Bringing entanglement to the real world: from fundamental aspects to applications in quantum communication and radiometry

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Thesis

Reference

Bringing entanglement to the real world: from fundamental aspects to applications in quantum communication and radiometry

POMARICO, Enrico

Abstract

The scope of this thesis is to explore different ways of bringing the phenomenon of quantum entanglement to our classical world. A first manner is to make entanglement an element of everyone's cultural background. I show that nontrivial quantum nonlocality tests can be performed with do-it-yourself optical sources. Furthermore, entanglement can be brought to the real world as a technological resource for improving everyday activities, like communication. Sources of entangled photons, suited to long distance quantum communication, need to be developed. I present a source of entangled photons realized via Spontaneous Parametric Down Conversion in an integrated cavity-waveguide. I show how this kind of sources can be engineered. I also report the realization of low-loss sources for the implementation of an experiment of faithful entanglement swapping adopting a nonlinear interaction between two single photons. Last, one can also attempt to physically generate and observe entanglement at macroscopic scales. I analyze the possibility of cloning a photon of an entangled pair and detecting the amplified state with human eyes. [...]

POMARICO, Enrico. Bringing entanglement to the real world: from fundamental

aspects to applications in quantum communication and radiometry. Thèse de doctorat : Univ. Genève, 2011, no. Sc. 4392

URN : urn:nbn:ch:unige-181079

DOI : 10.13097/archive-ouverte/unige:18107

Available at:

http://archive-ouverte.unige.ch/unige:18107

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

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UNIVERSITÉ DE GENÈVE FACULTÉ DES SCIENCES

Groupe de Physique Appliquée - Optique Prof. N. Gisin

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

par

Enrico Pomarico d'Italie

Thèse N^◦ 4392

GENÈVE

Atelier de reproduction de la Section de physique 2011

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DE GENEVE ...

FACULTÉ DES SCIENCES

Doctorat ès sciences Mention physiq ue

Thèse de

Monsieur Enrico POMARICO

intitulée:

"Bringing Entanglement to the Real World

From Fundamental Aspects to Applications in Quantum Communication and Radiometry"

La Faculté des sciences, sur le préavis de Messieurs N. GISIN, professeur ordinaire et directeur de thèse (Groupe de Physique Appliquée, Optique), P. MATALONI, professeur (Quantum Optics Group, Department of physics, Sapienza University of Rome, Italy), H. ZBINDEN, docteur (Groupe de Physique Appliquée), R. Th. THEW, docteur (Groupe de Physique Appliquée) et B. SANGUINETTI, docteur (Groupe de Physique Appliquée), autorise l'impression de la présente thèse, sans exprimer d'opinion sur les propositions qui y sont énoncées.

Genève, le 19 décembre 2011

Thèse - 4392

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Preface

This thesis is the result of the research activity conducted in the Group of Applied Physics (Optics) at the University of Geneva between the years 2007 and 2011 under the supervision of Prof. Nicolas Gisin and Prof. Hugo Zbinden. This manuscript summarizes and discusses the results of the projects I have worked on, which have been published or submitted for publication in research journals. These publications are listed in chronological order on pages iii-iv and appended at the end of the thesis. The thesis is written in a form as autonomous as possible from the papers. However, the articles contain technical details that can be helpful for the reading of the thesis. Every chapter includes sections where the obtained results are discussed and short-term perspectives for the specic investigation areas are provided.

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List of publications

A E. Pomarico, B. Sanguinetti, N. Gisin, R. Thew, H. Zbinden, G. Schreiber, A. Thomas, and W. Sohler,

Waveguide-based OPO source of entangled photon pairs, New Journal of Physics 11, 113042 (2009).

B E. Pomarico, B. Sanguinetti, R. Thew, and H. Zbinden,

Room temperature photon number resolving detector for infrared wavelengths, Optics Express 18, 10750 (2010).

C B. Sanguinetti, E. Pomarico, P. Sekatski, H. Zbinden, and N. Gisin, Quantum Cloning for Absolute Radiometry,

Phys. Rev. Lett. 105, 080503 (2010).

D P. Eraerds, E. Pomarico, J. Zhang, B. Sanguinetti, R. Thew, and H. Zbinden,

32 Bin Near-Infrared Time-Multiplexing Detector with Attojoule Single-Shot Energy Res- olution,

Rev. Scient. Instr. 81, 103105 (2010).

E P. Sekatski, B. Sanguinetti, E. Pomarico, N. Gisin, and C. Simon, Cloning Entangled Photons to Scales One Can See,

Phys. Rev. A 82, 053814 (2010).

F E. Pomarico, B. Sanguinetti, P. Sekatski, H. Zbinden, and N. Gisin, Applications of quantum cloning,

Optics and Spectroscopy 111, 545 (2011).

G E. Pomarico, J. D. Bancal, B. Sanguinetti, A. Rochdi, and N. Gisin,

Various quantum nonlocality tests with a commercial two-photon entanglement source, Phys. Rev. A 83, 052104 (2011).

H E. Pomarico, B. Sanguinetti, P. Sekatski, H. Zbinden, and N. Gisin,

Experimental amplication of an entangled photon: what if the detection loophole is ignored?,

New Journal of Physics 13, 063031 (2011).

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Other papers submitted for peer-review

I G. Manasseh, C. de Balthasar, E. Pomarico, B. Sanguinetti, N. Gisin, R. de Peralta, and S. Gonzalez,

Retinal and post-retinal contributions to the quantum eciency of the human eye, submitted to Journal of Vision, 2011.

J E. Pomarico, B. Sanguinetti, C. I. Osorio, H. Herrmann, and R. T. Thew, Engineering integrated pure narrow-band photon sources,

arXiv:1108.5542, submitted to New Journal of Physics, 2011.

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Introduction

In 1935 Schrödinger coined the word entanglement [1] to indicate

"not [...] one, but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought."

In this sentence, entanglement is considered not simply as a feature belonging to quantum theory, but as the one that distinguishes and identies it, that intrinsically comprises all the other aspects of the theory. In the second part of his thought, Schrödinger adds that entanglement imposes a way of thinking, a way of describing the world distant from our common classical intuition. Indeed, the fact that two systems, even if spatially separated, seem to work in a correlated way, as two facets of the same physical entity, is a counterintuitive eect for a variety of reasons. First of all, entanglement appears conned to the microscopic world, it manifests itself at scales innitely smaller than the ones we are used to and it is beyond human perception. Moreover, it is a phenomenon not well known outside specialized scientic environments and working with it comes out as a privilege of a limited community of scientists. In addition to this, we are not even led to utilize entanglement in our everyday life as a technological resource.

