The symplectic formalism applied to the phase-space representation of bosonic quantum systems provides us with a powerful mathematical tool for the characterisation of Gaussian states and transformations. As a consequence, quantum information protocols involving the latter are very well understood from a theoretical point of view. Nevertheless, it has become clear in recent years that the use of non-Gaussian resources is necessary in order to perform various crucial information-processing tasks. An illustration of this fact can for instance be found in situations where a Gaussian no-go theorem precludes the use of Gaussian transformations in order to achieve a task involving Gaussian states, such as quantum entanglement distillation, quantum error correction, or universal quantum computation. In the first part of this thesis, we develop a new method based on the generating function of a sequence, which gives rise to an elegant description of intrinsically non-Gaussian objects. Building on the generating function of the matrix elements of Gaussian unitaries in Fock basis, our approach gives access to the multi-photon transition probabilities via unexpectedly simple recurrence equations. The method is developed for Gaussian unitaries effecting both passive and active linear coupling between two bosonic modes. It predicts an interferometric suppression term which generalises the Hong-Ou-Mandel effect for more than two indistinguishable photons impinging on a balanced beam splitter. Furthermore, it exhibits an unsuspected 2-photon suppression effect in optical parametric amplification of gain 2, which originates from the indistinguishability between the input and output photon pairs. Finally, we extend our method to Bogoliubov transformations acting on an arbitrary number of modes. In the second part of this thesis, we introduce a class of Gaussian-dilatable bosonic quantum channels (characterised by a Gaussian unitary in their Stinespring dilation) called passive-environment channels. These channels are interesting from a quantum thermodynamical viewpoint because they correspond to the coupling of a bosonic system with a bosonic environment that is passive in the Fock-basis (that is, no energy can be extracted from it by using unitary transformations) followed by discarding the environment. Making use of the generating function, we provide a description of these channels in terms of Gaussian bosonic channels. We then introduce a new preorder relation called Fock-majorization, which coincides with regular majorization for passive states but also induces another relation in terms of mean boson number, thereby connecting the concepts of energy and disorder of a quantum state. We prove various properties of Fock-majorization, showing in particular that the latter can be interpreted as a relation indicating the existence of a heating or amplifying map between two quantum states. This new preorder relation happens to be relevant in the context of passive-environment bosonic channels. Indeed, we show that these channels are Fock-majorization-preserving, so that any two input states that obey a Fock-majorization relation are transformed into output states respecting a similar relation. As a consequence, it also implies that passive-environment channels are majorization-preserving over the set of passive states of the harmonic oscillator. The consequences of majorization preservation are discussed in the context of the so-called entropy photon-number inequality. Most of our results being independent of the specific nature of the system under investigation, they could be generalised to other quantum systems and Hamiltonians, providing new tools that may prove useful in quantum information theory. In the last part of our thesis, we lay out a resource theory of local activity for bosonic systems. We introduce a notion of local-activity distance, and compare it with the work that can be extracted from a quantum state under local unitaries assisted by passive global unitaries. With this framework, we hope to connect the area of continuous-variable bosonic channels together with quantum thermodynamics. / Le formalisme symplectique appliqué à la représentation des systèmes bosoniques dans l'espace des phases donne accès à un outil mathématique puissant pour la caractérisation des états gau-ssiens et transformations gaussiennes. Les protocoles d'information quantique impliquant ces derniers sont d'ailleurs très bien compris d'un point de vue théorique. Toutefois, il s'est avéré clair durant ces dernières années que l'utilisation de ressources non-gaussiennes est nécessaire afin d'effectuer des tâches cruciales de traitement de l'information. En effet, certaines tâches — telles que la distillation d’intrication quantique, le codage quantique ou encore le calcul quantique — impliquant des états gaussiens ne peuvent être effectuées avec des transformations gaussiennes. Dans la première partie de cette thèse, nous développons une nouvelle