Protocol and devices for practical quantum information processing

(1)

Thesis

Reference

Protocol and devices for practical quantum information processing

LUNGHI, Tommaso

Abstract

During my thesis I investigated several technologies and protocols aiming at practical quantum-cryptography applications. Firstly, I developed a free-running single-photon detector for telecom wavelengths featured by an extremely low noise that competes with the state-of-the-art superconducting single-photon detectors. Then I developed a testbench for metrological characterization of single-photon detectors. A special source of spontaneous emission and a radiometer have been developed during this work. Both the source and the radiometer are based on an Erbium-doped fiber and have been built using standard commercial components. In the third part of my thesis I discuss the first experimental demonstration of a bit commitment protocol provably secure. Finally I investigated an innovative approach to self-test the randomness underlying a quantum process. This approach allows generating unpredictable strings of bits with few calibrations of the device.

LUNGHI, Tommaso. Protocol and devices for practical quantum information processing . Thèse de doctorat : Univ. Genève, 2014, no. Sc. 4729

URN : urn:nbn:ch:unige-459406

DOI : 10.13097/archive-ouverte/unige:45940

Available at:

http://archive-ouverte.unige.ch/unige:45940

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

1 / 1

(2)

Université de Genève

Groupe de Physique Appliquée Faculté des Sciences Professeur Hugo Zbinden

Protocol and devices for practical quantum information processing

Thèse

présentée à la Faculté des Sciences de l'Université de Genève pour obtenir le grade de Docteur ès Sciences, mention physique

par

Tommaso Lunghi d'Italie

Thèse N

^◦

4729

GENÈVE

Atelier d'impression Repromail

10 Novembre 2014

(3)

(4)

Abstract

During my thesis I studied new technologies and protocols aiming at practical quantum-cryptography applications.

Firstly, I developed a free-running single-photon detector for telecom wavelengths.

This detector is characterized by an extremely low noise which before was achievable only using the state-of-the-art superconducting single-photon detectors. Therefore it is suitable for very long distance QKD.

Then I developed a testbench for metrological characterization of single-photon detectors. The testbench takes advantage of a source of spontaneous emission with extremely high power stability and a of radiometer for calibrating absolutely the power of the light beam incoming on the detector. The accuracy of the power measurement has been veried using a transfer power meter calibrated in a metrological laboratory. Both the source and the radiometer are based on an Erbium-doped bers and have been built using standard commercial components.

In the third part of my thesis I experimentally realized a practical bit commitment protocol provably secure. The protocol security is guaranteed by both relativistic and quantum constraints but allows security for only 16 ms. Quantum bit commitment was demonstrated impossible using only quantum constraints and this is the rst implementation of a bit-commitment protocol provably secure. This implementation is simple and very robust.

Finally I investigated an innovative approach to generate strings of bit with certied quantum randomness. Usually quantum random number generators can produce random strings only after carefully modeling the quantum process involved and properly calibrating the devices. This approach hardly catches all the possible imperfections involved in the measurement. Moreover the devices might operate dierently from the calibrated values. Although we use only few general assump- tions that do not model in details the quantum process, we are able to self-test all the possible classical sources of noise only by looking at the random strings and recording the measurement settings chosen by an external user.

iii

(5)

(6)

Résumé

Au cours de mon travail de thèse, j'ai développé des nouvelles technologies et pro- tocoles pour des applications pratiques en cryptographie quantique.

Premièrement, j'ai développé un détecteur des photons uniques free-running pour les longueurs d'onde telecom. Ce dètecteur est caractèrisè par un bruit extrême- ment faible comparable à ce des détecteurs supraconducteurs de photons uniques.

conséquence, il est approprié pour des applications commerciales des QKD.

Ensuite, j'ai développé un banc d'essai pour la caractérisation métrologique des détecteurs de photons uniques. Le banc d'essai tire prot d'une source d'émission spontanée avec une stabilité en puissance extrêmement élevée et d'un radiomètre pour calibrer de manière absolue la puissance du faisceau de lumière qui arrive sur le détecteur. La précision de la mesure de la puissance a été vériée avec un puissance mètre de transfercalibré dans un laboratoire de métrologie. La source et le radiomètre sont basés sur une bre dopée Erbium et ils ont été construits avec des composants commerciaux standard.

Dans la troisième partie de ma thèse, j'ai mise en ÷uvre un protocole pratique de bit committment certié par une prouve de sécurité. La sécurité du protocole est assurée par des contraintes aussi bien relativistes que quantiques qui cependant assurent la sécurité pour seulement 16 ms. Le bit committment quantique a été démontré impossible en utilisant seulement des contraintes quantiques. Ma réalisa- tion est la première mise en ÷uvre d'un protocole de bit committment. Cette mise en ÷uvre présente l'avantage d'être simple et très robuste.

Enn, j'ai étudié une approche novatrice pour générer des chaînes de bits aléa- toires dont la partie quantique est quantiable. Habituellement les générateurs quantiques de nombres aléatoires peuvent produire des séries aléatoires seulement après une modélisation minutieuse du processus quantique impliqué et une bonne calibration des appareils. Par cette approche est dicile tenir en compte de toutes les éventuelles imperfections liées à la mesure. De plus, il est dicile de moni- torer tous les variations de fonctionnement des appareils. Bien que nous utilisions seulement quelques hypothèses générales qui ne modélisent pas dans le détail le processus quantique, nous sommes en mesure d'autotester toutes les sources classiques de bruit éventuelles seulement en regardant les séries aléatoires et en enregistrant les paramètres de mesure choisis par un utilisateur externe.

v

(7)

(8)

Introduction

Much like classical information can be processed with digital computers, transmit- ted from place to place, manipulated with algorithms, and analyzed with the math- ematics of computer science, analogous concepts apply to quantum information. To eectively encode on, manipulate and read information out of a quantum system dedicated engineering techniques and new quantum protocols must be developed.

This is accompanied by the introduction of new quantities (or the re-denition of old ones) formulated within the quantum framework. These processes are generally referred to Quantum Information Processing (QIP).

The rst proposal of a practical quantum protocol, the so-called BB84, was proposed in 1984 [1]¹. With this protocol two distant parties (Alice and Bob) are able to share a secret key and bound the amount of information that could have leaked out even against an innite powerful adversary. This groundbreaking proposal triggered quantum cryptography, which is still one of the leading applications of quantum-information science.

At the beginning of this thesis, quantum cryptography was already a practical application and Quantum-Key-Distribution systems were already being commercialized [3]. From the beginning, real implementations were based on coherent-light pulses (strongly-attenuated to the single-photon level) as to be compatible with ex- isting optical-ber networks. However keys could only being distributed between two parties separated by 67 km at maximum, with a key rate of only 50 Hz [4].