Making entanglement intuitive and useful is not easy, but neither is it impossible: this is our ambition and the motivation of this thesis. Indeed, I will report a series of experiments devoted to explore dierent ways of bringing entanglement to the real world. A rst manner is to make entanglement an element of everyone's cultural background, a known phenomenon, like electricity or thermodynamics, or even like other eects of quantum origin, such as su- perconductivity. Furthermore, entanglement can be brought to the real world as a resource to exploit technologically in order to tremendously improve our common activities, like communication or computation. Then, one can also attempt to physically generate and observe entanglement at macroscopic scales.

Initially treated, at the time of the Einstein-Podolski-Rosen (EPR) paradox [2], as the object of philosophical discussions, entanglement became, thanks to Bell's contribution to the debate [3], a physical problem to be investigated experimentally. Now, it has become a fundamental phenomenon accessible to everyone. In the last thirty years, very small, but important steps, have been made towards the popularization of entanglement, providing in future a fundamental support for the research in this eld: the familiarization with this phenomenon can lead to a next generation of physicists that will fully understand it. Indeed, we have so much improved our abilities to generate and manipulate entanglement, that nowadays testing it can be even performed with do-it-yourself sources requiring simple optical equipment. In chapter

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1, I will report the realization of quantum nonlocality tests with one of these sources, pointing out that even novel and nontrivial conclusions about nonlocality can be acquired with them.

However, entanglement can oer much more than being just a fundamental curiosity. In- deed, quantum mechanics is not only a way to describe the microscopic world, but also a way to perform tasks impossible to achieve classically. Therefore, entanglement can be brought to the real world as a valid technological resource for improving everyday activities. An eort to develop and adapt sources of entanglement for specic applications needs to be carried out.

For example, quantum communication, dealing with long-distance distribution of entangled photon pairs, can guarantee provably secure cryptography. However, for implementing this goal, compact and practical photon sources, compatible with the quantum repeater architectures, adopting atomic quantum memories and standard telecom bres distribution, need to be developed. To this end, in chapter 2, I will present a source of entangled photons realized via Spontaneous Parametric Down Conversion (SPDC) in an integrated cavity-waveguide, suited for long distance quantum communication.

In the perspective of real applications, next-generation quantum communication protocols aim at engineering low-loss photon sources for generating pure photonic states or high quality entanglement. In chapter 3, I will show how to design integrated cavity-waveguides in order to emit SPDC photons into single distinct narrow-band spectral modes.

Exploring new physical systems and experimental solutions is also a fundamental direction to follow in the future. In this context, I will discuss the proposal of an experiment of entanglement swapping where sum frequency generation at the single photon level for a Bell measurement is adopted. I'm currently working on the experimental implementation of this idea. This scheme allows one to herald the generation of maximally entangled states at a distance and to perform device independent quantum key distribution (QKD). This approach has been shown with a setup more scalable than existing six photon schemes based on SPDC and linear optics.

So far, I have examined the possibility of exploiting the entanglement between microscopic objects in our macroscopic world. But can one produce macroscopic entanglement and see it?

Observing quantum features at large scales represents one of the most fascinating challenges of modern quantum physics. From a fundamental point of view, this can clarify the transition from the quantum to the classical domain, which is still an open question. In chapter 4, I will analyze the possibility of cloning a photon of an entangled pair and detecting the amplied state with human eyes, which are a particular kind of threshold detectors. The human vision threshold has been determined with a series of experiments. However, I will show that coarse-grained measurements, such as threshold detectors, turn out to be inappropriate for demonstrating micro-macro entanglement. If and how it can be revealed genuinely with currently available technology is still unclear and remains an interesting eld of investigation.

Bringing entanglement to scales one can see allows one to explore physics in the quantum- to-classical regime. In this thesis, I will show new ways of measuring in an absolute way and of detecting light in this regime, ranging from one photon to relatively high power levels. In chapter 5, I will describe the experimental demonstration of a primary standard based on the optimal quantum cloning of one to many qubits. Moreover, I will present the realization of photon number resolving detectors at infrared wavelengths, with a large dynamic range, high readout frequency and room temperature operation.

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Finally, I will try to give some perspectives on the possibility of really bringing entanglement to the real world, as a physical phenomenon, and above all, as a communication resource.

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Resumé de la thèse

En 1935 Schrödinger introduit le mot intrication [1] pour indiquer

"non pas [...] une, mais plutôt la caractéristique de la mécanique quantique, celle qui impose son éloignement des lignes de pensée classiques."

Dans cette phrase, l'intrication est considérée non seulement comme une caractéristique qui appartient à la théorie quantique, mais comme celle qui la distingue et l'identie, qui inclut intrinsèquement tout aspect de la théorie. En plus, l'intrication impose une façon de penser et de décrire le monde, qui est loin de notre intuition classique commune.

En eet, le fait que deux systèmes, bien que separés spatialement, semblent fonctionner de façon corrélée, comme deux parties de la même entité physique, est contre-intuitif pour diverses raisons. En premier lieu, l'intrication semble connée au monde microscopique, elle se manifeste au-delà de la perception humaine, à des échelles inniment petites par rapport aux nôtres. De plus, l'intrication n'est pas un phénomène bien connu hors des milieux scientiques spécialisés et travailler avec elle apparaît comme un privilège d'une communauté limitée de chercheurs. L'intrication n'est non plus un phénomène exploitée technologiquement dans notre vie quotidienne.

Rendre l'intrication intuitive et utile n'est pas facile, mais pas impossible non plus: c'est l'ambition et la motivation de cette thèse, dans laquelle est présentée une série d'expériences dévouées à explorer diérentes façons d'amener l'intrication au monde réel. L'intrication peut être amenée dans le monde réel dans le sense qu'elle peut devenir un élément du bagage culturel de tous, un phénomène connu, comme l'électricité ou la thermodynamique. Elle peut aussi faire partie de notre vie comme ressource technologique qui améliore nos activités communes, comme la communication ou le calcul. Enn, on peut aussi essayer de générer physiquement et observer l'intrication à des échelles macroscopiques.

Traitée d'abord, aux temps du paradoxe de Einstein-Podolski-Rosen [2], comme l'objet de discussions philosophiques, l'intrication est devenue par la suite, grâce à la contribution de John Bell [3], un problème physique à étudier expérimentalement. À présent, c'est devenu un phénomène accessible à tout le monde. Au cours des derniers trente ans, des pas très petits, mais importants, ont été entrepris en direction de la divulgation de l'intrication, en donnant un support fondamental pour le futur de la recherche dans ce domaine: la familiarisation avec ce phénomène peut aboutir à une prochaine génération de physiciens qui pourra le comprendre complètement. Eectivement, nos capacités à générer et manipuler l'intrication ont été améliorées au point que l'on peut actuellement la tester avec des sources de paires de photons intriqués "do-it-yourself", qui demandent un équipement optique simple. Dans

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le chapitre 1, je vais présenter la réalisation de quelques tests de non-localité quantique avec une des ces sources, en mettant en évidence que, même avec ces moyens simples, l'on peut atteindre des conclusions nouvelles et non triviales.

