linked to the band gap∆ in type I superconductors such that∆(T = 0) = 1.764kbTc.

Increasing the energy of the pairs can be done in different ways. Similarly to the critical temperature, a critical external magnetic field H_c (orB_c) and critical current density J_c can be measured. This can be represented on a phase diagram figure where the boundary between the superconducting state and the resistive state depends on those parameters (fig. 1.3). Type I superconductors are pure metals with small bandgaps (with typical Tc

around 1 K) hence they exhibit a very fragile superconductivity state and have limited practical applications. Type II superconductor are compounds or alloys and exhibit a mixed-state where single quanta of magnetic flux are allowed through the material up to a critical fieldHc2 much higher than Hc. Type II superconductor typically have higher T_c and H_c values and exhibit a more stable superconducting state. They have been the materials of choice for SNSPDs and other kind of superconducting detectors¹. A consequence of the nature of the Cooper pairs as the charge carrier is the kinetic inductance of the superconducting film. Nanowire made of superconductivity material exhibit a non-negligible inductance related to the material, temperature, and shape of the nanowire. The inductivity can be estimated from measured values [22, 23], and the final inductance value then depends on the length l, width wand thicknesst of the nanowire as well:

L_k = m nse²

l

w·t = λ²_L 0c²

l

w·t (1.2)

Wherem is the mass of the electron,nsis the superconducting electron density and λ_L is the London penetration depth, which can be estimated from the value of the penetration

1It is interesting to note that so called superconducting superheated granular detectors (SSG) made of type I superconductors have been investigated in the past for neutrino detection [20, 21] and seemed

(19)

depth at T=0, λ₀: λ_L= λ₀

r 1−

T Tc

4 (1.3)

Based on this calculation and experimental measurements on our superconducting thin films, we estimate the inductance of our 16 μm x 16μm SNSPDs between 500 nH to 1μH.

Figure 1.3: Phase diagram of type I and type II superconductor. Type II exhibit a mixed state (blue zone) in which vortex of magnetic flux can exist inside the superconducting material.

Image : Wikimedia Commons [24]

Energy-current relation and quantum efficiency

Intuitively, a photon bringing an energy lower than the bandgap of the superconducting thin film cannot break any Cooper pair. On the other hand, a high energy photon can bring enough energy to break multiples pairs. By applying a bias currentIb inside the nanowire, the energy of the pairs is increased so that a single photon can bring a sufficient amount of energy to break enough Cooper pairs and create a local resistive hotspot (step (ii) and (iii) of figure 1.2). There is therefore a specific threshold current which enables detections of photons at a given energy. The energy-current relation is a key feature of SNSPDs and was previously investigated with our devices using different incident wavelengths [25]. In the frame of this work, incident photons at 1550 nm were used for all the measurements. Typical detection vs. bias current curves (such as the one shown on figure 2.6) have a step-function shape. The transition region where the detection increases between 0 to its maximal value has been described as the consequence of Fano fluctuations, coming from the statistical nature of the quasiparticle creation process [26, 27, 28, 29]. The maximal value reached after the transition is referred to as the saturated efficiency of the detector, and it is crucial to use bias currents in this region to obtain the best performances of the thin film. The whole system detection efficiency (SDE) of the detector is one of the key characteristic of an SNSPD and is of course directly impacted by the quantum efficiency of the thin film. The SDE measurement setup and results obtained are presented in the next chapter, section 2.2.1.

(20)

Electro-thermal behavior

Figure 1.4: Typical detector readout. The two inset curves illustrate the current vs time behavior in the SNSPD (red) and inside the readout resistor and transformer (blue). A DC coupling is created using a transformer connected to the ground.

The time dynamics of a detection event is an important feature to understand the recovery time and maximum counting rate of a detector. After the hotspot formation in a nanowire section, the high resistive impedance of the thin film of material will force the current into the readout circuit. This signal will be pre-amplified at 40 Kelvin and read by the photon counting electronics at room temperature. The time dynamics of the current and temperature of the nanowire is central to the functioning of the device. Typical current behavior and DC readout circuit is illustrated on fig. 1.4. The DC coupling ensures the functioning of the readout at high detection rates where an AC coupling will create an increase of the bias current inside the detector due to charge accumulation on the capacitor² [31]. After a detection event, the nanowire is in a highly resistive state due to local Joule heating in the resistive strip (P_{J oule} =I_b²·R). Hence the current inside the nanowire will drop with a time constant τf all = Lk/(Rhotspot+Rs). During this short time (τ_{f all} typically is∼100 ps) the Joule heating in the resistive nanowire strip will decrease as well. This in turns influences the resistance of the hotspot, which starts cooling down. During the cooldown, as soon as the critical temperature Tcis reached, the nanowire impedance will fall down and current will start flowing back with a timing constant τ =L_k/R_s [32], with τ typically in the range of tens of nanoseconds.

