Made available in DSpace on 2016-06-02T20:15:20Z (GMT). No. of bitstreams: 1 2679.pdf: 25013011 bytes, checksum: c8fa361775e24d238927a782402fff59 (MD5) Previous issue date: 2009-10-16 / Universidade Federal de Sao Carlos / In this thesis we studied the quantum effects in networks of Josephson junctions under the induction of vortices and as a consequence of the size of the sample itself. For this, it also was carried out all the instrumentation required to achieve that goal. The superconducting devices known as Josephson junctions offer the opportunity to study a wide variety of concepts of basic physics, especially when they are in the form of twodimensional arrays called networks. In particular, these structures allow us to study quantum phenomena such as tunneling Josephson dc / ac, proximity effect, Coulomb blockade, quantum fluctuations and others like phase transition of Berezinsky-Kosterlitz-Thouless (BKT), all present in these devices. In particular, in this thesis we study two-dimensional networks of Josephson junctions of types SNS (superconductor-normal-superconductor) and SIS (superconductor-insulatorsuperconductor) with composition Nb -CuxAlyOz-Nb. The study of these samples was performed by obtaining the characteristic curves V × I with and without applied magnetic field. The analysis of these curves was performed by the law of power scale: ��������������for the SNS network, and ������������������/�������� for the SIS networks. The fact th��at ��t��w��o types of formulas adjustment is due to the asymptotic behavior present in these samples. Moreover, the temperature of the BKT transition was determined for ��������������������3. The analysis of the experimental obtained results clearly shows the dependence of quantum effects on the size of the samples studied. / Neste trabalho de Tese foram estudados os efeitos quânticos em redes de junções Josephson decorrentes da indução de vórtices e como conseqüência do tamanho da própria amostra. Para isso, também fora desenvolvida toda a instrumentação associada necessária para alcançar esse objetivo. Os dispositivos supercondutores conhecidos como junções Josephson oferecem a oportunidade de estudar uma ampla variedade de conceitos de física básica, principalmente quando eles se encontram na forma de arranjos bidimensionais denominados de redes. Em particular, estas estruturas permitem estudar fenômenos quânticos tais como tunelamento Josephson dc/ac, efeito de proximidade, bloqueio de Coulomb, flutuações quânticas e outras como a transição de fase de Berezinsky-Kosterlitz-Thouless (BKT), todos eles presentes nestes dispositivos. Em particular, nesta Tese estudamos redes de junções Josephson bidimensionais dos tipos SNS (supercondutor-normal-supercondutor) e SIS (supercondutor-isolante-supercondutor) com composição Nb-CuxAlyOz-Nb. O estudo dessas amostras foi realizado através da obtenção das curvas características V×I com e sem campo magnético aplicado. A análise dessas curvas foi realizada mediante a lei de escalas de potencias: ������������������������ para as redes SNS, e ������������������/�������� para as redes SIS. O fato de ter dois tipos de fórmulas de ajuste é devido ao comportamento assintótico presente nessas amostras. Além disso, a temperatura de transição de BKT foi determinada para ��������������������3. A análise dos resultados experimentais obtidos mostra claramente a dependência desses efeitos quânticos com o tamanho das amostras estudadas.

Cette thèse présente le travail expérimental effectué pour observer la dynamique quantique de Zénon (QZD) dans une architecture 'circuit-QED' tridimentionnelle fonctionnant à très basse température. Dans cette architecture, un circuit supraconducteur de type transmon, jouant le rôle d'un atome artificiel, est couplé au champ électromagnétique d'une cavité microonde. Les niveaux d'énergie de l'atome et de la cavité sont alignés d'une nouvelle manière, afin de manipuler les états de Fock individuels de la cavité, tout en minimisant sa non-linearité Kerr induite par le transmon. La dynamique Zénon est obtenue en pilotant classiquement le champ de la cavité, tout en excitant fortement une transition inter-niveaux d'énergie du transmon, conditionnée à un état de Fock particulier. Ce forcage maintient la population de l'état de Fock à zéro, et conduit à la dynamique Zeno. Cette dynamique est observée par mesure de sa fonction de Wigner à intervalles de temps réguliers, soit par tomographie de Wigner, soit par tomographie quantique standard et reconstruction de la matrice densité. Nous observons trois exemples de QZD, et analysons la décohérence observée à l'aide simulations quantiques du système. / This thesis presents experimental work aimed at observing the quantum Zeno dynamics (QZD) in 3D circuit-QED, where an artificial atom, consisting of a superconducting circuit called a transmon, is coupled to the electric field of a microwave cavity resonator. The transmon and resonator energy levels are aligned in a novel way enabling the manipulation of individual Fock states of the cavity, while minimizing its transmon-induced Kerr non-linearity. We induce the QZD by displacing classically the cavity field while continuously driving strongly a transmon transition specific to a particular Fock state, which keeps this Fock state population at zero. The QZD is then observed by measuring the Wigner function of the fields at regular time intervals, either by Wigner tomography or standard quantum tomography and reconstruction of the density matrix. We observe three examples of QZD, and analyze the observed decoherence with the help of quantum simulations of the system.