Toutefois, l'intrication peut orir beaucoup plus qu'une curiosité fondamentale. En fait, la mécanique quantique n'est pas seulement une façon de décrire le monde microscopique, mais aussi une façon d'exécuter des tâches impossibles à réaliser classiquement. Donc, l'intrication peut être amenée dans le monde réel en tant que ressource technologique pour améliorer nos activités quotidiennes. Il faut certainement faire un eort pour développer et adapter les sources d'intrication aux applications spéciques. Par exemple, la communication quantique, qui s'occupe de la distribution à longue distance de paires de photons intriqués, peut garantir une cryptographie avec une sécurité prouvable. Ceci nécessite le développement de sources de photons compactes, pratiques et compatibles avec les architectures du répéteur quantique, qui utilisent des mémoires quantiques atomiques et la distribution de photons dans les bres télécom standards. Pour ce faire, dans le chapitre 2, je vais présenter une source de photons intriqués realisée à travers le processus de uorescence paramétrique spontanée dans un guide d'onde intégré dans une cavité. Cette source est adaptée pour la communication quantique à longue distance.

Dans la perspective de réaliser des vraies applications, la communication quantique de la prochaine génération a pour but de développer des sources de photons avec des pertes minimales an de générer des états photoniques purs ou une intrication de haute qualité. Dans le chapitre 3, je vais montrer comme on peut concevoir les systèmes intégrés de guide-cavité pour émettre les photons de uorescence paramétrique dans des modes spectraux uniques et étroits en fréquence.

Explorer des nouveaux systèmes physiques et des nouvelles solutions expérimentales est aussi une direction fondamentale à suivre pour le futur. Dans ce contexte, je vais discuter la proposition d'une expérience de permutation de l'intrication où on utilise la somme de fréquence au niveau des photons uniques pour la mesure de Bell. Je suis actuellement en train d'implémenter expérimentalement cette idée. Ce schéma permet d'annoncer à distance la génération d'états maximalement intriqués et de réaliser la distribution de clé quantique indépendamment des systèmes de mesure. Cette approche utilise une installation plus exten- sible par rapport aux schémas à six photons basés sur la uorescence paramétrique et l'optique linéaire.

Jusqu'à maintenant, j'ai considéré la possibilité d'exploiter l'intrication entre objets micro- scopiques dans le monde macroscopique. Mais est-ce qu'on peut produire l'intrication macroscopique et la voir? Observer des caractéristiques quantiques à grandes échelles représente un des plus fascinants dés de la physique moderne. En eet, cela pourrait aider à clarier la transition du domaine quantique au domaine classique, qui représente encore une question ouverte. Dans le chapitre 4, je vais analyser la possibilité de cloner un photon d'une paire intriquée et de détecter l'état amplié avec les yeux humains, qui sont un type particulier de détecteur à seuil. Le seuil de vision humaine a été déterminé avec une série d'expériences.

Cependant, je vais montrer que des mesures trop grossières, comme celles des détecteurs à seuil, semblent inappropriées pour démontrer l'intrication micro-macro. Si cette intrication peut être révélée de façon appropriée avec la technologie disponible actuellement, et comment, n'est pas clair et reste un domaine intéressant de recherche.

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Amener l'intrication à des échelles auxquelles on peut voir permet d'explorer le régime entre la physique quantique et la physique classique. Dans cette thèse, je vais présenter des manières nouvelles de mesurer de façon absolue et de détecter la lumière dans ce régime, qui va d'un photon jusqu'à des niveaux de puissance relativement élevés. Dans le chapitre 5, je vais décrire la preuve expérimentale d'un standard primaire basé sur le clonage quantique optimal de un à plusieurs qubits. Le chapitre présente par ailleurs le développement de détecteurs qui résolvent le nombre de photons aux longueurs d'onde infrarouges, qui peuvent travailler sur une grande gamme de puissances, avec une haute fréquence de détection et à la température ambiante.

À la n de cette thèse, je vais essayer de donner des perspectives sur la possibilité d'amener réellement l'intrication dans le monde réel, en tant que phénomène physique et, surtout, comme ressource pour la communication.

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Chapter 1 Entanglement: a fundamental

phenomenon accessible to everyone

Entanglement can be brought to the macroscopic world in the sense that its knowledge or, even better, its understanding, is not a privilege of a limited community of scientists but can be achieved by everyone. After an introduction to the counterintuitive aspects of entanglement, we review quickly the fascinating historical debate about it and show how its seemingly bizarre eects can be observed experimentally with photons and are not only the object of philosophical discussions. Nowadays, our abilities to generate and manipulate entanglement have reached such a level that do-it-yourself sources of polarization entanglement are even commercially sold. In the last part of the chapter, we show that with this kind of source nontrivial nonlocality tests can be implemented. This could be of interest for showing the richness of the nonlocality phenomenon to students of undergraduate laboratory courses.

1.1 Entanglement and nonlocality: an ongoing debate

In classical physics, the state of a composite system is given by a combination of the states of its subsystems, individually and physically well dened. In contrast, in quantum mechanics, states with an intrinsic non separable nature can be dened. For instance, in a singlet state of a pair of spin-1/2 particles

|ψ⁻i= 1

√2 | ↑↓i − | ↓↑i

, (1.1)

each spin is in a state | ↑i or | ↓i, with the spin along the z-axis +¹₂ or −¹₂ respectively, while the value of the total spin along the z-axis is 0. The state is dened for the composite system, but not for each subsystem. In other terms, the two subsystems cannot be fully and individually described without considering their counterpart, they are two facets of the same physical entity: this is what is called entanglement.

Since two entangled systems work in a joint way, independently of the distance separating them, the measurement of one of them aects the state of the pair and can be "felt" on the unmeasured side. Therefore, entanglement manifests itself in the correlations of the outcomes

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of the measurements performed on the two systems, the type of correlation depending on the measured observables.

What makes entanglement a bizarre eect is not that what happens to a system seems in- uencing another distant one. Indeed, non local eects have already been treated in physics, for instance, as the apparent eects of local interactions with a surrounding eld or with a certain space-time geometry. But quantum correlations seem to be established instanta- neously, apparently violating the speed limit on the transmission of information implicit in the theory of relativity. This is why Einstein dubbed them "spooky actions at a distance" [4]

and used this argument to claim the incompleteness of quantum mechanics [2]: local realism should have been restored by assuming the existence of local hidden variables determining the measurements' outcomes.

However, in 1964 John Bell showed that the correlations between the results of the measurements on entangled particles are stronger with respect to what is expected by any physical theory of local hidden variables. By measuring them, a simple inequality (i.e. the Bell inequality [3]), based on the locality assumption, can be violated. Bell's theorem is extremely general and powerful. If quantum mechanical predictions are correct, then every kind of future physical theory has to give up the principle of local causality.