However if this dynamic is too fast, Joule heating of the hotspot will be self-sustaining, resulting in a stable resistive domain [13, 33]. Figure 1.5, taken from the work of Yang et al. [13], illustrate this phenomenon. It is essential to control this dynamic to ensure the proper functioning of the device. This can be done by adapting the resistance of the readout to the kinetic inductance created by the section and length of the nanowire, with L_k ∝ l

w·t. Nevertheless, increasing the bias current too much will always results in the formation of a self-heating hotspot, and the detector will remain in a latched state. This

(21)

Figure 1.5: Plot of the current I inside the nanowire depending on time (a) and temperature (b), for a device with Lk = 60nH and different values of load resistorR.

Images : Yang et al. [13]

limit is commonly called the latching current I_L of the device, and particular care has to be taken so that its value is higher than the saturation current of the detector. Another regime exists, where the hotspot is not self-heating, but an excessively fast dynamic of the bias current leads to an increase of the current density above the critical value J_c(T) for a given temperature during the cool down. This results in an oscillation-relaxation regime. The current at which this effect is observed is referred as the critical current Ic

of the detector.

Important characteristics of SNSPDs are directly linked to the dynamic of the bias current.

Indeed, as described above, a too low bias current effectively leads to a zero efficiency of the detector after detection. The efficiency of the detector will recover over time, according to the bias current dynamic and the energy-current relation. The recovery-time (RT) of the efficiency will be discussed in greater details in section 2.2.3. The detection rate of conventional SNSPDs is ultimately limited by the recovery time, hence by the time dynamic of the bias current [32]. If consecutive photons are absorbed with short time intervals below the recovery time, the average detection probability of the second photon will be lowered as the detector full efficiency was not yet recovered. Consequently, at high detection rates where successive detections can happen in time intervals of the order of τ, the average SDE drops. Definition of the SNSPD maximum detection rate, measurement and results obtained with single-meander SNSPDs are presented in section 2.2.2. Improving the maximum detection rate has been a large part of this work, and extensive discussions on possible solutions and results obtained are presented in chapters 3 and 4.

(22)

1.3. Thesis outline

Superconducting material consideration

The work reported in this thesis has been done using superconducting films of Molybdenum Silicide with a stochiometry of 80%-20% (Mo0.8Si0.2). Usage of MoSi thin films presents several advantages. Unlike crystalline structures commonly used for the fabrication of SNSPDs such as NbN or NbTiN films, MoSi is an amorphous material which makes it easier to deposit in a stable and reproducible way thus enabling fabrication with a high yield. The critical temperature Tc of MoSi is similar than that of WSi [34, 35] (which is another amorphous material commonly used for SNSPDs fabrication)³. The energy bandgap of MoSi is lower than that of NbN or NbTiN, making it a very sensitive material for which the saturated efficiency can be easily reached.

The detector performances of course depend on the superconducting film, and it is possible that some other material lead to better characteristics. In particular, the kinetic inductance of a superconducting nanowire highly depends on the material properties.

Materials with a lower inductivity such as NbN or NbTiN [37] might exhibit faster recovery time after detection and higher latching current values. Although primarily developed to push the limits of our MoSi SNSPDs, the concepts presented in this work could be applied to other sort of material as well and are not restricted to MoSi only. In particular, NbTiN thin films are currently investigated in our group, which have the potential to yield better performances than MoSi on almost all detection aspects. Combining superconducting films of such materials with the solutions proposed in this work could be possible and might improve the performances of commonly used single-meander SNSPDs made out of these materials as well.

1.3 Thesis outline

The work presented in this thesis focuses on improving performances of MoSi superconducting nanowire single photon detectors for quantum applications. In particular, efforts were dedicated to improve the efficiency of the detector at high detection rates (in the order of tens to hundreds of MHz). Similarly, the recovery time of the detectors is reduced, which can be essential for given applications. The first part of the present work briefly explains the design and fabrication process, as well as the measurement setups used for the characterization of our detectors (chapter 2). The second part introduces the main results obtained with multi-nanowire detector designs (chapter 3) and improved readout (chapter 4). Finally, in chapter 5, results obtained in quantum experiments that made

use of the detectors created during this work are presented.

(23)

Table 1.1: Comparison of single-photon detectors. The values are indicative of the technology potential, in the sense that the best performances of each category are revealed independently of the other categories. As explained above, this does not mean that one detector based on a specific technology exhibits these performances simultaneously. The data are updated from [2]. For high efficiency SNSPDs, see [4, 5, 6, 7]. For InGaAs SPAD, see [38, 39, 40]. Otherwise, see [2].

