Στην παρούσα εργασία μελετάμε τη λειτουργία των διαχωριστών δέσμης, καθώς και τη στατιστική κατανομή ενός και δύο σωματιδίων σε απλό και διπλό πηγάδι δυναμικού. Εξετάζουμε υπό ποιες συνθήκες τα δύο αυτά συστήματα μας δίνουν σύμπλεκτες καταστάσεις. Για τους διαχωριστές δέσμης καταλήγουμε στο συμπέρασμα ότι η καταλληλότερη διάταξή τους για να έχουμε μέγιστη απόδοση σύμπλεκτων καταστάσεων, είναι αυτοί να βρίσκονται σε διαδοχική σειρά μεταξύ τους. Από την άλλη μεριά, η μελέτη πηγαδιών δυναμικού, που έγινε γραφικά και αριθμητικά, μας έδειξε ότι τα γεωμετρικά χαρακτηριστικά τού κάθε πηγαδιού, δηλαδή το πάχος και το ύψος του, καθορίζουν τις ιδιοενέργειες τού συστήματος, τις πυκνότητες πιθανότητας των κυματοπακέτων και τελικά την πιθανότητα δημιουργίας σύμπλεκτων καταστάσεων. Γνωρίζοντας τη στατιστική κατανομή των σωματιδίων, ελέγχουμε τη συμπεριφορά τους άρα και την πληροφορία που αυτά μεταφέρουν. Τα παραπάνω βρίσκουν εφαρμογή στα qubits και τους κβαντικούς υπολογιστές. / In the current project we study the function of the beam splitters as well as the statistical behavior of one and two particles in a single and a double quantum well. We examine the conditions under which these two systems provide us with entangled states. For the beam splitters we come to the conclusion that the most appropriate array for having entangled states, is to put them in successive line. On the other hand, the graphical and numerical study of the quantum wells showed that the geometrical characteristics of a quantum well, that is to say thickness and height, define the energy of the system, the density probability of the wave packets and finally the probability for having entangled states. Having knowledge of the statistical behavior of the particles, we may then control the informations that they carry. All the above have many applications in qubits and quantum computers.

Estudamos o emaranhamento quântico de estados puros emaranhados tri-partidos quando uma das partes é um qubit. Apresentamos um método para encontrar as decomposições do estado tri-partido mais simples do que sucessivas decomposições de Schmidt. Esse método permite encontrar uma grande quantidade de diferentes famílias de estados emaranhados tri-partidos. Essas famílias são classificadas de acordo com dimensão dos blocos de Jordan de uma matriz obtida do estado emaranhado. Além disso, também demonstramos que estados pertencentes a famílias distintas não podem ser convertidos um no outro por operações locais estocásticas com comunicação clássica (SLOCC). No caso de dois estados pertencentes à mesma família, obtemos condições necessárias e su cientes para sabermos se estes podem ser convertidos um no outro por SLOCC. No caso de serão, também podemos obter a operação do tipo SLOCC que realiza a conversão. / We study the quantum entanglement of tripartite pure states when one of the parties is a qubit. We present a method to find the decompositions of tripartite entangled states which are simpler than two successive Schmidt decompositions. We will find many distinct families of entangled states with distinct decompositions. These families are classified according to the dimensions of the Jordan blocks of a matrix obtained from the entangled state. Furthermore, we show that states belonging to distinct families can not be converted into each other by stochastic local operations and classical communication (SLOCC). In case of two states belonging to the same family, we nd necessary and su?cient conditions to convert one state to the other. We can also find the SLOCC which realizes this conversion.

In this thesis, we demonstrate the creation and characterization of multiparticle entangled states of neutral atoms with the help of a high finesse cavity. Our experimental setup consists of a fibre-based high finesse cavity above the surface of an atom chip. It allows us to prepare an ensemble of 87Rb atoms with well-defined atom number. The atoms are trapped in a single antinode of an intracavity standing wave dipole trap and are therefore all equally coupled to the cavity mode. We present a scheme based on a collective, quantum non-destructive (QND) measurement and conditional evolution to create symmetric entangled states and to analyze them at the single-particle level by directly measuring their Husimi Q function. We use this method to create and characterize W states of up to 41 atoms. From the tomography curve of the Q function, we reconstruct the symmetric part of the density matrix via different reconstruction techniques and obtain a fidelity of 0.42. Furthermore, we have devised an entanglement criterion which only relies on comparing two populations of the density matrix. We use it to infer the degree of multiparticle entanglement in our experimentally created states and find that the state with highest fidelity contains at least 13 entangled particles. In addition, we show preliminary results on experiments to count the atom number inside a cavity in the QND regime and to create entangled states via quantum Zeno dynamics.