No / Vortices circulating in a ring made from a Josephson array in the insulating phase are studied. The ring contains a `dual Josephson junction' through which the vortices tunnel. External non-classical microwaves are coupled to the device. The time evolution of this two-mode fully quantum mechanical system is studied, taking into account the dissipation in the system. The effect of the quantum statistics of the photons on the quantum statistics of the vortices is discussed. Entropic calculations quantify the entanglement between the two systems. Quantum phenomena in the system are also studied through Wigner functions. After a certain time (which depends on the dissipation parameters) these quantum phenomena are destroyed due to dissipation.

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This research investigates the realization of parametric amplification in superconducting circuits and structures where nonlinearity is provided by Josephson junction (JJ) elements. We aim to develop a systematic analysis over JJ-based devices toward design of novel traveling-wave Josephson parametric amplifiers (TW-JPA). Chapters of this thesis fall into three categories: lumped JPA, superconducting periodic structures and discrete Josephson transmission lines (DJTL). The unbiased Josephson junction (JJ) is a nonlinear element suitable for parametric amplification through a four-photon process. Two circuit topologies are introduced to capture the unique property of the JJ in order to efficiently mix signal, pump and idler signals for the purpose of signal amplification. Closed-form expressions are derived for gain characteristics, bandwidth determination, noise properties and impedance for this kind of parametric power amplifier. The concept of negative resistance in the gain formulation is observed. A design process is also introduced to find the regimes of operation for gain achievement. Two regimes of operation, oscillation and amplification, are highlighted and distinguished in the result section. Optimization of the circuits to enhance the bandwidth is also carried out. Moving toward TW-JPA, the second part is devoted to modelling the linear wave propagation in a periodic superconducting structure. We derive closed-form equations for dispersion and s-parameters of infinite and finite periodic structures, respectively. Band gap formation is highlighted and its potential applications in the design of passive filters and resonators are discussed. The superconducting structures are fabricated using YBCO and measured, illustrating a good correlation with the numerical results. A novel superconducting Transmission Line (TL), which is periodically loaded by Josephson junctions (JJ) and assisted by open stubs, is proposed as a platform to realize a traveling-wave parametric device. Using the TL model, this structure is modeled by a system of nonlinear partial differential equations (PDE) with a driving source and mixed-boundary conditions at the input and output terminals, respectively. This model successfully emulates parametric and nonlinear microwave propagation when long-wave approximation is applicable. The influence of dispersion to sustain three non-degenerate phased-locked waves through the TL is highlighted. A rigorous and robust Finite Difference Time Domain (FDTD) solver based on the explicit Lax-Wendroff and implicit Crank-Nicolson schemes has been developed to investigate the device responses under various excitations. Linearization of the wave equation, under small-amplitude assumption, dispersion and impedance analysis is performed to explore more aspects of the device for the purpose of efficient design of a traveling-wave parametric amplifier. Knowing all microwave characteristics and identifying different regimes of operation, which include impedance properties, cut-off propagation, dispersive behaviour and shock-wave formation, we exploit perturbation theory accompanied by the method of multiple scale to derive the three nonlinear coupled amplitude equations to describe the parametric interaction. A graphical technique is suggested to find three waves on the dispersion diagram satisfying the phase-matching conditions. Both cases of perfect phase-matching and slight mismatching are addressed in this work. The incorporation of two numerical techniques, spectral method in space and multistep Adams-Bashforth in time domain, is employed to monitor the unilateral gain, superior stability and bandwidth of this structure. Two types of functionality, mixing and amplification, with their requirements are described. These properties make this structure desirable for applications ranging from superconducting optoelectronics to dispersive readout of superconducting qubits where high sensitivity and ultra-low noise operation is required.