Detector Temp. Detection Timing DCR Max. count Spectral

type (K) efficiency jitter rate range

PMT (NUV-NIR) RT 40% at 500 nm 300 ps 100 kHz 10 MHz NUV-NIR

PMT (IR) 200 K 2% at 1550 nm 300 ps 200 kHz 10 MHz IR

MCP-PMT RT 25% at 500 nm 55 ps 100 Hz 10 MHz NUV-NIR

Si SPAD (TJ) RT 65% at 650 nm 400 ps 25 Hz 10 MHz Visible

Si SPAD (SJ) RT 49% at 550 nm 35 ps 25 Hz 10 MHz Visible

CMOS SPAD RT 50% at 550 nm 80 ps 50 Hz 10 MHz Visible

VLPC 6 K 88% at 694 nm 270 ps 20 kHz - Visible

MKID 0.1 K 90% at 285 nm 50 ns 1 Hz 100 kHz X-ray–FIR

TES 0.1 K 98% at 1550 nm 100 ns 3 Hz 100 kHz NIR

InGaAs SPAD 240 K 55% at 1550 nm 50 ps 1 kHz 100 MHz NIR

SNSPD 1-3 K 98% at 1550 nm 3 ps 10⁻³ Hz 200 MHz X-ray–MIR

(24)

2 Design, nano-fabrication, and mea- surement setups

The optimization of existing detector design and creation of new solutions is at the core of the work presented in this document. Although the main results discussed in this thesis concern novel SNSPD designs, a large amount of effort has also been produced to optimize the performances of single-meander SNSPDs fabricated in our group. Hence design, fabrication optimization, and testing of the detectors have been a consequent part of the effort needed to obtain the results presented in this document. In this chapter, the design tools and main nano-fabrication processes will be introduced. The second part of this chapter focuses on the measurement setups used for the characterization of our devices and presents results obtained with Molybdenum-Silicide single-meandered SNSPDs fabricated in our lab.

(25)

2.1 SNSPD design and nanofabrication

The first step needed before starting the fabrication process is of course the design of the different elements of the detector. The geometry of the nanowire, integrated elements (namely, resistors and superconducting kinetic inductances), contact pads and external shape of the detector are defined using kLayout. The .gds file format is an industry standard for computer aided design (CAD) and is used by all the cleanroom tools used during the fabrication process presented hereafter. GDS files can be produced via the software’s user interface, however this approach is highly time consuming. Producing design files via Python scripts allows the creation of multiple designs with different dimensions and shapes (2.1).

kLayout

The KLayout software works with the GDS standard for CAD conception. The software allows the creation, visualization, and edition of GDS design file with sub-nanometer resolution. The tool is particularly useful to visualize GDS files created via Python.

Figure 2.1: Screenshot of KLayout’s user interface. Each layer (i.e the colors listed on the right hand side) corresponds to the geometry of a specific fabrication process. Each device can be visualized individually via the ’cell’ list on the left-hand side of the interface.

gdsCAD for Python

Creating hundreds of different designs with various dimensions cannot be done manually.

The python packagegdsCAD provides tools to generate.gds files using python scripts.

An extensive amount of work during this thesis has been dedicated to develop a python software tool to create various SNSPD designs elements and connect them together to generate the full .gds file needed for fabrication. This software has been used to produce

(26)

2.1. SNSPD design and nanofabrication all the advanced designs presented in this document. It allows for different connection of multi-nanowires detectors, with additional components such as integrated resistors and inductors. The dimensions of every component can be modified by the user. This permits the creation of multiple designs of similar constructions with varying dimensions. Several hundreds of detector design variations were produced and fabricated.

Nano-fabrication

Nano-fabrication refers to the different processes used to create micro and nano structures into various materials. These techniques are extensively used in the manufacturing of integrated electronics and allow for high precision, high yield, and reproducibility.

Extensive work has been performed during this thesis to improve the fabrication process of the SNSPDs fabricated in the lab, giving higher yield, reproducibility, and improved overall performances. The fabrication was performed at center for micro and nanotechnologies at the Swiss Institute of Technology, Lausanne (EPFL - CMi). Figure 2.2a shows the typical stack of patterned materials used for the fabrication of a detector, while figure 2.2b shows an actual SEM image of the top layer once connected to contact electrodes.

(a) Scaled representation of the layer stack obtained after the SNSPD patterning process.

The z-axis was scaled by a factor 100 for a better view of the different layers of the optical cavity.

(b) Colored SEM image of the electrodes (yel- low) made of 10 nm Ti and 90 nm Au layers deposited on top of the patterned superconducting material (red).

Figure 2.2: Illustration of the fabrication stack of patterned layers of different materials.

The optical cavity is closed by a final layer of 10 nm SiO2. See appendix B.5 for the detailed process flow.

The different nanofabrication processes used to fabricate the devices are described in greater details in appendix B. And some of the process optimizations are presented in

(27)

Packaging

Once the wafer fabrication is done, the devices are individually separated by etching through the wafer using a deep reactive ion etching (DRIE) process (details in appendix B).

The final devices “lollipop” shape enable the use of a self-aligned packaging technique, with the head of the lollipop matching the diameter of zirconium fiber optic sleeves [41].

The electrodes are accessible outside the sleeve and are wire-bonded to a coaxial cable SMP connector (fig. 2.3). Once the devices are packaged on their holder, they are placed in a cryostat and cooled down to 0.8 Kelvin.