Bell's contribution brought new elements in the debate about the compatibility between quantum theory and relativity. In the 80's, with the formulation of the No-Signalling theorem [6, 7], entanglement was revealed not to allow the instantaneous transfer of information between two observers. Indeed, if an entangled state is shared between Alice and Bob, Bob observes no dierence in the probability of the outcomes of the measurements he performs, whatever observable Alice is measuring on her side. Therefore, superluminal communication remains forbidden with entanglement.

However, if the conceptual dierences between quantum theory and relativity can "peace- fully coexist" is still an open question [8]. Quoting Bell's words [9]

"we have an apparent incompatibility, at the deepest level, between the two fundamental pillars of contemporary theory... It may be that a real synthesis of quantum and relativity

theories requires not just technical developments but radical conceptual renewal."

1.2 From theory to optics laboratories

Bell's reconsideration of the EPR argument gave new life to the study of entanglement, essentially ignored for thirty years after the Einstein-Bohr debate concerning its interpretation.

Indeed, the Bell theorem could be experimentally tested, thus yielding the opportunity to con- vert the EPR debate from philosophy to physics. Testing nonlocal correlations predicted by quantum mechanics experimentally became a concrete idea after the Clauser-Horne-Shimony- Holt (CHSH) formulation [10] of the original Bell inequality, focused on two particle entanglement and on the measurement of the correlations between dichotomic observables, involving only coincidence counts.

It's not by chance that photons have suddenly been recognized as good candidates for CHSH Bell tests. Optics, always intimately related to the foundations of quantum mechanics, reached important technological advances in the 60's, like the invention of the laser, and could

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1.2 From theory to optics laboratories

allow to easily manipulate photons in dierent degrees of freedom, such as polarization, linear momentum, angular momentum and so on.

In 1981 and 1982 A. Aspect performed the rst CHSH-Bell tests using photon pairs produced by calcium cascade sources [11, 25]. In the following years, the complexity of the Bell tests has been progressively reduced by exploiting parametric nonlinear processes, such as Spontaneous Parametric Down Conversion (SPDC), in order to realize ecient, practical and compact sources of entangled photon pairs.

1.2.1 Spontaneous Parametric Down Conversion

SPDC is a quantum nonlinear optical process in which a photon with frequency ωP is converted with a certain probability, inside aχ₂-nonlinear crystal, into two photons, usually called signal (s) and idler (i), of lower frequency ω_s and ω_i respectively [13]. This process must satisfy energy and momentum conservation, such that

ω_p =ω_s+ω_i, (1.2)

~kp =~ks+~ki, (1.3)

where~k_j (with j =p, s, i) is the wavevector of pump, signal and idler photons respectively.

Momentum conservation, which is also called phase-matching, relies basically on maintaining a proper phase relationship between the interacting waves along the propagation direction, so that the amplitude contributions from dierent locations of the nonlinear crystal are all in phase and add up constructively. Since the phase-matching condition can not be satised in an optical medium with ordinary dispersion, it is usually achieved via birefringent phase matching or via quasi-phase matching.

The former technique exploits the material's birefringence, that is the dependance of the refractive index on the direction of polarization of the optical radiation, to satisfy the equation (1.3). Depending on the crystal material, the emitted elds can have the same (Type I phase- matching) or orthogonal (Type II) polarization. For instance, theβ-Barium Borate (BBO) crystal is negative uniaxial and allows eoo Type I or eoe Type II phase matching, where e ando stand for extraordinary and ordinary polarization respectively.

The quasi-phase matching is instead achieved via spatially periodic modulation of the crystal nonlinearity along the direction of propagation. Allowing for a certain phase mismatch, such periodicity introduces an opposite phase at specic positions, bringing the phases of the eld contributions produced along the crystal into good alignment. This is performed via periodically poled (PP) crystals, where the modulation of the ferroelectric polarization of the material is attained by applying on it strong electric elds. The resulting phase-matching condition is then given by

~kp =~ks+~ki+K,~ |K~|= 2π

Λ, (1.4)

whereK~ represents the eective grating-type~k-vector andΛthe poling period. By an appropriate choice of Λ, one can quasi-phase-match practically any desired non-linear interaction between the pump, signal and idler elds over the entire interaction length and with dierent

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combinations of polarization of the three elds, like Type 0, where the three elds have the same polarization. Periodically poling is usually realized with materials like Lithium Niobate (LN) or Potassium Titanyl Phosphate (KTP).

SPDC can be realized either by pumping a bulk crystal or by conning the pump light along a waveguide, typically a few cm of length and a few µm of diameter, embedded in the nonlinear material. The photon pair rate can be further increased by placing the crystal inside an optical cavity to realize an Optical Parametric Oscillator (OPO).

In bulk birefringent crystals phase matching is achieved by properly tilting them, while in periodically poled crystals or waveguides by controlling their temperature, which is a more stable method.

Bulk crystals, like BBO, show an SPDC eciency, that is the ratio between the number of generated photon pairs and the number of pump photons, of approximately 10⁻¹² to 10⁻¹¹. Periodically poled crystals lead to higher photon pair production rates, since quasi phase matching often makes it possible to utilize longer crystals and a larger nonlinear coecient than is accessible with birefringent phase matching. In waveguides one can reach, with a relatively low pump power, conversion eciencies up to 10⁻⁶. According to [14], similarly to what happens in cavity SPDC, the spatial connement inside long waveguides increases the mode overlap between the pump, signal and idler elds and produces an enhancement of the SPDC into a reduced spectral photons' bandwidth.

A critical aspect of SPDC sources is the need to couple the downconverted photons into optical bres. Good bre coupling with short bulk crystals or using collinear emission can be in principle obtained by properly adapting the pump-mode with the bre-matched modes of the idler and the signal eld [15, 16, 17]. Single mode waveguides can also guarantee a high spatial coupling of photons into the bre [18, 19]. In any case, good quality crystals and optics optimization are crucial for reaching this goal.

1.2.2 Photonic entanglement

Photon pairs produced by SPDC can be entangled using dierent tricks and various degrees of freedom. We consider below only polarization, time-bin and energy-time entanglement.

Polarization entanglement can be created, for example, by pumping with a laser a Type II BBO crystal with non collinear emission (gure 1.1). The two photons of the generated pairs have orthogonal polarizations (ordinary and extraordinary) and emission directions belonging to two dierent cones. For a specic angle between the crystal optical axis and the pump, the two cones can intersect along two spatial directions. Along these two modes indistinguishability of which photon belongs to which emission cone is created: the polarization of each emitted photon is undened, but perfectly anti-correlated with the polarization of the other one [20]. By selecting with pinholes and single mode bres the two spatial modes, one can generate the state

|Ψ⁻i= 1

√2

|His|Vii−e^iφ|Vis|Hii

, (1.5)

where |H(V)i are states of horizontal (vertical) polarization and φ a phase which is implemented by using two additional BBO crystals, which also correct for the temporal walko of the photons. Other sources of polarization entanglement are reported in [21, 22].