méthode basée sur la fonction génératrice d'une suite qui donne lieu à une description élégante d'objets intrinsèquement non-gaussiens. Se basant sur la fonction génératrice des éléments de matrice d'unitaires gaussiens dans la base de Fock, notre approche donne accès aux probabilités de transition multi-photon via des équations de récurrence étonnamment simples. La méthode est développée pour des unitaires gaussiens produisant des couplages linéaires passifs et actifs entres deux modes bosoniques. Elle prédit un terme d'interférence destructive qui généralise l'effet Hong-Ou-Mandel pour plus de deux photons indistinguables pénétrant dans un diviseur de faisceau équilibré. De plus, elle met en évidence un effet inattendu de suppression de deux photons dans un amplificateur paramétrique optique de gain 2. Cette suppression résulte de l’indistinguabilité entre les paires de photons d’entrée et de sortie. Finalement, nous étendons notre méthode à des transformations de Bogoliubov agissant sur un nombre de modes arbitraire. Dans la seconde partie de cette thèse, nous introduisons une classe de canaux quantiques bosoniques gaussiens-dilatables (caractérisés par un unitaire gaussien dans leur ``Stinespring dilation") appelés canaux à environnement passif. Ces canaux sont intéressants du point de vue de la thermodynamique quantique puisqu’ils correspondent au couplage d’un système bosonique avec un environnement bosonique qui est passif dans la base de Fock (en d’autres termes, il est impossible d’en extraire de l’énergie avec des transformations unitaires), suivi du rejet de l’environnement. Grâce à la fonction génératrice, nous fournissons une description de ces transformations en termes de canaux quantiques bosoniques gaussiens limités par le bruit du vide. Nous introduisons ensuite une nouvelle relation de pré-ordre appelé ``majorization" de Fock, qui coïncide avec la ``majorization" usuelle pour les états passifs mais induit une autre relation en terme du nombre moyen de bosons, connectant ainsi les concepts d’énergie et de désordre d’un état quantique. Dans ce contexte, nous prouvons des propriétés variées de la ``majorization" de Fock et montrons en particulier que cette dernière peut être interprétée comme une relation indiquant l’existence d’une transformation d’amplification entre deux états quantiques. Cette nouvelle relation de pré-ordre s’avère appropriée dans le contexte des canaux bosonique à environnement passif. En effet, nous montrons que ces canaux conservent la ``majorization" de Fock, de sorte que n’importe quels deux états d’entrée obéissant une relation de ``majorization" de Fock sont transformés en états de sortie vérifiant une relation similaire. En particulier, cela implique que les canaux à environnement passif préservent la ``majorization" pour l'ensemble des états passifs de l’oscillateur harmonique. Les conséquences de la préservation de la ``majorization" sont examinées dans le contexte de la ``entropy photon-number inequality". Étant indépendants de la nature spécifique du système étudié, la plupart de nos résultats peuvent être généralisés à d’autres systèmes et hamiltoniens quantiques, donnant lieu à de nouveaux outils qui pourraient s’avérer utiles en théorie de l’information quantique. Dans la dernière partie de notre thèse, nous mettons en place une théorie de l’activité locale pour les système bosoniques. Nous introduisons une notion de distance en terme d'activité locale et la comparons avec le travail qui peut être extrait d'un état quantique avec des unitaires locaux assistés par des unitaires globaux passifs. Le but à long terme est de se baser sur cette théorie afin de connecter les domaines des canaux bosoniques à variables continues et de la thermodynamique quantique. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Submitted by Isaac Francisco de Souza Dias (isaac.souzadias@ufpe.br) on 2016-03-02T19:08:33Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese José Ferraz.pdf: 2743054 bytes, checksum: 9154337dac4a587934aab71697b77a90 (MD5) / Made available in DSpace on 2016-03-02T19:08:33Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese José Ferraz.pdf: 2743054 bytes, checksum: 9154337dac4a587934aab71697b77a90 (MD5) Previous issue date: 2008-05-29 / CNPQ / Neste trabalho, utilizamos as técnicas de controle temporal coerente e de manipulação da fase óptica do campo óptico para investigar e controlar os diferentes caminhos quânticos induzidos em transições de dipolo elétrico envolvendo a absorção de dois fótons no átomo de rubídio. As transições foram excitadas por pares de pulsos de separação temporal variável e analisamos a resposta do meio atômico em função dessa separação. Três situações experimentais são analisadas envolvendo transições com diferentes características. No primeiro experimento, utilizamos luz incoerente de um laser de corante com duração temporal de nanosegundos, mas com tempo de coerência de picosegundos, para excitar a transição de dois fótons, envolvendo