The ultimate bottleneck of these systems was represented by the high noise level of the single-photon avalanche diodes at telecom wavelengths: because of the unavoidable² losses in an optical ber, the single photons carrying the information get lost. The secure key can be distilled only until the signal-to-noise ratio is smaller than a security value, which limits the maximal distance. Longer distances (up to 250 km [6]) were achieved only by using superconducting nanowire, i.e. single- photon detectors based on superconducting materials that achieve dark count rates of only a few s⁻¹. Unfortunately they require cryogenic operations which are not ideal for commercial applications.

Driven by this application, eorts have been devoted to improve the performances of single-photon detectors. This highlighted the signicant lack of precision

1A similar idea was previously proposed in [2]

2It was a common belief that the losses of the single-mode ber cannot be lower than 0.2 dB/km at 1550 nm. This limit, however, has been recently overcome, e. g. [5]).

(11)

in the characterization protocols: in scaling down from high-photon-ux regimes to the single-photon regime there is an important loss of precision of the power measurement. Recently, this has been investigated by a consortium of metrology laboratories in the quantum candela [7] European Project. Thanks to this project dierent protocols for characterizing the eciency of single-photon detectors (and other single-photon detector properties) have been cross-checked and validated leading to an improvement both in uncertainty and consistency. However, the methods studied in this project require high-skilled competences and expensive technologies which can rarely be found outside a metrology laboratory.

However quantum cryptography is not only QKD. As an example, the generation of unpredictable sequences of bits by using a (Quantum) Random-Number Generator (RNG) started as a building block for QKD but it has also potential applications in other elds, such as classical cryptography, data analysis [8] and gambling. Recently, an analysis of cryptographic public keys available on the web revealed that they were created from very weak randomness, a fact that can be exploited to get hold of a signicant number of the associated private bits [9]. Quan- tum processes can generate completely unpredictable outcomes. But in practical realization, quantum processes are aected by classical imperfections that might be controlled to produce predicted outcomes. To improve the unpredictability of the outcomes, the device must be carefully modeled together with all its imperfections.

Encompassing all the complexities involved within a real implementation is hard and some loopholes might always be hidden.

Following the discovery of QKD and its unconditional security, researchers tried to achieve other cryptographic tasks with unconditional security. One of them was bit commitment. A commitment scheme allows a party, Alice, to x a certain value (to commit) in such a way that she cannot change that value and the recip- ient, Bob, cannot learn anything about that value until Alice decides to reveal it.

Such commitment schemes are commonly used in cryptographic protocols and it would be particularly useful for secure voting [10]. Unfortunately, early quantum commitment protocols were shown to be awed. In fact, Mayers showed a no-go theorem for unconditionally secure commitment based on quantum theory: a com- putationally unlimited attacker can break any quantum commitment protocol [11].

This seemed to preclude any chances for this kind of protocol to be realized.

During my thesis I have been working on developing and characterizing new technologies for QIP applications. Here, I summarize my work and I review their main results. The structure of the thesis follows the order presented in this introduction.

In each chapter I rstly introduce the subject, then I present my contributions.

In particular:

In the rst chapter I describe the realization of two single-photon detectors for telecom and visible wavelengths. The former detector is currently the state- of-the-art semiconductor commercial device in term of noise. Among its pos-

(12)

xi sible applications, it is suitable for long-distance QKD. The visible device has been realized to investigate the advantages of gating a silicon single-photon detector. This biasing technique, unusual in silicon semiconductor solutions, opens up the way to new applications and notably allowed to perform two challenging experiments.

In the second chapter I focus on metrological characterizations of single- photon detectors concerning the eciency measurement. I realized an optical source that emits constant power and a radiometer to measure this power absolutely, i.e. without relying on any previous calibration. Thanks to these devices, one can calibrate the eciency with less than 1% of relative uncertainty without any metrological equipment.

To obtain such low uncertainty, it is crucial to characterize the afterpulsing, a characteristic phenomenon of telecom semiconductor single-photon detectors. The statistical characterization of the afterpulsing is dicult since it depends on the internal status of the detector at the beginning of each run of the measurement. I set up a tool that precisely prepares the detector for the acquisition allowing for eective measurement of the afterpulsing.

The third chapter is dedicated to quantum random number generation. Dur- ing my work I demonstrated an innovative approach to correctly determine the randomness of a process without modeling the internal working of the devices. This method corrects automatically for any possible classical imperfections.

The forth chapter is dedicated to bit commitment. In particular I circum- vented the no-go theorem by Mayers by using quantum and relativistic constraints. I experimentally realized a bit commitment protocol unconditionally secure demonstrating commitment time of 15 ms.

In the conclusions I summarize the main results of this work and provide my considerations and outlooks.

(13)

(14)

1 Single-photon avalanche photodiode: physics and technology

The detection of extremely dim light is used in a growing variety of experiments.

In biology and medical science, for example, detection of single photons allows the location of specic cells for studies and diagnostic [12, 13]. In astronomy, photons from the stars travel fast and reach very long distances but only few of them can be collected on the Earth [14]. In quantum information science, single photons can be exploited to encode, communicate and manipulate information. In fact, certain computational tasks are performed more eciently with quantum objects than with classical ones. All these applications prot from ecient detection systems.

Historically, the rst detectors able to register single optical photons were pho- tomultiplier tubes (PMTs) [15]. It was with McIntyre's work on Geiger-mode avalanche photodiodes (APDs) [16, 17, 18] that the possibility of single-photon detection using a semiconductor device became a reality. Nowadays semiconductor SPADs compete with superconducting-nanowire single-photon detectors [19], i.e. a new approach where single photons destroy the superconducting state of a nanowire and suddenly increase the device resistance. Superconducting detectors can attain performances close to the ideal [20], but they are not handy because they operate at temperatures below 2.7 K.

Semiconductor single-photon-APDs (also called SPADs) can attain very large ef- ciency [21], high temporal resolution [22] and they can operate at high speed [23]¹. The spectral response of the device depends on the material used in the fabrication: silicon-based SPADs enable photon counting at visible wavelengths while, in the infrared region, more complex heterostructures of Indium-Gallium-Arsenide (InGaAs) and Indium-Phosphorous (InP) are employed. However, SPADs are far from being ideal detectors since they are aected by some undesirable properties.

In particular, they are susceptible to defects in the semiconductor material which increase their noise characteristics. These defects are the origin of dark counts and afterpulsing. Silicon SPADs generally show good performance in terms of noise and afterpulsing. On the contrary, in the infrared region, high-quality devices are dicult to realize due to the more complex structure and InGaAs/InP SPADs

1However, these characteristics are rarely achieved on the same device

(15)

are lower quality than the silicon ones. Compared to superconducting nanowires single-photon detectors, SPADs have some important advantages since they are more compact, they can operate continuously for days and they do not require expensive and complex cooling systems.

Improving the device architecture, the material quality and the fabrication pro- cedure ultimately leads to signicant improvements in performance of the devices.

However this is a long and challenging process which does not always succeed. A simpler and eective approach consists in developing dedicated electronics which adapts the device to the specic application and reduces signicantly the unwanted noise. It is obvious that both approaches are essential in order to attain the ideal performances.