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1.3 From laboratories to everyone

Figure 1.1: Schematic of the generation of polarization entanglement via a Type II nonlinear crystal.

Time-bin entanglement consists in the indistinguishability of the creation time of a photon pair between two discrete values,t₀ and t₁ [23]. By sending a pulse through an unbalanced interferometer, two consecutive pulses with a xed phase relationφemerge at the output. If these pulses are sent through a nonlinear crystal, a pair of entangled photons can be created in a coherent superposition of the timest₀ and t₁. The time-bin entangled state can be written as

Energy-time entanglement is a continuous version of the time-bin entanglement [24]. It can be produced by parametric down conversion in a nonlinear crystal pumped by a coherent continuous wave (CW) laser. In this case the crystal splits the pump photons into pairs of photons of arbitrary lower energies, but whose sum is equal to the energy of the original photon. The photon pair may be created at a random time, within the coherence time of the pump photon, but if the signal is detected at any time, then we know that the idler is present at the same time. Therefore, the energy and the emission time is uncertain for each photon, but the sum of their energies and dierences of their creation times are well dened. Time-bin and energy time are robust degrees of freedom for long-distance distribution of entanglement in bre.

1.3 From laboratories to everyone

Since the CHSH-Bell test performed by Aspect in 1981 [11], several technological advances towards the realization of high quality photonic entanglement have been made. This allowed several experiments to report consistent violations of the CHSH inequality.

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However, the experimental imperfections, which all these tests are susceptible to, open loopholes that can be exploited by a local theory to reproduce the experimental data. Two relevant loopholes are the detection and the locality loophole. The former relies on the fact that particles are not always detected in both channels of the experiment. The latter is related to the necessity of separating the two sites enough to prevent any light-speed communication between them from the measurement settings are set until the detection events have occurred.

At the moment both loopholes have been closed [25, 26, 27, 28, 29], but not yet within the same experiment.

In any case, in the last thirty years a deep expertise in the experimental study of entanglement has been achieved. Indeed, the technology necessary for generating entanglement is well known and entanglement sources can be extremely compact, cheap and stable in time.

Moreover, entanglement in some degrees of freedom, like polarization, can be analyzed in a practical and even very accurate way, such that quantum nonlocality tests can be easily performed. This is why, now, sources of polarization entanglement are even commercially sold in a do-it-yourself conguration [30]. They can produce 10 times more signal and require much less space than the Aspect experiment.

Therefore, the study of entanglement do not have to be necessarily conned to a few privileged laboratories, but it can be extended to a wider community of users, for instance students of undergraduate laboratory courses, or showed in outdoor demonstrations (such as

"La Nuit de la Science" in Geneva).

1.4 Quantum nonlocality with a commercial entanglement source

In this section, we describe the work done in Paper G, showing that quantum nonlocality tests alternative to CHSH, requiring multiple binary measurement settings, can be carried out with a commercial entanglement source (QuTools [30]).

1.4.1 Testing quantum nonlocality: not only CHSH

A CHSH-Bell test requires to perform two specic binary measurement settings on each of two entangled particles and to evaluate the correlations of the outcomes for the four possible combinations of settings. Therefore, it needs a rather simple conguration, an implementation conceptually easy with minimum experimental eort.

However, in recent years, the generalization of Bell inequalities for a larger number of measurement settings or outcomes with respect to CHSH have been theoretically investigated.

From a fundamental point of view, they allow for an understanding of the nonlocal correlations unattainable with CHSH. For instance, in the case of three possible 2-outcome measurements per side, one inequality, calledI₃₃₂₂ [31] can be violated by specic mixed 2-qubit states that do not violate CHSH. Or, inequalities I₄₄₂₂ [32, 33], with four 2-outcome measurements per side, are instead maximally violated by non-maximally entangled states, unlike CHSH.

Some theoretical models, providing an alternative understanding approach to quantum nonlocality, such as the Elitzur, Popescu, and Rohrlich (EPR2) model [34], utilize chained inequalities [35], which are generalizations of CHSH with multiple settings, for studying the local content of the quantum correlations.

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1.4 Quantum nonlocality with a commercial entanglement source

Inequalities based on multiple settings represent also an useful tool in the presence of noise and detection ineciency. For instance, in the presence of high-dimensional entanglement, that is, when the quantum systems sharing entanglement have dimensions larger than two, these inequalities can tolerate a detection eciency of 61.8% for closing the detection loophole [36], lowering the limit imposed by CHSH in experiments of entangled qubits. Chained inequalities provide, instead, QKD security tests stronger than CHSH, allowing for a better evaluation of the knowledge of an eavesdropper in a communication system [37].

1.4.2 The QuTools source

The QuTools source is a commercially available source generating photon pairs at 810 nm entangled in polarization via SPDC in a bulk BBO crystal cut for a Type II phase-matching and pumped by a continuous wave diode laser at 405 nm. The entanglement in polarization is generated as explained 1.2.2. Details on this source can be found in [38]. Linear polarizers are used for measuring the two photons into dierent polarization bases. They limit the reconstruction of the generated entangled state and the estimation of the correlations used for the inequalities to the equatorial plane of the Poincaré sphere.

A partial tomography of the singlet state prepared with the commercial source shows that it has some imperfections: the state can be approximated as a Werner state of the form ρ_W = V|ψ⁻ihψ⁻|+ (1−V)¹₄, with visibility V = 0.94. The measurement settings for the estimation of the correlation terms required by the inequalities we want to measure have been optimized, taking into consideration the reconstruction of the state (see Paper G for further details).

1.4.3 Quantum nonlocality tests with multiple settings Inequalities inequivalent to CHSH

We have measured the CHSH inequality and other Bell inequalities inequivalent to CHSH, in particular I₃₃₂₂ [31] and two dierent types of I₄₄₂₂, called AS₁ and AS₂ [32, 33]. These inequalities are optimal to detect nonlocality in scenarios involving three and four settings.

For each of the three dierent inequalities, we observe a violation of the local boundI_L(Table 1.1).

The violations for the two I₄₄₂₂ inequalities are stronger than for I₃₃₂₂, indeed, their tolerance to noise is higher with respect to I₃₃₂₂. The CHSH inequality conrms to be the most robust to noise. In all the cases the obtained violations agree quite well with the values expected from the tomography.