Figure 2.3: Packaged SNSPDs. The optical fibers are self-aligned with the center of the meandered nanowire thanks to the matching diameter between the detector head and zirkonium ferrule.

(28)

2.2. Measurement setups and performances of MoSi SNSPDs

2.2 Measurement setups and performances of MoSi SNSPDs

2.2.1 System Detection Efficiency

The System Detection Efficiency (SDE) refers to the ability of the whole system to detect incoming single photons. The SDE depends on the coupling efficiency with the photon source ηcoupling (fig. 2.4a), the absorption efficiency of the superconducting layer η_absorb (fig. 2.4b), and internal quantum efficiencyηQE (fig. 2.4c) which is the efficiency of the hotspot generation process after photoabsorption and was presented previously in section 1.2.

η(I_b) =η_coupling·η_absorb·η_QE(I_b) (2.1)

The coupling efficiency can be optimized by minimizing optical fiber connections and using a self-align packaging technique [41] to couple the fiber on the detector. A high filling factor of the meander will also help improve the coupling.

The absorption efficiency depends on the film thickness, which typically has to be kept to a few nanometers to prevent loss of quantum efficiency. Integration of the superconducting nanowire into an optical cavity which optimizes the field intensity at the film location help improve the absorption efficiency.

The quantum efficiency of the detector depends on how close the bias current is to the maximum current density allowed in the nanowire. As explained in section 1.2, properly designed SNSPDs show a saturated region in their bias current vs. efficiency relation : with a sufficiently high current, no further improvement of the quantum efficiency is observed. To obtain this behavior, a superconducting film with a critical temperature T_c much above the working temperature of the detector is necessary. Otherwise, the bias current cannot be increased high enough to reach the saturated quantum efficiency.

(a) Coupling efficiency (b) Absorption efficiency (c) Internal quantum efficiency

Figure 2.4: Illustration of the three components of the system detection efficiency.

(29)

Chapter 2. Design, nano-fabrication, and measurement setups

Optical fibres

SNSPD

DC

CW Laser

Powermeter

easyphi

Var. Att.

1 2 3

Switch Polar.

control.

Cryostat

AMP ^RF

Bias tee

DC+RF

Counter Current

source Electrical cables

0.8-2.5K

40K AMP

monochromator

1550 nm

Figure 2.5: Representation of the system detection efficiency characterization setup.

The experimental setup for SDE measurement uses three variable attenuators in series, which can be seen on the setup schematic, figure 2.5. A precise calibration of each attenuator separately is possible via a calibrated powermeter. After calibration of each attenuator, it is possible to calculate the estimated photon flux passing through all of them being connected in series. A typical photon flux used for this measurement is10⁵ average photons per second with a CW laser at 1550 nm. This ensures that the probability of generating two consecutive photons at time intervals shorter than the recovery time of the detector is almost 0. Obtaining saturated efficiency, such as on figure 2.6 is a good indication of the validity of a design. In this text, we will sometimes refer to the saturated efficiency value at low detection rate (i.e around 10⁵ detection per second) as the “nominal efficiency” of the detector.

25.0 27.5 30.0 32.5 35.0 37.5 40.0 42.5 45.0 Total bias current [ µ A]

0 20 40 60 80 100

Sy st em D et ec ti on E ffi ci en cy [% ]

10

^-2

10

^-1

10

⁰

10

¹

10

²

10

³

10

⁴

10

⁵

10

⁶

10

⁷

D ar k C ou nt R at e [c ps ]

Figure 2.6: System Detection Efficiency of a single-meander SNSPDs as a function of the bias current I_b. Saturated efficiency is obtained at a bias current of I_b = 37.5 μA. The blue curve (right-axis) shows the dark count rate of the same device.

(30)

2.2.2 Maximum Detection Rate

The previous section described the efficiency of the detector when working with relatively low photon flux, which is defined as a low probability of consecutive photons being absorbed in the detector at time intervals shorter than the recovery time of the detector.

However, many applications such as QKD could benefit from detection rates up to the GHz range, and it is therefore important to characterize the behavior of the detector under regimes where the average incoming photon flux exceeds the ability of the detector to remain at maximum efficiency due to photo absorptions during the detector dead time.

10

⁴

10

⁵

10

⁶

10

⁷

10

⁸

10

⁹

Detection Rate [Hz]

0 20 40 60 80 100

Sy st em D et ec ti on E ffi ci en cy [% ]

Absolute Efficiency Normalized Efficiency

Figure 2.7: Efficiency vs. detection rate of the same single-meander SNSPD, measured at a bias current of I_b = 41μA. The normalized efficiency curve shows the same data, with the efficiency at low count rate normalized to 1. A loss of 50% of the nominal efficiency is observed at a detection rate of 4.2 MHz.

Using the same setup as described above on figure 2.5 and used to measure the SDE, we now fix the bias current of the detector to the maximum possible value (i.eI_b ∼I_c).