Electronics for SPADs plays an important role in my thesis. In this chapter, I will begin by summarizing the SPAD operating principle and the characteristics of the device. Then I will report about my contributions to this topic devoted to tailor the detector biasing and operating conditions to the intended applications. I will give two successful examples.

In the rst one I investigated the positive impact that gating silicon detectors might have in quantum optics experiments, realizing a gated silicon-SPAD. The detector achieves its maximal detection eciency by applying a large excess bias (40 V). Gates of 40 V of amplitude make the discrimination of the avalanches challenging, therefore a dedicated readout circuit has been designed.

In the second example I report on a passive-quench active-reset circuit for free-running InGaAs SPADs. InGaAs detectors are rarely used in free-running conditions because of their high noise. To overcome this problem we chose a specic diode where the detector and the quenching circuit are monolithically integrated.

This signicantly reduces the afterpulsing. Then we operate the detector at low temperature. In these conditions, the detector is featured by an extremely low noise (1 count per second) at the expense of a small repetition rate (50 kHz). This suits perfectly to quantum-key distribution with distances longer than hundreds of km, distances achievable only with state-of-the-art superconducting nanowires.

1.1 General principle

Single photons can be counted by avalanche photodiodes when they are operating in the so-called Geiger mode. When a large reverse bias is applied to a p-n junction, a high electric eld is generated in the depletion region of the diode. A charge carrier pushed by this eld may acquire enough energy to ionize an atom during a collision against the crystal lattice. This eect is called impact ionization. After each collision, a secondary electron-hole pair is generated and can originate new ionization events. As a result, an avalanche current is produced.

When the reverse voltage across the junction increases beyond a certain value, called

(16)

1.2 Physics of a SPAD 3 the breakdown voltageV_b, a charge carrier in the depletion layer may generate a very large number of secondary electron-hole pairs giving rise to a large and continuous breakdown current. It is important to emphasize that the breakdown current has to be initiated by a seed charge otherwise no current ows in the diode. This is the basic principle that allows detecting of light at the single-photon level.

Figure ?? shows an idealized current-to-voltage characteristic (I-V) of a SPAD.

When a reverse bias voltage is applied, no current ows through the diode until the breakdown voltage is overcome. We dene the excess bias (V_e) as the bias voltage relative to V_b, i.e. V_e =| V −V_b |, where V is the absolute value of the voltage. For V_e ≥0the characteristics might follow two branches: as long as there is no seed charge in the depletion region, no current ows. When a single charge carrier is present in the depletion layer, a breakdown current might be triggered.

This current is very large, so it is simple to detect this transition with an electronic circuit. After this current has been detected, it has to be quenched to restore the diode to the non-conducting condition. This is done by reducing the voltage across the diode below the breakdown voltage as indicated by the arrow in Fig. ??. After the breakdown current has been quenched, the bias voltage can be restored in order to use the SPAD again.

I

-V

detection

V

_bd

Linear mode Geiger mode Quench

V

_bd

+V

_ex

Figure 1.1: I-V characteristics of a SPAD.

1.2 Physics of a SPAD

SPAD characteristics are determined by its structure. Figure ?? shows a transverse view of a generic SPAD: it mainly consists of two regions, the absorption region and the multiplication region. In the absorption region, the photon get absorbed generating the seed electron-hole pair. This pair is then pushed toward the multi-

(17)

plication region by a small eld or by diusive processes. There the electron-hole pairs are accelerated by a strong electrical eld and may ionize the lattice atoms creating the breakdown current. Depending on the actual implementations, the two regions might be physically separated as in the picture or they might coincide.

They might also consists of dierent materials which require further layers to match the crystal lattice.

In the following section I analyze the characteristics of a SPAD by referring to this picture.

Figure 1.2: Schematic of an ideal SPAD structure. The structure consists of two regions:

the multiplication region, where a strong electrical eld is generated to trigger the avalanche multiplication, and the absorption region where the photon is absorbed. In the absorption region, a low electrical eld pushes the carriers to the multiplication region. In the picture, the region thicknesses are arbitrary.

1.2.1 Dark count sources

The detection mechanism at the basis of a SPAD detects the presence of a free carrier in the multiplication region, generated either by photon absorption or by other eects. A dark count is an avalanche that is not created by the incoming light. Dark counts can be grouped in two categories: the primary dark counts and the so-called afterpulses.

Primary dark count rate

The probability of having a primary dark count follows a Poissonian distribution uncorrelated from any previous primary dark counts. This is a clear distinction between primary dark counts and afterpulses, where an avalanche inuences the probability of having an afterpulse later.

(18)

1.2 Physics of a SPAD 5 Three main sources contribute to the generation of primary dark counts: generation and recombination processes (G-R processes), trap-assisted tunneling (TAT) and band-to-band tunneling (BBT). The generation of these noise counts is sketched in Fig. ?? and explained:

Figure 1.3: Representation of the primary dark-count processes involved in SPADs. The y-axis represents the energy-band diagram as a function of the transverse position.

G-R processes consist of thermal excitations that generate electron-hole pairs in the absorption region. Impurities in the semiconductor material facilitate this process through a two-step excitation: electrons are promoted from the valence band to the defects located in the mid-gap and then promoted again to the conduction band² [24]. The probability of a G-R process decreases exponentially with decreasing temperature.

In the multiplication region, the electrical eld strongly enhances the probability that an electron may tunnel from the valence band to the conduction band passing through an impurity center in the bandgap. In this case we refer to Trap-Assisted-Tunneling, TAT [25]. At very high elds, intensity carriers can even tunnel directly from band to band without the assistance of impurity centers (Band-to-Band-Tunneling, BBT [26]). Both BBT and TAT increase by increasing the electrical eld in the multiplication region. Therefore by increasing the bias voltage across the diode BBT and TAT process increase.

BBT and TAT do not depend on the temperature.

To reduce the primary dark-count rate, many strategies are possible. On one hand, the quality of the material used for the multiplication region (Indium phos- phide or Silicon) reduces the density of defects and the TAT [27]. On the other

2This process is called Shockley-Read-Hall generation-and-recombination process

(19)

0 1 2 3 4 5 6

0

2 0 0 0 4 0 0 0 6 0 0 0

Dark count rate (s-1 )

E x c e s s b i a s v o l t a g e ( V )

(a)

- 1 1 0 - 1 0 0 - 9 0 - 8 0 - 7 0 - 6 0 - 5 0

0

5 0 1 0 0 1 5 0

2 0 0 t h e r m a l n o i s e

T e m p e r a t u r e ( C ) e l e c t r i c a l - f i e l d n o i s e

(b)

Figure 1.4: (a) Typical dark-count rate as a function ofVe.(b) Typical dark-count rate as a function of the temperature for a givenV_e. Decreasing the temperature reduces the G-R process due to thermal recombination. Below a certain temperature the dark-count noise is dominated by the tunneling contributions and it is not aected anymore by the temperature.

hand, by cooling the photodiode the number of G-R recombinations is reduced.