Chained inequalities and EPR2 nonlocality

The chained inequality withN settings for Alice ({α1, α2, ..., αN}) andNfor Bob ({β1, β2, ..., βN}) [35] can be written as a correlation inequality as

I_chain^(N⁾ = E(α₁, β₁) +E(β₁, α₂) +E(α₂, β₂) +...+

+E(α_N, β_N)−E(β_N, α₁)≤2(N −1). (1.7)

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I_L I^exp I^tom I^exp−I_L p_noise(%) (σ units)

I_CHSH 2 2.731±0.015 2.683 49 27

I₃₃₂₂ 4 4.592±0.024 4.769 25 13

AS1 6 7.747±0.026 7.750 67 23

AS₂ 10 12.85 ±0.030 12.819 95 22

Table 1.1: Measurement of the CHSH inequality and of the inequalities inequivalent to CHSH.

I_L is the local bound, I^exp is the value of the Bell parameter obtained experimentally with the optimized settings, I^tom is the expected value from the partial tomography, I^exp−I_L is the dierence between the obtained value and the local bound in terms of number of standard deviationsσ and p_noise(%) is the critical level of white noise that can be added to the system while still keeping a violation.

We limit ourselves to6settings per side. In the Table 1.2 it is shown that these inequalities are violated in a way consistent with the expected results. Notice that the larger the number of settings, the weaker the violation. Indeed, the fraction of noise that we can add to the system and still keep the violation decreases for an increasing number of settings.

N I_L I^exp I^tom I^exp−I_L p_noise (%) (σ units)

2 2 2.731±0.015 2.683 49 27

3 4 4.907±0.019 4.925 48 18

4 6 7.018±0.023 6.999 44 15

5 8 8.969±0.026 8.996 37 11

6 10 10.91±0.028 10.954 33 8

Table 1.2: Measurement of the chained inequalities with N settings per side. ForN = 2the result for the CHSH inequality is reported.

According to the EPR2 model [34], chained inequalities can be used to put an upper bound on the local content of the prepared state. One can imagine that only a fraction of the photon pairs produced by the source has nonlocal properties, while the other behaves in a purely local way. Hence, the measured value of I_chain^(N) decomposes as a sum of the local bound I_L with probability p_L and of some possibly larger value I with probability 1−p_L. The latter satises the no-signaling principle. Therefore

I^exp =p_LI_L^(N)+ (1−p_L)I_{N S}^(N). (1.8) Since the local and the no-signaling values of the I quantity are at most I_L^(N⁾ = 2(N −2) andI_{N S}^(N⁾= 2N respectively, the local part of the produced state is bounded by the maximum valuep^max_L :

p_L≤p^max_L =N −I^exp

2 . (1.9)

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1.4 Quantum nonlocality with a commercial entanglement source

The minimum value of p^max_L that we have measured is 0.491±0.012, with a chained inequality of 4 settings per side, which is in good agreement with what we expected taking into account the generated state. This result means that at least half of the photon pairs produced by the source are nonlocal, a result that cannot be shown with the CHSH inequality.

To our knowledge, this is the rst experiment that xes an upper bound on the local part of the quantum correlations according to the EPR2 approach, even though existing experimental results could also be reinterpreted to provide such a bound as well.

Randomness certied by the no-signaling principle

When measuring a singlet state, locally random outcomes can be observed. The violation of a Bell inequality can certify the randomness produced during the experiment because it excludes any algorithm, meant as a local hidden variable, that can possibly predict the measured outcomes [39]. Note that in order to discard any such algorithm, the detection loophole should be closed during the experiment. In our case, we quantify the amount of true randomness created in our experiment, assuming fair sampling of the detected events: the state of the particles coming onto a detector does not aect the fact that a detector res or not, so that the detected pairs of particles fairly represent the ones produced by the source.

We consider all the marginal probabilities P(a|x) that Alice nds the outcome a when she measures x, which are compatible with the observed Bell inequality violation I^exp. We searched for the largest marginal probabilityP^∗(a|x)numerically among all possible quantum correlations, i.e. correlations that can be achieved by measuring a quantum state, and we foundP^∗(A|X) = 0.684±0.014, achieved for the CHSH inequality.

Note that in order to extract a truly random bit string out of measured outcomes, classical key distillation techniques should be used [40]. The ratio between the number of measured bits and the number of truly random, uniformly distributed, bits that is produced by this procedure is given by the min-entropy of Alice's outcomeAconditioned on her measurement choiceX: H_min(A|X) =−log₂maxaP^∗(A|X). In our case we ndH_min = 0.55±0.03for the CHSH violation, meaning that approximately one random bit every two measurements have been created.

1.4.4 Discussion

We have shown that nontrivial nonlocality tests alternative to CHSH can be performed even with a rather simple commercial source. In particular, we have measured Bell inequalities with multiple measurement settings. We have reported violations of I3322, of two I4422, and of chained inequalities with up to 6 settings per side. Violations of these inequalities have not been shown before. Moreover, by using the chained inequalities, we have put an upper bound on the local content of the prepared state at 0.491±0.012, meaning that at least half of the photon pairs produced by the source have nonlocal correlations. We have also quantied the amount of true randomness created in the experiment.

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Chapter 2 Entanglement: a technological resource

Entanglement can be brought to the real world in the sense that it can be exploited as a technological resource, achieving what is impossible to do classically. For example, using entanglement for communication goals may provide advantages in the secrecy of our information exchanges. Quantum communication deals with long-distance distribution of quantum resources, such as entangled photon pairs. In the perspective of a real implementation of this task, photon sources with a compact design, showing compatibility with the quantum repeater architectures, using atomic quantum memories and standard telecom bres distribution, are necessary. In this chapter, we present the realization of an integrated cavity-waveguide SPDC source, which generates energy-time entanglement of narrow-band photon pairs at the telecom wavelength. This represents the rst integrated cavity system producing SPDC at this wavelength. Although integrated OPO technology requires further optimization, it can be very promising for quantum communication.

2.1 Towards a new quantum technological revolution

Around 1970 S. Wiesner presented a paper, entitled "Conjugate coding", about the theoretical possibility of accomplishing a specic task with quantum mechanics that cannot be performed classically: the creation of "quantum money" impossible to counterfeit [41]. De- spite its novelty, his paper needed some time to be understood and went unpublished until 1983, giving start, together with the contribution of Bennett and Brassard [42], to the devel- opment of quantum cryptography.

The new way of thinking of quantum mechanics as a reservoir of radically new practical applications involved entanglement as well. Indeed, only by the early 1980s, the experimental conrmations of the predictions about entanglement brought physicists to take entanglement and quantum nonlocality seriously, not anymore as sources of embarrassment or fundamental curiosity, but as valid resources to be explored and developed. In 1985 David Deutsch rst showed how to exploit quantum entanglement to perform a computational task impossible for a classical computer [43], and in 1991 Ekert [44] proposed for the rst time to guarantee the

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security of a cryptographic protocol through the violation of a Bell inequality on an entangled state.

In the 90's the idea of manipulating entanglement for applications, like cryptography, computation and communication, became widespread. Physicists understood that a dierent way of thinking, a "quantum thinking", was needed, based on arguments and concepts not necessarily intuitive, but rich of new potentialities. Quantum mechanics is not only a way to describe the microscopic world, but a way to do things beyond the classical possibilities.