Estudamos o emaranhamento quântico de estados puros emaranhados tri-partidos quando uma das partes é um qubit. Apresentamos um método para encontrar as decomposições do estado tri-partido mais simples do que sucessivas decomposições de Schmidt. Esse método permite encontrar uma grande quantidade de diferentes famílias de estados emaranhados tri-partidos. Essas famílias são classificadas de acordo com dimensão dos blocos de Jordan de uma matriz obtida do estado emaranhado. Além disso, também demonstramos que estados pertencentes a famílias distintas não podem ser convertidos um no outro por operações locais estocásticas com comunicação clássica (SLOCC). No caso de dois estados pertencentes à mesma família, obtemos condições necessárias e su cientes para sabermos se estes podem ser convertidos um no outro por SLOCC. No caso de serão, também podemos obter a operação do tipo SLOCC que realiza a conversão. / We study the quantum entanglement of tripartite pure states when one of the parties is a qubit. We present a method to find the decompositions of tripartite entangled states which are simpler than two successive Schmidt decompositions. We will find many distinct families of entangled states with distinct decompositions. These families are classified according to the dimensions of the Jordan blocks of a matrix obtained from the entangled state. Furthermore, we show that states belonging to distinct families can not be converted into each other by stochastic local operations and classical communication (SLOCC). In case of two states belonging to the same family, we nd necessary and su?cient conditions to convert one state to the other. We can also find the SLOCC which realizes this conversion.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2017-02-13T13:44:40Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertação final.pdf: 3576056 bytes, checksum: 4650485627f1eb13bb131bcbf6ab588a (MD5) / Made available in DSpace on 2017-02-13T13:44:40Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertação final.pdf: 3576056 bytes, checksum: 4650485627f1eb13bb131bcbf6ab588a (MD5) Previous issue date: 2014-03-28 / CAPES / A criação de estados emaranhados em polarização permite testar experimentalmente questões fundamentais da mecânica quântica, tais como os argumentos de EPR sobre a incompletezadateoriaquântica,atravésdadesigualdadeCHSH.Alémdisso,essesestados emaranhados, têm potenciais de aplicações como, por exemplo, em computação quântica e criptografia quântica. Neste trabalho, se estuda uma fonte muito eficiente para a produção de estados de fótons emaranhados em polarização baseada em um interferômetro de tipo Sagnac. Estes fótons correlacionados são criados em um cristal não linear PPKTP mediante o processo de conversão paramétrica descendente (PDC) tipo-II, quando o cristal é bombeado por pulsos de fentossegundos. Verificando as correlações das medidas de polarização produzidas por esta fonte, observamos fortes violações das desigualdades de Bell para estados de polarização, isto é, verificamos a desigualdade CHSH. / Creation of polarization entangled states allows experimentally to test fundamental properties of quantum mechanics, such as the EPR argument about the incompleteness of the quantum theory, through CHSH inequality; in addition to potential applications as in quantum computing and quantum cryptography. This work studies a very efficient sourceofphotonentangledstatesofpolarizationbasedonaSagnacinterferometer. These photons are created from a nonlinear PPKTP crystal pumped by fentosecond pulses by theprocessofparametricdown-conversion(PDC)type-IIpumpedbyfemtosecondpulses. Analysing correlations of polarization measurements produced by this source we observed strong violations of Bell inequalities for the polarization states, i.e, CHSH inequality.