However, this solution aects only dark counts originated by thermal excitations and does not aect TAT and BBT. Therefore, below a given temperature, the noise is dominated by tunneling and no reduction of dark counts can be obtained by lowering the diode temperature further. These concepts are summarized in Fig. ??.

When the excess bias is increased at xed temperature, the dark-count rate increases (see Fig. ??(a)). For a given excess voltage, decreasing the temperature results in a strong decrease of the dark-count rate (see Fig. ??(b)) which is less eective below a certain temperature (indicated by the dotted line).

Afterpulsing

During the avalanche breakdown, charge carriers may be trapped at atomic defect sites in the multiplication region³. The subsequent de-trapping of these carriers at a later time can trigger spurious additional avalanches known as afterpulses. If an avalanche occurred at time t= 0, the probability that a charge is trapped and then released at time t is proportional to

P_a(t|0)dt= A

τe⁻^τ^tdt, (1.1)

where the factor A accounts for the probability that a trap is lled during the

3The defects responsible for the afterpulsing are dierent from those responsible for the TAT.

The formers are trap sites close to either the conduction or the valence band. The latters are mostly located in the middle of the bandgap.

(20)

1.2 Physics of a SPAD 7 initial avalanche and it proportional to the number of charges involved in the avalanche [28]. τ corresponds to the lifetime of the electron in the trap site and evolves as a function of the temperature according to

τ =e⁻^Ea^kT, (1.2)

where Eais the activation energy, k is the Boltzmann's constant andT is the temperature. Each kind of trap corresponds to a dierent τ. The total probability distribution is given by the sum of many exponential decays. In the literature, all attempts to characterize the afterpulsing have assumed that only few traps participate to this phenomena [29]. This hypotesis is motivated considering that shallow defects are de-trapped faster by a strong eld (Frenkel-Poole eect [30]) and only the deepest traps are involved in the afterpulsing. Therefore it is a common practice to t the temporal distribution of the afterpulsing considering only a few traps. Recently, Itzler and co-workers have objected that this consideration might be arbitrary [31]. To support their objection, they experimentally compared afterpulsing measurements from dierent groups for InGaAs/InP SPADs, and found that the measured de-trapping rates are surprisingly comparable. More important, the number of traps seems to depend only on the temporal range of investigation:

when the interval of time under investigation is extended by a couple of orders of magnitudes, an additional trap resulting better t the curve. Itzler proposes a dierent model which considers many traps participating to the afterpulsing. This seems to be consistent with the literature of trap centers in InP material. Accord- ing to their model, the experimental data can be tted with a power law formula, Pa(t | 0) = t^−α, where the parameter α changes for dierent distributions of the trap centers. They analyzed data from several groups and they found an agree- ment for α ∼1.18 which suggests an inverse distribution, 1/R, of the de-trapping rate. Unfortunately, they do not provide conclusive results therefore the physical signicance of de-trapping time constants mathematically extracted from the afterpulsing curve remains unclear. This makes it dicult to study the physics of the defects that give rise to afterpulsing in InGaAs-based SPADs and prevents direct comparison of dierent approaches for reducing the number of trapping sites.

Afterpulses can be reduced either by improving the quality of the chip to reduce the number of traps or by reducing the current involved in the avalanche (and consequently the number of carriers trapped) with a fast quenching circuit.

Nevertheless the most straightforward mitigation of afterpulses consists in forcing the SPAD to be inactive after each detection. By biasing the diode below V_b for a suciently long time, all the trapped carriers are de-trapped and swept from the multiplication region without the possibility of triggering avalanches. Unfortu- nately, imposing these long hold-o times reduce the maximal count rate.

The impact of the afterpulses in a SPAD is visualized in Fig.??, where the dark- count rate is plotted as a function of the hold-o time. In this graph the measured

(21)

dark-count rate decreases with the hold-o time since we suppress the components given by afterpulses. At long hold-o time, only the primary dark-count rate is seen. This limits also the maximal count rate to 1/hold-o time. As for the pri-

1 0 2 0 3 0 4 0 5 0

1 0 0 0 1 0 0 0 0 1 0 0 0 0 0

F r e e - r u n n i n g m o d e G a t e d M o d e

H o l d - o f f t i m e (µs )

Figure 1.5: Dark-count rate as a function of the hold-o time for a SPAD driven in free- running and gated conditions. Gating a detector better quenches the avalanche and reduces the afterpulsing. The afterpulses are completely suppressed after 10 µs (20 µs) for gated detectors (free-running) limiting the count rate to 100 s⁻¹ (50 s⁻¹). Source: [32]

mary dark count rate, temperature aects the afterpulsing rate. By lowering the temperature, the lifetime of the carriers trapped in the defects increases. Hence the temporal decay of the afterpulsing is extended. This contrasts with the reduction of the primary dark-count noise. Therefore the operating temperature for a SPAD is usually determined as a trade-o between afterpulsing and dark-count rate.

1.2.2 Time resolution

The temporal resolution of a SPAD can be quantitatively measured in terms of timing jitter. This quantity corresponds to the temporal uncertainty between the arrival of a photon and the discrimination of the avalanche. It depends on the structure of the SPAD as well as on the electronics used to discriminate the breakdown avalanche. Figure ?? shows a typical histogram of the avalanche discrimination time. The zero refers to the peak of the distribution. The histogram is often asym- metrical due to the presence of a tail. The decay time of the tail can be faster or slower according to the specic structures. In general, the tail is due to photogenerated carriers that reach the multiplication region late. On the other hand, the width of the central portion of peak is due to the uncertainty in building up the avalanche and in discriminating it. It depends on the uniformity of the electrical

(22)

1.2 Physics of a SPAD 9 eld in the multiplication region and on the electrical eld strength [27]. This explains why the timing jitter decreases as the bias voltage is increased (see the inset in Fig. ??). A good review about the dierent sources of the timing jitter can be found in [33]. The discrimination circuit may introduce additional jitter if not well adjusted. As a rule of thumb, the smaller is the electrical noise on the avalanche signal, the lower is the jitter introduced.

Figure 1.6: Jitter distribution for a free-running InGaAs/InP SPAD operating at dierent eciencies. The inset shows the FWHM of the jitter distribution for dierent eciencies.

1.2.3 Detection eciency

The detection eciency is the probability that a photon sent toward the photodiode will make the detector click. It depends on the contribution of several factors:

Coupling eciency: the coupling eciency is the probability that the photon enter in the photodiode. Indeed, the impinging photons might not be well coupled into the SPAD or they might be reected away by a partially-reecting surface before entering in the semiconductor. These photons cannot trigger an avalanche. The coupling eciency is generally high and reproducible and it is not a limiting factor for the SPAD.