níveis altamente excitados, níveis de Rydberg. A resposta do sistema é analisada através de um processo de mistura de quatro ondas, resolvida no tempo, e a seleção dos diferentes caminhos quânticos envolvidos no processo é feita a partir do controle da polarização dos campos do laser incidente. Interferências na freqüência central do laser, interferências "ópticas", e no dobro dessa freqüência, interferências quânticas, são observadas. Nos outros dois estudos, a transição de dois fótons é excitada por pulsos com duração temporal da ordemde 100 fentosegundos. No primeiro caso, investigamos uma transição de dois fótons pura, entre os níveis 5S e 7S do rubídio, onde uma fase externa, dependente da freqüência, é adicionada em um dos pulsos, enquanto o outro tem seu atraso temporal controlado. A fluorescência detectada é uma medida direta da população do estado excitado. Novamente, um sinal interferométrico é observado, cujo controle coerente é efetuado por uma combinação da fase externa e do atraso temporal. O último experimento envolve uma transição seqüencial, cuja ressonância de um fóton leva a efeitos de propagação observados no sinal de interesse. Outro aspecto importante é que a taxa de repetição do laser era maior que as taxas de relaxação dos níveis envolvidos, de forma que efeitos de acumulação na população e na coerência também estão presentes. A resposta do sistema é analisada através do processo de mistura paramétrica de quatro ondas, resolvido no tempo. O sinal interferométrico, com controle de polarização e da freqüência de detecção, permite uma demonstração clara da origem quântica nas interferências "ópticas". / In this work, we use the techniques of temporal coherent control and phase manipulation of the optical field to investigate and control different quantum pathways in the two-photon absorption in rubidium atoms. Three experimental situations are studied involving transitions with different characteristics. In all of them, the medium response is analyzed as a function of the temporal delay between the pulse pairs responsible for the two-photon transition. In the first experiment, we use incoherent light from a dye laser with pulse duration in the nanosecond scale, but with coherence time in the picosecond scale, to excite the two-photon transition, which involves highly excited levels, Rydberg states. The system response is analyzed through a time-resolved four-wave mixing process, and the quantum pathway selection is realized by polarization control of the incident laser fileds. Interferences in the central laser frequency - "optical" interferences - and at twice this frequency - quantum interferences - are observed. In the subsequent two studies, the two-photon transition is excited with 100 fs pulses. In the first case, we investigate a pure two-photon transition, the 5S - 7S rubidium transition, where an external frequency depedent phase is added in one pulse, while the temporal delay of a second pulse is controlled. We observe an interferometric signal, in which coherent control is achieved with external phase and temporal delay combination. The last experiment involves a sequential transition, which has a one-photon resonance that leads to propagation effects observed in the signal. The laser repetition rate is greater than the atomic system relaxation rates, leading to accumulation effects in the population and coherence, which leads to important effects. A time-resolved parametric four-wave mixing is used to investigate the system response. The interferometric signal, with polarization and detection frequency control, allows us to clearly demonstrate the quantum origin of the "optical" interferences.

Ce manuscrit de thèse s’intéresse à l’étude théorique et à l’observation d’effets quantiques résultantde la manipulation de photons en fréquence. Ainsi nous rapportons une expérience d’interférenceà deux photons, pour laquelle l’intrication et la manipulation des photons survient dans le domainedes fréquences. Nous montrons que cette figure d’interférence est sensible à la dispersion des deuxphotons jumeaux et que ce phénomène peut être compensé de manière non-locale. D’un autre coté,nous étudions la réalisation d’une marche aléatoire quantique établie par la modulation de phase.Nous mettons en évidence un comportement intéressant de ces marches et suggérons un schémaexpérimental. / This manuscript deals with a theoretical and experimental study of quantum effects taking place inthe frequency domain. On one side, we report a two photons interference experiment, where both theentanglement of the photons and their manipulation take place in the frequency domain. We showthat this interference pattern is sensitive to the dispersion of both photons and allows us to perform anonlocal dispersion cancellation. On the other side we study the implementation of a quantum walkbased on the phase modulation. We predict an interesting behavior of these quantum walks andsuggest a physical implementation.