Actually, technologies based on quantum physics already exist and are widely used, such as laser, semiconductors, superconductors and so on. However, we are going towards a new kind of quantum technology revolution, which exploits quantum physics at the level of individual quanta, for which the manipulation and the control of microscopic resources, such as photons, single atoms, single ions, is required.

2.2 Quantum communication

Quantum communication aims at distributing quantum information between two or more remote locations. The main goal of this research eld is to perform quantum key distribution (QKD), that opens the possibility of performing provably secure cryptography.

Photons are appropriate carriers of ying qubits and photonic distribution can be implemented either in free-space or in optical bre. Since free-space links demand a direct line-of-sight connection and suer from variability of weather conditions, bre transmission is preferable in real-world applications.

Fibre-based QKD protocols, inspired on the BB84 protocol, but using phase encoding, which is more bre-compatible than the polarization, are already commercially available [45].

However, they are ultimately limited to a distance of a few hundreds of kilometers [46], because of photon absorption in optical bres. In fact, transmission in standard telecom bres, where the absorption is minimum, decreases exponentially with the distance L as 10⁻^αL¹⁰, with α the absorption coecient of around 0.2 dB/km at 1550 nm. When the transmitted signal is smaller than the noise counts in the receiving photon detectors, a secret key can be no longer established. Amplifying a single photon, similarly to the increase of the signal strength in classical communication, is prevented by the no cloning theorem [47]. Therefore, long-distance quantum communication requires dierent technologies than today's QKD systems.

2.2.1 Reaching longer distances via quantum repeaters

The use of satellites can be a possibility for long-distance quantum communications [48], but another fascinating solution is provided by quantum repeaters [49, 50]. The philosophy under the idea of the quantum repeater is the philosophy of the quantum technology revolution, according to which it's not convenient to conceive quantum applications with a classical way of thinking. If amplication is not allowed because of the no cloning theorem, then a quantum state should be distributed between remote locations by avoiding its direct transmission and by exploiting another process, tipically quantum, which is teleportation or, more generally, entanglement swapping.

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2.3 SPDC sources of entanglement for quantum repeaters

The quantum repeater works in the following way: the transmission distance is divided into short elementary links, where entanglement is established and stored into quantum memories [51] in a heralded way. Neighboring nodes perform entanglement swapping operations until the whole distance is covered. Quantum memories allow to wait for entanglement to be established in neighboring links and to synchronize the swapping operations. They must be able to store photons in a reversible way, without loosing the coherence of the quantum states [51]. Furthermore, rates can be increased if quantum memories are multimode, i.e. able to store hundreds of quantum bits simultaneously [52].

Fundamental ingredients for quantum repeaters are sources of entangled photon pairs.

2.3 SPDC sources of entanglement for quantum repeaters

SPDC is currently the most robust and ecient process for generating photonic entanglement. Some features are desirable for SPDC sources to be compatible with quantum repeaters architectures.

• Narrow bandwidth of the emitted photons. This allows to match the spectral linewidths of atomic quantum memories, usually of the order of 10 to 100 MHz. Narrow- band photons have long coherence times, allowing also more tolerance with respect to bres' length uctuations and chromatic dispersion, which can be experimental limita- tions for synchronization in Bell state measurements.

• Telecom wavelength adaptation. One or both photons of the pairs have to be generated at the telecom wavelength in order to be suited for propagation in standard telecom bres. When this is not the case, wavelength conversion interfaces can be adopted [53], but with the drawback of adding supplementary photon losses.

• Single mode bre coupling. Coupling SPDC photons into bres is necessary not only for transmitting them at a distance, but also for purifying their spatial mode. This is crucial for obtaining high multi-photon interference visibility when dierent links need to be interfaced.

• Ecient photon pairs creation. A light emitting source can be characterized by the spectral radiance, which, in the context of quantum sources, is related to the mean number of photon pairs generated per mode hni. Usually, in SPDC sources, in order to reduce multipair simultaneous emission, the quantityhni is limited at a value of the order of 0.1. Reaching this value with easily achievable pump power is what we mean with ecient photon pairs creation. In [54] it has been demonstrated that waveguides easily satisfy this requirement. Moreover, in [54] it is also shown that the spectral radiance, that ishni, remains constant independently of the spectral ltering.

• Low collection losses. Reducing the losses of photons from the moment in which they are generated to when they are available for distribution, processing or storing is very important. The main sources of losses are due to absorption inside the crystal, to the coupling into single mode bres and to the ltering. Low losses allow for a high

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emitted spectral brightness, desirable for having high signal rates, at a specic generated radiancehni.

• Easy handling and stability in time.

These are very general criteria to be adapted to the specic quantum repeater protocol.

However, generating narrow-band photons with SPDC is one of the most critical aspects.

Indeed, SPDC sources usually produce broad frequency spectra (of the order of THz). In order to reduce the photons' bandwidth two approaches can be followed. The rst is to use external passive ltering. In [54] an easy and practical technique, based on thermally stabilized bre Bragg gratings, for 10 pm (1.2 GHz)-ltering at the telecom wavelength is adopted. However, with bre technology one can achieve only some picometers ltering. For matching the atomic linewidths, external Fabry-Perot cavities can be used [56], but they are usually not very practical and can require time-consuming (o-line) alignment procedures.

Placing a nonlinear crystal inside an optical cavity, in order to realize OPOs [57, 58, 59, 60, 61, 62, 63, 64], represents a good alternative, since it allows to naturally produce narrow- band photons and to exploit the enhancement of the intracavity SPDC process with respect to the single pass scheme [57, 58]. The OPO sources reported so far produce photon pairs uniquely in the visible and near IR regime, between 700 and 900 nm, with bandwidths in the MHz level. Some of these sources generate single-mode polarization-entanglement [62], which is complicated to stabilize in ber-based quantum communication applications. Somo other OPOs show long-term stability [63, 64], but in general at the cost of complex routines.

2.4 An integrated cavity-waveguide source of entangled photon pairs

In Paper A we have presented a SPDC source based on a Ti-indiused PPLN waveguide resonator, i.e. a waveguide with end-face dielectric multi-layer mirrors reective at telecom wavelength, generating narrow-band energy-time entangled photon pairs at this wavelength.

The integrated conguration oers various advantages. The stabilization of the cavity resonance is simply related to the control of the temperature of the device, and not to a complex alignment system. Moreover, it allows to avoid the use of external Fabry Perot cavities, making the experimental setup of the source pretty simple and compact.

Table 2.1 compares our source with the main OPO-based photon pair sources recently reported. Our system is the rst OPO source with an integrated conguration and at the telecom wavelength. Even though a reduction of the overall losses is necessary by a dierent design of the waveguide resonator, as we shall see in the next sections, the high brightness, the bre coupled single mode emission and the energy-time entanglement generation, make integrated cavity-waveguides a promising approach for quantum communication applications.