Then, the incoming photon flux is progressively increased while monitoring the number of detection for each incoming flux value. Figure 2.7 shows the efficiency vs. detection rate of the detector. We define the detection rate at 50% of the nominal efficiency as the maximum detection rate of the detector and use this value to compare the ability of the detectors at high rates. Typical MoSi meander such as the one presented in this chapter show a maximum detection rate below 10 MHz.

Improving this limitation of SNSPDs has been the main objective of this work. The

(31)

2.2.3 Recovery Time

We define the recovery time as the time needed for the efficiency to come back to 90% of the nominal efficiency value after a detection event. This time is given by the bias current dynamics after a detection, and the efficiency vs. Ib characteristic. Indeed, the efficiency will be fully recovered when the bias current reaches the beginning of the saturated region.

Detectors with long saturation plateau are therefore typically faster than those with almost no saturated region. The recovery time of the detector is strongly correlated with the maximum detection rate, however it is interesting to obtain a direct measurement of this value. We proposed a measurement setup recording time stamps of detection event while periodically illuminating the detector with a bright pulse of light to force a detection.

The setup is presented on figure 2.8. The histogram of the detection events occurring after the forced detection provides a direct measurement of the efficiency vs. time after detection. A more detailed description of the setup can be found in our publication [42].

Figure 2.8: Schematics of the experimental setup for the hybrid-autocorrelation method.

The delay generator (DG) provides a trigger signal for the laser, as well as a timing reference for the Time to Digital Converter board (TDC).

Single-meander detectors typically provide recovery time at 90% efficiency above 100 ns.

The recovery time is directly related to the current flowing in the detector. Detector with faster timing constant due to low kinetic inductance typically recover faster. In addition, the length of the saturated efficiency region also plays a crucial role : if the bias current used is much higher than the saturation current (i.e. the current at which the saturated efficiency value is reached) then the full efficiency will be obtained before the current actually fully recovered to its original value. Figure 2.9 shows the histogram obtained with a single-meander MoSi SNSPD.

The same experiment was also performed with two and three subsequent bright pulses at short time interval, which let us confirm that the recovery-time of the detector was not modified by multiple consecutive absorptions and remains the same as measured with a single forced detection event.

The direct measure of the recovery time is particularly useful for specific applications.

This measurement, along with novel SNSPD designs presented in section 3.4, allowed us to select a detector with a particularly short recovery time which was necessary to perform the quantum communication experiment presented in section 5.3.

(32)

50 0 50 100 150 200 250 300 350

Time [ns]

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Counts

1e3

Ib =26.0µA Ib =28.0µA Ib =30.0µA Ib =32.0µA Ib =34.0µA Ib =36.0µA

(a) Histogram of the number of counts recorded over time, while forcing the detector to switch to its resistive stage at time t = 0. The measurement is repeated over an integration time of 60 seconds to obtain the distribution.

50 0 50 100 150 200 250 300 350

Time [ns]

0.0 0.2 0.4 0.6 0.8 1.0 1.2

NormalizedEfficiency

(b) Same data presented on fig. 2.9a, normalized to the nominal efficiency. Recovery times to 90% of the nominal efficiency are highlighted for each different currents. Values from 123 ns to 340 ns are obtained, which highlights the importance of using high bias currents on detectors with saturated efficiencies.

Figure 2.9: Recovery time of a single-meander SNSPD biased with different currents.

2.2.4 Jitter

The timing jitter refers to the timing fluctuation between the photon absorption time and the detection time at which the event is recorded. A delay is of course expected, as the detection mechanism, propagation of the signal, amplification, and discrimination processes are not instantaneous. This delay however has to be highly consistent from one measurement to the other. It is important to characterize the jitter of our detectors, since many of the quantum experiments in which they will be used require time resolution below 100 ps [43].

Start Stop

Optical fibres

SNSPD

DC

Laser

Powermeter

easyphi discri rapide

(ID280)

Var. Att.

1 2 3

Polar.

control.

Cryostat TCSPC

AMP ^RF

Bias tee

DC+RF

Counter

Current source

Electrical cables SYNC

signal

0.8-2.5K

40K AMP

monochromator

Switch

Figure 2.10: Jitter characterization setup

(33)

A typical jitter measurement consists in acquiring data of a large number of detections and plot the histogram of the time recorded between the photo emission and the detection event. This is achieved by using a laser at 1550 nm from NuPhoton Technologies Inc.

with extremely short pulse duration (6 ps), which also provides an electronic trigger signal when a pulse is emitted. The pulses are attenuated to obtain an average number of photon per pulse µ∼0.01, which guarantees that detections occur at the single-photon level. A dedicated Time-Correlated Single Photon Counting module (TCSPC) is connected to the laser trigger signal and the output signal of the detector, as shown on figure 2.10. The time bins and temporal resolution of the TCSPC module used for the measurement are in the order of few ps, which guarantee high resolution.

−150 −100 −50 0 50 100 150

Time [ps]

0x10³ 2x10³ 5x10³ 8x10³ 10x10³ 12x10³ 15x10³ 18x10³ 20x10³

N um be r of oc cu re nc es

Figure 2.11: Timing distribution of the detection time with respect to the laser trigger signal. The jitter characterizes the spread of this distribution. The full width at half maximum (FWHM) jitter of the device presented here is 39.1 ps.