Absorption eciency: the absorption eciency is the probability that the incoming photons are absorbed either in the absorption or the multiplication region and create the seed electron-hole pair. When the photons travel in the semiconductor material, the probability for them to get absorbed increases exponentially with the distance traveled in the material times the absorption coecient. The material absorption coecient varies with the wavelength and determines the spectral sensitivity of the SPAD. Figure ?? plots the absorption coecient as a function of the wavelength for several materials.

(23)

SPADs sensitive to visible and near-infrared wavelengths (≤ 1000 nm) have an absorption region made of Silicon, while the absorption region for SPADs sensitive to infrared light(between 1250-1600 nm) is based either on Indium- Gallium-Arsenide (InGaAs) or, less frequently, on Germanium (Ge).

Avalanche triggering eciency: the avalanche triggering eciency is the probability that the photo-generated electron-hole pair succeeds in triggering an avalanche current. Each electron-hole pair has a dierent probability to trigger the breakdown current which depends on the position where the electron- hole pair has been generated and on the electrical eld prole of the SPAD.

This probability increases with the strength of the electrical eld in the multiplication region, fact which explains why the detection eciency of a SPAD increases with the bias voltage.

Avalanche discrimination eciency: the avalanche discrimination eciency is the probability that the breakdown current is discriminated. Usually, the discrimination circuit of passive and active-quenched SPADs (see Sec. ??) can discriminate the avalanche eciently. On the contrary, when SPADs are gated with GHz gates the avalanche current is smaller and it is more dicult to discriminate eciently the avalanches.

Figure 1.7: Absorption spectra (left) for dierent materials as a function of the wavelength.

Penetration depth (right) as a function of the wavelength. The penetration depth corresponds to the distance where the probability to be absorbed has decreased of a factor1/e.

Source: www.laserfocusworld.com.

(24)

1.3 The advantages of gating a Silicon SPAD 11

1.3 The advantages of gating a Silicon SPAD

According to the wavelength of the photons to be absorbed, the device can be grown based on dierent materials.

Silicon SPADs (Si-SPADs) are reliable and ecient devices for detecting light in the visible and near-infrared range. The fabrication technique used to grow the Silicon is very mature and produces samples with high purity. Thanks to low impurity level density, dark counts due to TAT and afterpulsing are largely suppressed. Therefore Si-SPADs can attain large eciencies and low dark count rates at the same time, and they are not much aected by afterpulsing. Today Si-SPADs are grown according to three kinds of architectures: thin SPADs, Complementary- Metal-Oxide-Semiconductor SPADs (CMOS) and thick SPADs. The Si-SPAD used in this work is based on a particular thick architecture, named SLIK structure [34].

1.3.1 Silicon SPAD structure

A lateral view of the device is presented in Fig.??. The diode is back-illuminated and the incoming photons cross a thick absorption region (∼ 30 µm) which is designed to guarantee high absorption probability. An electrical eld in the absorption region pushes the photogenerated hole toward the multiplication region (on the bottom). The multiplication region is strongly doped in order to conne the large electrical eld which sustains the avalanche process in a small region.

Thanks to the high quality of the device, the structure can be built with a large surface area (500 µm of diameter). The thick absorption region allows large detection eciencies (up to 85% at 600 nm [35]). The dark-count rate is larger than in other architectures because of the big volume of the diode and it is dominated by thermal G-R processes. Therefore it can be reduced down to few s⁻¹ by lowering the temperature [36]. Unfortunately, the temporal jitter is large (∼500 ps), mostly dictated by the uncertainty on the position where the electron-hole pair is generated. To bias the diode in Geiger-modes a breakdown voltage on the order of hundreds of volts is required, and achieving the maximal eciency requires an excess bias of 10-30 V.

1.3.2 Thesis contribution

Given the growing number of applications that would prot from improved SPAD performances and the eort devoted to this, we are beginning to reach the limits of Si-SPADs performance. For example, the long hold-o time constitute a limitation especially for free-running operations since stray light can deactivate the detector while the interesting photons are impinging. Starting from the practical needs of

(25)

Figure 1.8: Lateral view of a SLIK structure: the incoming photon is absorbed with large probability thanks to the thick absorption region. An electric eld pushes the photogenerated electron toward the multiplication region (on the bottom, the p-n junction) where a strong electric eld generates the avalanche.

our laboratory, we identied two general situations where free-running operations severely reduce the experiment capabilities. These situations are represented in Fig. ?? (a)-(b) and described below.

Photons of interest buried in the noise: in this scenario (Fig. ?? (a)), the detector is illuminated by faint light and the time interval between subsequent photons is, on average, smaller than the dead time. The photons of interest are hidden in the beam, but their arrival time is known, e. g. heralded by another eect. Under these conditions, a free-running detector is saturated or even blinded, reducing the detector probability of being on when the photon of interest arrives. This situation, which triggered this work, has been encountered in [37, 38].

Photons of interest after a strong pulse: in this scenario (Fig. ?? (b)) a strong pulse impinges on the detector before the arrival of the photon of interest. Hence, when the photon of interest arrives, a free-running detector is either in its hold-o time or its noise is highly increased by afterpulsing.

This situation can be found in optical time-domain reectometry [39] and in quantum-memory experiments that require strong preparation pulses [40].

Similar considerations have been done also in uorescence spectroscopy [41, 42].

In both scenarios, a gated detector would improve the experiment yield since it can be activated on demand, i.e. while the arrival of the interesting photon is heralded in the scenario (a) or just after the strong pulse has impinged in scenario (b).To gate a thick diode, a large voltage pulse (of about 40 V) must be provided to attain the maximal eciency. Gating the diode with such large pulses requires an ecient readout system to discriminate the avalanches: due to the diode capacitance, the SPAD acts as a derivative circuit for the gate signals and two spurious

(26)

1.3 The advantages of gating a Silicon SPAD 13

(B) (A)

Figure 1.9: Experimental scenarios where a gated detector plays an essential role. (a) Applying a gate ensures that the detector is active when the photon of interest arrives, even if the detector is constantly illuminated. (b) Applying a gate ensures that the detector is not blinded by the preceding strong pulse.

electrical spikes of 7 V appear at the output of the detector in correspondence with the rising and falling edges. These peaks prevent the avalanche from being discriminated. To suppress these spurious peaks we designed the electrical circuit outlined in Fig. ??. The detector is initially biased below the breakdown voltage.

In parallel with the diode we added an auxiliary line, that simulates the capacitance and the resistance of the detector. This line reproduces the derivative circuit and the variable capacitance is adjusted to produce two spikes equal to the one at the cathode of the diode. The signals from the auxiliary line and signals from the diode are then subtracted. If an avalanche occurs, it appears only in the diode line so it will not be canceled and can easily be discriminated. Thanks to our circuit, the two spurious electrical signals are suppressed down to 150 mW while the avalanches are larger than 1 V.