2.4.1 Clustering in the emitted spectrum

The PPLN waveguide resonator is pumped by a cw diode laser at 780 nm, as shown in Figure 2.1, for generating photon pairs at around 1560 nm with a 0.91 pm (117 MHz)

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2.4 An integrated cavity-waveguide source of entangled photon pairs

Wang Kuklewicz Bao Scholz Our source

[59] [60] [62] [64] Paper A

Wavelength [nm] 860 795 780 893.4 1560

Bandwidth [MHz] 18 22 9.6 2.7 117

Single mode output X X X

Coupling into bre X X X X

Entanglement generation X X X X

Spectral Brightness 0.12 0.7 6 330 17

[s⁻¹M Hz⁻¹mW⁻¹]

Table 2.1: Comparison between the main recently reported OPO-based photon pair sources according to dierent criteria. Notice that the brightness values are not compared at the same generated spectral radiancehni. However, in the listed sources the spectral radiance is limited for reducing emission of multipairs.

bandwidth. The photon emission has to satisfy energy conservation and quasi phase-matching (guaranteed by xing the sample temperature, as in normal waveguides), but also double resonance, i.e. signal and idler frequencies have to match the resonant modes of the cavity.

Without the cavity, photons would have been generated in a range tens of nanometers wide.

In the presence of the cavity, the spectrum is allowed only within specic spectral intervals, called clusters (Figure 2.1).

Because of the waveguide material dispersion, the spacing in frequency between the cavity modes vary. The resonant frequencies for both the idler and the signal satisfy the energy conservation (they lie on a vertical line in the diagram in Figure 2.1) only in these specic regions some nanometers wide. This eect is extremely sensitive to the temperature depen- dence of the resonant frequencies. This eect was already known [65, 66, 67], but has not been reported by any previous work about SPDC in doubly resonant OPO systems. The reason could be attributed to the fact that, in the high nesse OPOs with bulk crystals reported in the literature, the thickness of the crystal is usually much smaller than the cavity length, making the eective dierence in the dispersion at the idler and signal wavelengths negligible.

We were interested in stabilizing the photon emission in the cluster at around 1560 nm.

However, the resonance turned out to be extremely sensitive to temperature uctuations: it could be totally lost with a change of temperature of around 0.07^◦C. For this reason a thermal stability of the order of10⁻³^◦Chas been guaranteed by locking the temperature with a side- of-fringe method, consisting of a P.I.D. regulation of the temperature using feedback directly from the detected signal.

2.4.2 Energy-time entangled states with highly coherent photons

Once the emission of photons at around 1560 nm is established, we use 10 pm lters to isolate a single frequency mode with 0.91 pm (117 MHz)-bandwidth. With a time correlation measurement by means of a time-to-digital converter (TDC), we have measured a coincidence peak showing a double exponential behaviour, typical of a doubly resonant OPO (Figure 2.1), from which the photons' coherence time of (2.7 ± 0.2) ns has been estimated. This value is

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Figure 2.1: Top: setup of the experiment. Bottom left: envelope of the unltered SPDC spectrum with diagram illustrating the origin of the clustering. Bottom right: coincidences peak versus the signal-idler delay.

almost an order of magnitude higher than previously reported sources in the telecom regime [54].

Since our source is pumped in a CW mode, it generates energy-time entanglement. Photon pairs are created at a random time within the coherence time of the pump τ_pump, but the dierence between the emission times of the photons of the same pair is dened inside the coherence time of the photons (τ_coh << τ_pump). In the frequency domain, the individual energy values of the down-converted photons are unknown, but their sum is well dened (within the bandwidth of the pump) by energy conservation.

Energy-time entangled photon pairs can be characterized by a Bell-type experiment in the conguration proposed by Franson [24] with two separated equally unbalanced Mach- Zehnder type interferometers. However, in our case, we send the two photons, which have similar wavelength around 1560 nm, to only one folded Franson interferometer [69], after which they are ltered and then detected. By post-selecting only the indistinguishable events where both the down-converted photons take the short or the long arm of the interferometer and scanning the temperature of the interferometer, we measure interference fringes in the coincidence count rate (Figure 2.2). Noticed that in the folded Franson interferometer, by changing the temperature, we vary the sum of the phases of both photons. The raw fringe visibility is (81.2 ± 5.5)%, sucient for violating the limit of ^√¹₂ given by Bell inequalities, and (94.4±5.8)%, if we subtract the accidental coincidences due to the noise of the detectors.

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2.4 An integrated cavity-waveguide source of entangled photon pairs

short long

1560 nm

short - long

short - short long - long

&

long - short

Figure 2.2: Top: folded Franson interferometer for the characterization of the energy-time entanglement. Top right: coincidences versus signal-idler delay after the interferometer. Bottom: coincidences in the selected window as a function of the time during which the temperature of the interferometer is scanned.

These results conrm the good quality of the energy-time entangled states generated by the source.

In order to better estimate the interference visibility, one should integrate the measurement longer at the dierent values of the phase. This requires to stabilize longer single values of the phase, limiting the uctuations in the path dierence of the interferometer, given essentially by environmental temperature changes. In our case, this is not trivial because the arms' dierence of our interferometer is large, therefore our measurement suers more thermal uctuations.

Moreover, in the folded Franson interferometer, by changing the temperature, we vary the sum of the phases on both photons, whereas with two Franson interferometers only one phase is scanned and the other one is kept constant. This implies that the interference change more quickly with respect to the usual case. A better isolation system and a more accurate temperature control could certainly help for the improvement of the visibility measurement.

Bringing entanglement to the real world: from fundamental aspects to applications in quantum communication and radiometry

Thesis

Reference

Bringing entanglement to the real world: from fundamental aspects to applications in quantum communication and radiometry

B RINGING E NTANGLEMENT

T O T HE R EAL W ORLD:

F

F

A

T

A

I

Q

C

A

R

Enrico Pomarico d'Italie

DE GENEVE ...

Doctorat ès sciences Mention physiq ue

Monsieur Enrico POMARICO

"Bringing Entanglement to the Real World

From Fundamental Aspects to Applications in Quantum Communication and Radiometry"

Thèse - 4392 ­

Preface

List of publications

Contents

Introduction

Resumé de la thèse

Chapter 1

Entanglement: a fundamental

phenomenon accessible to everyone

1.1 Entanglement and nonlocality: an ongoing debate

1.2 From theory to optics laboratories

1.3 From laboratories to everyone

1.4 Quantum nonlocality with a commercial entanglement source

Chapter 2

Entanglement: a technological resource

2.1 Towards a new quantum technological revolution

2.2 Quantum communication

2.3 SPDC sources of entanglement for quantum repeaters

2.4 An integrated cavity-waveguide source of entangled photon pairs

Thèse - 4392