The timing histogram of a single-meandered SNSPDs is shown on fig. 2.11. The full width at half maximum (FWHM) of the distribution is usually defined as the jitter of the detector. Jitter values around 40 ps are typically obtained with our MoSi detectors, which is much lower than what has been reported in the past for the same material [44]. Some of our detectors even achieved values as low as 26 ps [10]. This is nevertheless higher than what can be obtained with materials as NbN and NbTiN [45] in which single-meandered SNSPDs have demonstrated jitters of ∼15 ps.

(34)

3 Detection rate improvement based on multi-elements designs

An important part of this thesis has been dedicated to overcoming limitations of conventional free-running SNSPDs in terms of maximum detection rate and recovery time. This chapter starts with an introduction presenting the limits of conventional single-meander SNSPDs and reviews different existing solutions (section 3.1). The solutions investigated during this thesis are presented in sections 3.2 and 3.3, and a novel design aiming at overcoming the limitations found is proposed in section 3.4. Finally, the photon-number resolving capability of those designs is discussed (section 3.5), as well as the potential of the solution to help build fast and efficient large-area detectors for multi-mode fiber coupling (section 3.6).

(35)

3.1 Reduced recovery-time and higher detection rates

The most common SNSPDs are based on a single meander and yield detection rates of tens of MHz, but the system detection efficiency decreases with detection rates in the MHz range. During this thesis, a great amount of effort has been put to overcome this limitation by testing different designs and proposing novel solutions. Indeed, as explained in chapter 1, the detection rate of SNSPDs is ultimately limited by the time dynamics of the bias current after detection, which is itself limited by electro-thermal considerations [32]. The impact on the detector detection rate and recovery time of conventional SNSPDs has been discussed in sections 2.2.2 and 2.2.3.

Shorter recovery times, hence higher detection rates, can be obtained by reducing the kinetic inductance of the detector. One approach to reduce the overall recovery time is cascade switching SNSPDs [46], also known as SNAPs, however their efficiency after detection still drop to zero as with conventional SNSPDs. Similarly, sub-nanosecond recovery times (RT) can be obtained with extremely short nanowires coupled to integrated waveguides [47], but such detectors have so far not shown high system detection efficiency when coupled to an optical fiber. Gated SNSPDs can solve the latching issue and effectively yield to detection rates of hundreds of MHz [48, 49, 50] but they are limited to applications that can be synchronized with the detector bias current. Arrays of detectors (referred in this text as “multipixels SNSPDs” and discussed in detail in section 3.2) can be used to keep the efficiency up at high detection rates [51, 52, 53]. Multi-element designs such as these have two main advantages : each element has a smaller kinetic inductance, and only one part of the whole detector is disabled after a detection event, leading to an effective non-zero efficiency after detection. In the case of multi-pixel SNSPDs, this comes at the cost of using multiple coaxial readout lines, which increases the cooling power needed to operate the system, and also demands a proportionally scaled and complex electronics readout circuitry with multiple discriminators and time-tagging units. Results obtained with this solution are presented on section 3.2. Row-columns array designs can reduce the number of coaxial lines needed, but still require at least one readout line per row and per column [54, 55], as many amplification channels, and additional processing to manage the timing-accurate readout of those different channel. Moreover, large inductors are needed to prevent crosstalk between pixels, which slows down their individual detection rate. RF-biased SNSPDs [56] allow for efficient multiplexing of detectors onto a single coaxial line, however the detection efficiency obtained with an RF bias seems to suffer from the oscillating bias current, and the complexity of RF signal generation is significantly higher than for conventional DC-biased SNSPDs.

Increasing the detection rate of SNSPDs without increasing i) the number of coaxial lines, ii) the constraints on the size and cooling power of the cryostat, and iii) the complexity and costs of the operating and readout electronics, is therefore of great practical advantage. This would contribute to spreading the use of SNSPDs further.

During this thesis, I investigated possible solutions to improve the detection rate of

(36)

3.2. Multi-Pixel SNSPDs SNSPDs while minimizing the impacts on the aforementioned points. In addition of multipixel detector, I investigated series and parallel structures, their potential and limitations, which are discussed in section 3.3. I then proposed a solution that mitigates issues found in parallel designs and enabled latch-free operation at high detection rates, which is presented in section 3.4. All measurements presented in this chapter are performed with continuous light at 1550 nm, at a temperature of 0.82 K, except for the photon-number resolving data presented in section 3.5 which was taken using a 33 ps pulsed laser at 1550 nm.

3.2 Multi-Pixel SNSPDs

3.2.1 Design

Multi-pixel SNSPDs consist in an array of nanowires, which together cover the same surface area as a single conventional SNSPD meander. As explained above, among other advantages such design allow for higher detection rates. We created 4-pixels designs and fabricated them following the same process described in appendix B for conventional SNSPDs (figure 3.1).