The electronics has been tested on dierent commercially-available Si-SPADs. The tested diodes were provided by Excelitas (C30921SH Si APD) [43] and Laser Com- ponents (SAP500) [35]. Both diodes are based on a thick structure [44] (respectively 35 µm thick and 15 µm thick), and are characterized by a large detection area (0.5 mm diameter). The maximal detection eciency of the SAP 500 is reached at 655 nm, while the C30921SH attain the maximum at 800 nm. The results presented here refer only to the Excelitas diode and can be found in App. ?? and [45]. A more detailed analysis on both the detectors can be found in App. ?? and [46].

With this electronics, one can drive the SPADs and obtain the same performance as in the free-running mode. I investigated the advantages of gating a Si-SPAD detector in both the proposed scenarios. Here we provide a brief intuition about

(27)

Output

Balun Vbias

Cblock

Rball

50 W Cvar

40 V

20 ns

Figure 1.10: Electronic readout to bias the SPAD and discriminate the avalanche.

our arguments.

Scenario(a): when the photon of interest is buried within a faint coherent light, the probability to detect it depends also on the probability of being active. The higher the power of the background light, the less likely the detector will be active at a certain time. In the considered case, doubling the detection rate of the input light reduces the detection probability for the heralded photon from 45% to 30%. Moreover, the reduction of eciency is larger for more ecient detectors.

Scenario(b): to demonstrate the advantage of a gated detector in the second scenario we directly compare the avalanche rate induced by a strong pulse in free-running and gated mode. In free-running operation the detector is inactive after the strong pulse because of the dead time, then its background rate is increased by afterpulsing, phenomenon that lasts, in the considered case, for 1 µs. Gated Si-SPADs are not aected by afterpulsing due to the strong pulse since no avalanche is triggered by the strong pulse and, intuitively, the noise distribution should be constant since it depends only on the primary dark-count rate. However this intuition is wrong because it does not consider an additional noise named charge persistence eect (see below): this additional noise is induced by the strong pulse, and lasts for a time comparable to that of the afterpulsing. However, even considering this additional noise, the gated solution shows lower noise gure compared to the free-running one.

Charge persistence: during the characterization of the Si-gated detector in the second scenario, particular eorts have been devoted to characterize the charge persistence noise. An example of this noise is reported in Fig. ??. The picture shows the avalanche triggering probability as a function of the delay between the end of the gate and the strong pulse for two dierent temperatures. If the laser pulse impinges on the detector during the gate (0-20 ns of delay), the number of

(28)

1.3 The advantages of gating a Silicon SPAD 15 detections saturates to the repetition rate of 10 kHz. For longer delays, the gate arrives after the laser, but the strong light can still provoke an avalanche when the gate is applied. The slope of decay of this noise depends on the temperature. The noise has been veried proportional to the power of the strong light, and the decay time is shorter for higher temperatures. The intriguing feature that prevents us from clearly addressing the phenomena is the linear decay in log-log scale. Because of the thick structure we exclude diusion eects since the whole device is lled with an electrical eld and the total time to cross the entire structure, estimated from the jitter (∼500 ps), is much lower than the decay time of the charge persistence.

Defects in the diode structure may trap photo-generated holes as they occur in the multiplication region for afterpulsing. The release of these electrons can happen during the gate, thus giving rise to an avalanche. The trap lifetimes are shorter at higher temperatures and the noise count rate is expected to increase linearly with the power of the laser pulse. Both these behaviors have been experimentally veried. However, the slope of the curve is not consistent with the few-traps model of the afterpulsing. Instead, it is consistent with the power law proposed by Itzler and co-workers that consider many traps, see Sec. ?? [31]. During my work, I could not address clearly the origin of this noise. A direct comparison of the afterpulsing curves of the diode with the charge persistence curve might help. In our setup this was impossible due to the limited count rate of the gate pulser (100 kHz).

Figure 1.11: Counts due to persistence noise as a function of the delay between the gate and the laser pulse for two dierent temperatures, i.e., 20 and -40^◦C (repetition rate of 10 kHz).

(29)

1.4 Low noise free-running SPAD for telecom wavelengths

Silicon becomes transparent at wavelengths longer than 1000 nm, therefore SPADs for telecom wavelengths are based on a dierent material. In0.53Ga0.47As ternary compounds well absorb light in the infrared spectrum because of their small bandgap (0.75 eV compared to 1.11 eV for Silicon). However, such a small bandgap cannot sustain the large electrical eld for the avalanche multiplication without suering from a large tunneling noise. This would make the device useless. For this rea- son the multiplication layer is made of Indium-Phosphorous compounds (bandgap 1.35 eV) which have a larger bandagap and a lattice constant that can be matched with the InGaAs. The device structure is named Separate Absorption, Grading, Charge and Multiplication (SAGCM) heterostructure.

1.4.1 SAGCM structure

A typical lateral view of the SPAD structure is shown in Fig. ?? [47]. The thickness of the absorption region is usually designed to attain a maximal detection eciency of 50% [48]. When the photon is absorbed, the photogenerated electron-hole pair is separated by the electric eld and the hole drifts to the InP multiplication region.

The interface between the multiplication and the absorption regions consists of two dierent materials with dierent bandgaps. This creates an energy barrier increasing the transit time of the holes through the diode and consequently the overall jitter. To reduce the height of this barrier, thin InGaAsP graded layers are grown between the InGaAs and the InP region. These intermediate layers also allow tailoring the electrical-eld prole. Finally, on top of the diode a double diusion of p-type Zinc atoms connes the electric eld in the active area [49].

The breakdown voltage of the diodes is of 70 V and the maximal eciency is obtained for excess bias of 6 V.

In this structure the dark-count rate is usually dominated by the tunneling noise in the multiplication region [50]. A recent study [51] has shown how to increase the multiplication width and reduce the tunneling contribution to the noise. For the diodes that have thicker multiplication region, the noise is dominated by G- R recombination processes in the absorption region which, as seen above, can be reduced by lowering the temperature.

1.5 Readout circuit

Infrared detectors are usually aected by more severe noise characteristics than Silicon SPADs: in 1998 Ribordy and co-authors [52] compared several SPADs at telecom wavelengths. At 173 K, for example, InGaAs/InP diodes were featured by

(30)

1.5 Readout circuit 17

Figure 1.12: Lateral view of a SAGCM heterostructure: the incoming photon crosses the SPAD until it reaches the InGaAs absorption region where it gets absorbed.

The photogenerated hole is pushed by the electrical eld toward the multiplication region where a strong electric eld generates the avalanche. The strong eld is conned with a double-diused Zinc region. On the right is a sketch of the electric eld prole is shown.

a dark count rate of 38 s⁻¹ when the detection eciency is 16% at 1550 nm. Typical hold-o time of 20 µs must be applied in order to suppress the large afterpulsing probability. At that time, InGaAs/InP devices were used only in single-photon applications and only few groups were studying how to improve the material fabrication. Because of that, many eorts have been devoted to develop a complex quenching circuit able to sense the avalanche, quench it, and quickly recover the operating condition. Three main families of circuits have been developed:

Passive quench: in this approach, a passive resistor is responsible for quenching the avalanche. The quench can be very ecient but it is easily degraded by parasitic capacitance. Moreover, faster quenches are obtained at the expense of a long recovering time when the bias across the diode is rising and the eciency is not well dened. Passive quench is the approach used in this work, so I will extensively describe it in the following section.