Dans cette thèse, nous démontrons la création et la caractérisation d'états intriqués dans un ensemble atomique à l'aide d'un résonateur optique de haute finesse. Notre dis- positif expérimental consiste en une cavité fibrée placée en dessous d'une puce à atomes. Les atomes sont tous piégés dans un seul ventre du piège dipolaire créé dans la cavité. Ainsi, ils sont également couplés au mode lumineux de la cavité. Nous présentons une méthode basée sur une mesure collective et non-destructive et une évolution conditionnelle qui sert à créer des états intriqués et symétriques puis à les analyser, avec la résolution d'une particule unique, en mesurant d'une manière directe leur fonction Husimi Q. En utilisant cette méthode, nous créons et caractérisons des états W contenant jusqu'à 41 atomes. Nous reconstituons la partie symétrique de la matrice densité à partir des données expérimentales de la fonction Husimi Q en utilisant différentes méthodes de reconstruction quantique et nous obtenons une fidélité de 0.42. Par ailleurs, nous avons établi un critère d'intrication qui consiste à comparer seulement deux populations de la matrice densité. Nous l'utilisons pour déterminer le degré d'intrication présent dans les états expérimentalement créés et nous trouvons que l'état de fidélité maximale contient au moins 13 particules intriquées. Pour finir, nous présentons des résultats préliminaires concernant des expériences de dénombrement d'atomes dans la cavité en régime de mesures non-destructives ainsi que des expériences de création d'états intriqués en se servant de la dynamique Zénon quantique. / In this thesis, we demonstrate the creation and characterization of multiparticle entangled states of neutral atoms with the help of a high finesse cavity. Our experimental setup consists of a fibre-based high finesse cavity above the surface of an atom chip. It allows us to prepare an ensemble of 87Rb atoms with well-defined atom number. The atoms are trapped in a single antinode of an intracavity standing wave dipole trap and are therefore all equally coupled to the cavity mode. We present a scheme based on a collective, quantum non-destructive (QND) measurement and conditional evolution to create symmetric entangled states and to analyze them at the single-particle level by directly measuring their Husimi Q function. We use this method to create and characterize W states of up to 41 atoms. From the tomography curve of the Q function, we reconstruct the symmetric part of the density matrix via different reconstruction techniques and obtain a fidelity of 0.42. Furthermore, we have devised an entanglement criterion which only relies on comparing two populations of the density matrix. We use it to infer the degree of multiparticle entanglement in our experimentally created states and find that the state with highest fidelity contains at least 13 entangled particles. In addition, we show preliminary results on experiments to count the atom number inside a cavity in the QND regime and to create entangled states via quantum Zeno dynamics.

Made available in DSpace on 2016-06-02T20:15:31Z (GMT). No. of bitstreams: 1 5792.pdf: 2150785 bytes, checksum: 967083b129be653705657afbcab00714 (MD5) Previous issue date: 2014-02-27 / Universidade Federal de Sao Carlos / This thesis consists of three studies in the context of cavity quantum electrodynam- ics. Firstly, we investigate the quantum-to-classical transition of a dissipative cavity .eld by measuring the correlations between two non-interacting atoms coupled to the cavity mode. We note that there is a time window in which the mode presents a classical be- havior, which depends on the cavity decay rate, the atom-.eld coupling strength and the number of atoms. Then, considering the steady state of two atoms inside the cavity, we note that the entanglement between the atoms disappears while the intracavity mean number of photons (ñ) increases. However, the mutual information, the classical corre- lations and the quantum discord reach asymptotic non-zero values even in the limit of (continue...) / Esta tese é constituída por três estudos no contexto de Eletrodinâmica Quântica de Cavidades. Primeiramente, investigamos a transição quântico-clássica de um campo de uma cavidade dissipativa através da geração de correlação entre dois átomos de dois níveis não interagentes acoplados a um modo da cavidade. Em primeiro lugar, mostramos que há uma janela de tempo na qual o modo da cavidade exibe um comportamento clássico, que depende da taxa de decaimento da cavidade, do acoplamento átomo-campo e do número de átomos. Em seguida, considerando o regime estacionário, vemos que o emaranhamento entre os átomos desaparece à medida que o número médio de fótons intracavidade (ñ) é aumentado. Entretanto, a informação mútua, as correlações clássicas e a discórdia quântica atingem valores assintóticos não nulos mesmo no limite (continua...)