One disadvantage of this design is the need for multiple coaxial lines (one for each pixel) which are required to read the individual signals. As seen on fig. 3.2, each pixel is fully independent from its neighbours and a cryo amplifier is used for each readout. Hence four coaxial cables are used from the 0.8 Kelvin stage to the 40 Kelvin stage where the amplifiers are placed. Additional coaxial cables are used from this stage to the outside of the cryostat where the pixels signal are further amplified and discriminated, each with its specific electronics. This additional load on the cyrostat cooling power, as well as additional readout complexity, prevents easy scaling of the solution to high number of pixels. Nevertheless, impressive results have been obtained with this solution. Recent work on 16 pixels interleaved arrays demonstrated SDE of 50% at 500 MHz and reached rates of 1.2 GHz with a SDE of ∼12% [52]. Large arrays up to 64 pixels have even been demonstrated [57] but the practical cost of such system is much higher than what is usually considered standard for single-photon detector applications.

3.2.2 Results

We tested the multipixel devices with the same characterization setups used with conventional SNSPDs. Results presented here were obtained with a device similar to the one on fig. 3.1b. The detector has four pixels separated from each other by 633 nm. Each pixel is made of a 6 nm thick, 100 nm wide (90 nm on the device imaged on fig 3.1b) nanowire. The filling factor of each pixel is 60%. All pixels were illuminated with CW light at 1550 nm through a single SMF fiber. The four outputs were each discriminated

(37)

(a) Squared pixels design. The length of each nanowire is equal, so that the recovery time is consistent for each pixel. No additional spacing was added between the pixels.

(b) Round multipixels design. Here the two central pixels have a shorter length than the top and bottom ones, and are expected to have a slightly higher maximum detection rate. Ad- ditional spacing between the pixels was added to avoid thermal crosstalk (see section 3.2.3).

Figure 3.1: SEM images of two multipixels SNSPDs designs. Colors are added on the picture to highlight the position and contacts of the four different pixels. The expected optical mode of the fiber is represented by the white circle. In these two cases, the exposed area of each pixel has been calculated so that the average number of photon absorbed is equal. Hence the central pixels have a reduced exposed area. We will refer to the pixels with numbers 1 to 4 in the text, from bottom to top.

Figure 3.2: Schematics of a multipixel detector readout. Each nanowire is connected individually to its own amplification electronic via a coaxial line.

(38)

3.2. Multi-Pixel SNSPDs separately using the four inputs of our ID900 Time Controller. We obtained saturated efficiencies of 5.5%, 14.9%, 19.1%, 13.3% for each pixel respectively from top to bottom.

Figure 3.3a shows the SDEvs. bias current curve for each pixels, with colors matching the representation on fig 3.1b. It is interesting to note that the efficiencies are not equal on the two inner or outer pixels, as one could expect. This issue has been observed on several devices and might indicate a small offset created by the self-alignment method used when coupling the optical fiber on the detector. Hence a lower efficiency is observed on the top pixel (pixel 1). The dashed purple line gives the calculated sum of each measurement, which corresponds to the global efficiency of the detector. It is important to note that, in this case, the sum was performed after the independent measurement on each pixel. A final setup would require to sum the output of the four different discriminators in real time.

The normalized efficiencyvs. detection rate of each pixel is plotted on figure 3.3b with the same color code. As expected, each single pixel reaches a higher maximum detection rate than single-meander SNSPDs. Rates of 14.5 MHz, 20 MHz, 24.5 MHz and 20.5 MHz are observed for each pixel respectively. This is around 5 times higher than the rate observed on the single-meander device presented in chapter 2 (figure 2.2.2) and corresponds to the expected reduced kinetic inductance of each pixels. The measurements are taken independently on each pixel consecutively. The sum of the efficiencies gives an indication on what count should be obtained when using such a detector with the 4 simultaneous output summed. Detection rates around 78 MHz could be obtained with a 50% loss of efficiency compared to the value at low detection rate. Increasing the incoming photon flux leads to further drop of the efficiency, but detection rates of more than 200 MHz with an average SDE of∼3% could be obtained in this regime. We also measured the jitter of each pixel independently and obtained values of 35 ps to 38.3 ps FWHM which is consistent with typical values obtained with single meander SNSPDs.

These measurements demonstrate that increasing the detection rate of SNSPDs while minimizing the loss of efficiency is possible with multiple shorter nanowires. However the increased thermal load on the cryostat and the electronic complexity quickly become an issue when scaling up the system to more nanowires.

3.2.3 Thermal Crosstalk

When first testing multipixel detectors, we observed coincidences between adjacent pixels output signals. Output pulses of adjacent pixels had a non-zero probability to be triggered at the same time. This effect is most likely caused by thermal crosstalk between the pixels : the heat generated by the hotspot heats up the neighbouring pixel, the local temperature rises and lowers the critical current density J_s(T) of the nanowire which switches to its resistive state. This effect has been described before and can even be used to improve certain characteristics of the detectors by taking advantage of the thermal

(39)

15 20 25 30 35 40 45

Bias Current [µA]

0 10 20 30 40 50 60 70

SystemDetectionEfficiency[%]

pixel 1 pixel 2 pixel 3 pixel 4 pixels sum

(a) SDE of each pixels. The total efficiency is lower than that of conventional single-meanders SNSPDs, because of the additional distance between the pixels.