Active quench: faster quenches can be obtained with active components.

Once the quenching circuit senses the avalanche, it actively lowers the voltage across the diode below the breakdown. After having waited a user-controlled hold-o time, another signal changes the impedance at the diode in order to allow very short recovery time. Active-quenching circuit can be driven in gated mode with high gate rate (tens of MHz). This technique can faster quench the diode, however the electronics is more complex to be implemented.

Rapid gating: in the passive-quench approach, the total charge through the diode during the avalanche is increased by the parasitic capacitance. Active

(31)

quench circuits react faster, quenching the avalanche in nanoseconds range.

When the arrival time of the incoming photon is known, the detector can be biased above the breakdown voltage synchronously with the photon arrival and only for a very short time. If the gates are suciently short (on the order of hundreds of picoseconds), the avalanches have no time to build up.

With such a short gate, afterpulsing is greatly reduced (see for example [53]) and the detector can be driven at a very high repetition rate, in the GHz range. However, since the avalanche current is small, it is also hard to discriminate, especially because the electronic noise caused by the rapid gating technique is larger than the avalanche signal. Many dierent approaches have been successfully implemented to discriminate the avalanche. They can be grouped in two big categories: the self-dierencing techniques [54] and the sine-gating ones [55]. In the former, the electronic circuit compares the output electrical signals corresponding to two subsequent gates by making the dierence between the two signals. When the avalanche occurs in one gate and not in the other, the electrical signals are dierent and the avalanche can be discriminated. Otherwise they are the same and the output is zero. In the latter approach, the detector is gated with a perfect sinusoidal gate. The electrical noise will aect only few frequencies, i.e. the gate frequency and its multiple harmonics. The avalanche introduces a deformation of the signal that contains dierent frequencies. By correctly ltering the output signal the avalanche can be discriminated. Once all the harmonics are correctly suppressed the detector becomes extremely sensitive and is able to achieve an extremely high eciency (50 % at 1310 nm) with negligible afterpulsing (smaller than 0.4 % after 10 ns) [53]. The stabilization of this device is however challenging. In App. ?? and [56] we discuss a dierent approach based on a simple low-pass lter. This technique has the advantage that the main frequency can be adjusted and it suer less from instability.

1.5.1 Passive quenching

In a passive-quench circuit, illustrated in Fig.??, the diode is reverse biased through a ballast resistor R_L of several hundreds of kΩ. One can represent the photodiode as the parallel impedance of the junction capacitance (few pF) and the junction resistance, respectively Cd and Rd. In addition, a parasitic capacitance, Cs (typically of few pFs), due to components packages and wiring must be added. Avalanche triggering corresponds to closing the switch in the diode equivalent circuit (Fig.??(b)).

The avalanche current discharges Cs and Cd and reduces the voltage across the diode. In the steady-state conditions, the current owing in the photodiode is given by the resistor R_d and R_L. If this value is smaller than 100 µA the avalanche

(32)

1.5 Readout circuit 19 is spontaneously quenched, otherwise no quench occurs [57]⁴ and the avalanche current is self-sustained. In general, larger R_L are preferred since they better quench the diode.

After the avalanche has been quenched, the diode begins to recovers to the operating condition. While the capacitors are recharging, the voltage across the diode recovers to the desired valueV_b+V_ewith a time constant ofR_L(C_d+C_s). When the reversed bias exceeds the breakdown voltage, avalanches can be triggered even if the voltage has not fully recovered yet. This creates a twilight time zone where the eciency of the device is not well dened. Smaller R_L guarantees smaller recovery time and reduces the twilight zone. For these reasons R_L is usually chosen as a trade-o between the quenching speed and the recovery time.

Figure 1.13: (a) (Left) Passive-quench circuit. (b) (Right) Passive-quench analogous circuit. Source [57].

In Sec. ??, we have seen that afterpulsing can be reduced by reducing the total avalanche current owing in the diode. For a passive-quench circuit, the total amount of charge that ows during the avalanche is

Q_av =Ve·(Cd+Cs). (1.3) Note that the avalanche charge is increased by the parasitic capacitance. Fig- ure ?? shows the impact that the parasitic capacitance may have on the total avalanche current. Discrete components have larger C_s which is increased by the device package. After that, wiring and electronic board contribute to this unwanted capacitance. Using un-packaged components close to the diode reduces C_s and consequently the afterpulsing.

4Since the avalanche process is statistical at lower current it might happen that none of the crossing carriers ionizes an atom. This quenches the avalanche process.

(33)

Figure 1.14: Avalanche-current-pulse outputs from two passive quench circuits. The black curve corresponds to a circuit built with discrete components, while the red curve corresponds to the same circuit implemented with un-packaged chips, where low-parasitic chip-to-chip wire bonding was employed to minimize Cs. Picture taken from [58].

1.5.2 Thesis contribution: Negative-Feedback SPAD

Recently, Princeton Lightwave has developed a new kind of avalanche photodiode, named negative-feedback avalanche photodiode, NFAD [50], which features two appealing characteristics:

a thicker multiplication region which greatly reduces the tunneling noise but at the expense of a bigger volume, which increases the thermal noise.

Because of this, primary dark counts due to thermal noise are the major contribution of noise even at a very low temperature (down to -100^◦ C for the diode tested in [59]).

a monolithic integrated resistor: a thin-lm resistor integrated monolithically to the p-metal contact (Fig.?? ??) which passively quenches the growing of the avalanche. When the avalanche grows, the resistor reduces the voltage across the diode as it occurs in the passive quench. Thanks to the monolithic integration, the parasitic capacitance is reduced and along with it the avalanche current.

This diode does not allow fast operations because of the passive quench circuit.

However, the thick multiplication region together with the eective quenching circuit could guarantee limited noise gure and allow for free-running operation. In a rst step, we developed a compact free-running detector to verify if the diode was suitable to be used in real applications. The rst version of the detector was cooled with a three-stage thermoelectric cooler which allowed operations down to -50^◦ C.

(34)

1.5 Readout circuit 21

(a) Structure of the NFAD. Note

the thin lm resistor on the top. (b) Top view of the NFAD.

Then we built on our previous results to check if reliable operations would be allowed at lower temperature. We characterized down to -110^◦ C and we veried a strong reduction of the primary dark counts (down to few s⁻¹of noise) accompanied by an increasing of the afterpulsing decay time which further limits the operation at high frequency rate.

Experimental realization The SPAD under test was a Princeton Lightwave NFAD (model no. E2G2) with an active area of 25 µm and a series quench resistor of 500 kW. The diode cathode is capacitively coupled to a large bandwidth (40 MHz- 6 GHz) 40 dB amplier. The voltage drop induced by the avalanche current is discriminated and its duration is extended to 10 ns. This signal is also used to keep the voltage below the breakdown voltage for a user-controlled hold-o time. The diode is installed on a three-stage thermoelectric cooler, and sealed in a custom box together with the electronics. The quality of the detector can be expressed in terms of the afterpulsing characteristics. Figure ?? compares the afterpulse probability for our passive quench detector with the state-of-the-art active quench circuit realized with discrete components [60] at the same detection eciency (10%). Details about the characterization setup will be provided in Ch.??. The afterpulsing probability is two orders of magnitude lower than the active quench solution. This quantitatively matches the expected reduction of total avalanche current obtained with NFAD detectors [50]. After the rst development, the detector already showed very low noise for an InGaAs/InP SPAD. The overall quality of the developed SPAD is represented in Fig.?? where the dark-count rate as a function of the hold-o time for two dierent eciencies is reported. The primary dark-count rate is extremely low, featuring 600 s⁻¹ (2000 s⁻¹) of dark counts at 10% (20%) of eciency. This was the lowest dark-count rate achieved in an InGaAs SPAD. Moreover, the fast quench results in low afterpulse which is suppressed after only 5 µs (15 µs) for 10%

(20%) of eciency. More details on the results can be found in App. ?? and [61].

(35)

Figure 1.16: Comparison between an active-quench [60] circuit and the detector developed in this work.

Figure 1.17: Dark-count rate as a function of the hold-o time for two dierent eciencies.

Temperature: -50^◦ C.

(36)

1.5 Readout circuit 23 Due to the thick multiplication layer, the dark count rate was limited by the thermal noise, so a reduction of the dark count rate is expected at lower temperatures.

Therefore we built on our previous work and we investigated the performance of NFADs at lower temperatures, down to -110^◦ C. We achieved two orders of magnitude of reduction on the primary dark-count rate. Figure ?? shows the measured dark-count rate as a function of single-photon detection eciency at 1550 nm for temperatures between -50^◦ C and -110^◦ C. For this data, the detector hold-o time was set to 20 µs. More details on the results can be found in App. ?? and [62]. De- spite the lower operating temperature, the detector is practical since the cooling is provided by a free-piston stirling cooler (Twinbird SC-UE15R) which is maintenance free and has a specied cooling power of 20 W at -110^◦ C. It can run continuously without requiring cryogenic gas. Lowering the temperature extends the decay time of the afterpulsing. However, the ecient quench due to the monolithic integration partially compensates for this drawback. In this setting the afterpulsing probability grows with decreasing the temperature, but at the lowest temperature, for an eciency of 11.5% the afterpulse probability was 2.2%, which is acceptable for most applications. The extremely low dark-count rate and the good afterpulsing probability also allow operations with higher detection eciency up to 30% at the expense of increasing the hold-o time (few tens of microseconds). The rst ver-

Figure 1.18: Dark-count rate as a function of the detection eciency for dierent temperatures ranging from -50^◦ C to -110^◦ C. For comparison, characterization of a second diode (NFAD2) is plotted (dashed line), showing similar performance.

sion of the detectors developed during this work, commercialized by IdQuantique, has been largely employed in several experiments thanks to its extremely low noise gure [63, 64]. I believe that the version operating at lower temperature would

(37)

impact even more quantum optic experiments since it shows primary dark count close to the ideal (which has never been achieved with semiconductor devices at 1550 nm) but at the same time guarantees a compactness that cannot be obtained with superconducting nanowire single-photon detectors. This detector is ideal for application in long-distance QKD, since the transmission probability of the photons carrying the encoded information becomes very low and a small dark-count rate, well below the photon arrival rate, does not increase the bit error rate too much.

Moreover, as the photon-detection rate becomes rather small, a hold-o time on the order of tens of µs can be tolerated by reducing the afterpulsing probability suciently. Using this detector, Korzh and co-authors have recently demonstrated that a secret-key can be distributed over 307 km [65].

1.6 Conclusion

With the growing number of applications that require sensitivity to light at the single-photon level, semiconductor avalanche photodiodes are more and more employed because of their reliable performances and their compactness. However, these devices are far from being ideal since they suer from noise such as dark count and afterpulsing. Depending on the spectral region under investigation, SPAD can be grown based on silicon materials (for visible wavelengths) or InGaAs/InP heterostructures (for infrared wavelengths). On the one hand Si-SPADs attain large detection eciency and are less aected by primary dark count noise and afterpulsing. On the other hand, electronic circuits for InGaAs photodiodes are much more developed to compensate for the higher noise. These circuits are able to adapt the SPAD operations to the applications and to suppress the unwanted noise.

Si-SPADs have always operated in free-running conditions. However, with the improving of the capability to generate and manipulate single-photons, we are ap- proaching the limits of Si-SPAD performances. In particular, free-running operations do not allow the exibility to choose when to activate the detector, which can be a drawback when the photon of interest is hidden in a background noise or when it arrives just after a strong pulse. Starting from practical needs of our laboratory, we developed a gated Si-SPAD based on a thick architecture. We also investigated the advantages coming from the gating technique.

Contrary to Si-SPAD, InGaAs/InP SPAD usually operates in gated conditions because of the large noise of the diode. Some specic diode architectures allow reduction of the primary dark count rate by lowering the temperature. However this advantage is negatively balanced by the long-lasting afterpulsing whose decay time increases at lower temperatures. The monolithic integration of the quenching circuit in the diode has been demonstrated an ecient way to compensate for the parasitic capacitance and it eectively quenches the avalanche, reducing also

Protocol and devices for practical quantum information processing

Thesis

Reference

Protocol and devices for practical quantum information processing

Université de Genève

Groupe de Physique Appliquée Faculté des Sciences Professeur Hugo Zbinden

Protocol and devices for practical quantum information processing

Thèse

présentée à la Faculté des Sciences de l'Université de Genève pour obtenir le grade de Docteur ès Sciences, mention physique

par

Tommaso Lunghi d'Italie

Thèse N

4729

GENÈVE

Atelier d'impression Repromail

10 Novembre 2014

Abstract

Résumé

Contents

Introduction

1 Single-photon avalanche photodiode: physics and technology

1.1 General principle

I

-V

V

V

+V

1.2 Physics of a SPAD

1.2.1 Dark count sources

1.2.2 Time resolution

1.2.3 Detection eciency

1.3 The advantages of gating a Silicon SPAD

1.3.1 Silicon SPAD structure

1.3.2 Thesis contribution

(B) (A)

40 V

20 ns

1.4 Low noise free-running SPAD for telecom wavelengths

1.4.1 SAGCM structure

1.5 Readout circuit

1.5.1 Passive quenching

1.5.2 Thesis contribution: Negative-Feedback SPAD

1.6 Conclusion