10⁵ 10⁶ 10⁷ 10⁸

Detection Rate [Hz]

0 20 40 60 80 100

NormalizedDetectionEfficiency[%] ^{pixel 1}pixel 2 pixel 3 pixel 4 pixels sum

(b) Normalized efficiency vs. detection rate for each pixel. The lower kinetic inductance improves their maximum detection rate of each pixel compared to single-meander devices.

Figure 3.3: Results obtained with a 4-pixels SNSPD. Each pixel was measured independently. The sum was obtained by adding the results of each pixels. A real-time use of the device requires using four different discriminators and summing theirs outputs in real time.

avalanche [58]. In our case, this effect is unwanted because the neighbouring nanowires must remain superconducting for subsequent photodetections. We investigated the issue using a start-stop timestamp setup which allowed us to display the histogram of coincident detections, as shown on fig. 3.4. This figure shows the histogram of the timing difference between two pixel clicks. We used a low average number of incoming photon per second µ(approximately10⁵ photons per second), which ensures that the coincidence peaks seen on fig. 3.4 are due to interaction between the pixels and are not generated by different photo detection at short time intervals. The localised timing distribution obtained show that the output of these two pixels are indeed correlated. Such correlations occurs only in neighbouring pixels.

The amount of time needed for the hotspot to heat up the neighbour pixel enough so that its critical current decreases belowIb is given by the time difference between the blue pixel click (dashed blue line on the figure), and the measured point. As expected, lowering the bias current increases the coincidence delay, as a higher temperature is needed to lower the critical current density Jc(T) under the bias current density. Interestingly, there are other distributions of coincident detections at later timings. This suggest that the same phenomenon can also be triggered by a photon being absorbed in the second or the third line of the meander, as illustrated on figure 3.4. In such case, the time needed for the nanowire to switch to the resistive state is increased and the distribution becomes less sharp.

(40)

3.2. Multi-Pixel SNSPDs

Figure 3.4: Illustration of the thermal crosstalk between pixels. A hotspot in a nanowire close to the edge of a pixel will trigger a hotspot in the neighbour pixel. Different timing can be observed depending on which exact line of the meander absorbed the photon. The blue dashed line indicates the timing of the blue pixel click. The measured points are the green pixel timings for different bias currents.

This information is of great interest when designing multi-nanowire SNSPDs such as those presented in this chapter. The thermal crosstalk might introduce false detections, this can be corrected by introducing a deadtime in the readout electronics of all outputs after a single detection. However this defeats the purpose of the design, which is reaching higher detection rates. Moreover, as single photon can deactivate two pixels at the same time, the possibility for subsequent photon detection at high rates could also be hindered by the thermal crosstalk.

Based on this information, we created designs where pixels are separated by a distance above 600 nm, where no thermal crosstalk was observed (fig. 3.1b). This solution decreases the global fill factor of the detectors (which lowers the total SDE), a trade-off could be found using closer pixels while still limiting the thermal crosstalk to a fairly low probability. It could also be interesting to better thermally insulate the pixels from each other, and use substrates with higher thermal conductivity which would act as an heatsink to help dissipate the energy of the hotspot. The optimization of the mirror cavity could also help to recover high efficiencies with lower fill factors.

Superconducting nanowire single photon detectors for high-rate quantum communication

Thesis

Reference

Superconducting nanowire single photon detectors for high-rate quantum communication

Université de Genève Faculté des Sciences Groupe de Physique Appliquée Professeur Hugo Zbinden

Superconducting nanowire single photon detectors for high-rate

quantum communication

Thèse

Matthieu Perrenoud

Dedication

“

”

Abstract

Résumé

Contents

1 Introduction

1.1 Quantum technologies and single-photon detection

1.2 SNSPDs detection mechanism

I

1.3 Thesis outline

2 Design, nano-fabrication, and mea- surement setups

2.1 SNSPD design and nanofabrication

2.2 Measurement setups and performances of MoSi SNSPDs

25.0 27.5 30.0 32.5 35.0 37.5 40.0 42.5 45.0 Total bias current [ µ A]

0 20 40 60 80 100

Sy st em D et ec ti on E ffi ci en cy [% ]

10

10

10

10

10

10

10

10

10

10

D ar k C ou nt R at e [c ps ]

10

10

10

10

10

10

Detection Rate [Hz]

0 20 40 60 80 100

Sy st em D et ec ti on E ffi ci en cy [% ]

Time [ps]

N um be r of oc cu re nc es

3 Detection rate improvement based on multi-elements designs

3.1 Reduced recovery-time and higher detection rates

3.2 Multi-Pixel SNSPDs