Thesis (PhD (Electrical and Electronic Engineering))--University of Stellenbosch, 2010. / Dissertation presented for the degree of Doctor of Philosophy in Engineering at the University of Stellenbosch / ENGLISH ABSTRACT: Planar weak link structures, such as micro-bridges, variable thickness bridges and nanobridges, have always attracted a lot of attention. Their potential to behave as real Josephson elements make them useful devices, with numerous applications. Powerful techniques, such as focused ion-beam and electron-beam lithography, were successfully used and are well understood in planar weak link structure fabrication. In this dissertation the results of an experimental study on planar weak link structures are presented. For the first time these structures have been successfully fabricated using AFM nanolithography on hard high-temperature superconducting YBCO tracks, where diamond coated silicon tips were used as a ploughing tool. Superconducting YBCO thin films were deposited on different substrates, using inverted cylindrical magnetron sputtering. The films were used to fabricate micro-bridges, variable thickness bridges and nano-bridges, by using conventional photolithography, argon ion-beam milling and AFM nanolithography. The measured I-V characteristics of the fabricated micro-bridges (width down to 1.9 µm), variable thickness bridges (thickness down to 15 nm) and nano-bridge (width down to 490 nm) showed well defined DC and AC Josephson effect characteristics. For better understanding of the behaviour of these types of weak links, critical current versus temperature measurements, and magnetic field modulation of the critical current measurements, were also performed, with the results and discussions given inside the chapters. The major challenges that were experienced in the laboratory during the fabrication processes and the operation of the fabricated devices are also discussed, with the solutions given where appropriate. / AFRIKAANSE OPSOMMING: Swak-skakel vlakstrukture, soos mikrobr.ue, br.ue met veranderlike dikte en nanobr.ue, het nog altyd baie aandag getrek. Hul het die potensiaal om soos werklike Josephson-elemente te kan funksioneer en is, as gevolg hiervan, nuttige toestelle met veelvuldige toepassings. Kragtige tegnieke, soos gefokuste ioonstraal- en elektronstraal litografie, is suksesvol gebruik en word goed verstaan in die vervaardiging van swak-skakel vlakstrukture. In hierdie proefskrif word die resultate van ¡¦n eksperimentele studie van swak-skakel vlakstrukture voorgel.e. Vir die eerste keer is hierdie strukture suksesvol vervaardig, deur gebruik te maak AFMnanolitografie op harde, ho¡Le-temperatuur supergeleier YBCO (Yttrium Barium Koperoksied) spore, waar diamantbedekte silikonpunte gebruik is as ploeginstrument. ¡¦n Dun lagie van supergeleidende YBCO is op verskillende substrate gedeponeer, deur gebruik te maak van omgekeerde silindriese magnetron verstuiwing. Die dun lagies is gebruik in die vervaardiging van mikrobr.ue, br.ue met veranderlike dikte en nanobr.ue, deur die gebruik van gewone fotolitografie, argon-ioonstraal frees en AFM nanolitografie. Die gemete I-V eienskappe van die vervaardigde mikrobr.ue (met breedte so laag as 1.9 µm), veranderlike-dikte br.ue (dikte tot 15 nm) en nanobr.ue (breedte so min as 490 nm) toon goed gedefinieerde GS en WS eienskappe van die Josephson-effek. Ten einde die gedrag van hierdie tipes swak-skakels beter te kan verstaan, is metings gedoen van kritieke stroom teenoor temperatuur, asook magnetiese veld modulasie van die kritieke stroom. Hierdie resultate en besprekings daarvan word binne die toepaslike hoofstukke aangebied. Die grootste uitdagings wat in die laboratorium, sowel as met die toetsing van die vervaardigde toestelle ondervind is, word ook bespreek. Waar moontlik, word toepaslike oplossings voorgestel.

<p>Ispitivan je generalisani Frenkel-Kontorova model pod&nbsp;dejstvom spolja&scaron;njih periodičnih sila,&nbsp;i njihov uticaj na &Scaron;apiro stepenike.&nbsp;Deformacija substratnog potencijala prouzrokuje&nbsp;pojavu velikih polucelih i drugih subharmonijskih&nbsp;stepenika u sistemu.&nbsp;Rezultati dobijeni u radu su od značaja&nbsp;u talasima i spinovima gustine naboja&nbsp;kao i u Džozefsonovim spojevima.</p> / <p>Properties of the Shapiro steps in dierent<br />commensurate structures of the ac + dc driven<br />Frenkel-Kontorova model with dierent generalized<br />substrate potential have been examined.<br />Deviation from the sinusoidal potential produces<br />appearance of large subharmonic steps.<br />Presented results could be of great importance<br />for thestudies of all real systems closely related<br />to the dissipative dynamics of the FK model<br />such as studies of the charge- or spin-density wave<br />systems and the systems of Josephson-junction arrays.</p>

This thesis presents a theoretical study of Bose-Einstein condensates in a doublering trap. In particular, we determine the ground states of the condensate in the double-ring trap that arise from the interplay of quantum tunnelling and the trap’s rotation. The trap geometry is a concentric ring system, where the inner ring is of smaller radius than the outer ring and both lie in the same two-dimensional plane. Due to the difference in radii between the inner and outer rings, the angular momentum that minimises the kinetic energy of a condensate when confined in the individual rings is different at most frequencies. This preference is in direct competition with the tunnel coupling of the rings which favours the same angular momentum states being occupied in both rings. Our calculations show that at low tunnel coupling ground state solutions exist where the expectation value of angular momentum per atom in each ring differs by approximately an integer multiple. The energy of these solutions is minimised by maintaining a uniform phase difference around most of the ring, and introducing a Josephson vortex between the inner and outer rings. A Josephson vortex is identified by a 2p step in the relative phase between the two rings, and accounts for one quantum of circulation. We discuss similarities and differences between Josephson vortices in cold-atom systems and in superconducting Josephson junctions. Josephson vortices are actuated by a sudden change in the trapping potential. After this change Josephson vortices rotate around the double-ring system at a different frequency to the rotation of the double-ring potential. Numerical studies of the dependence of the velocity on the ground state tunnel coupling and interaction strength are presented. An analytical theory of the Josephson vortex dynamics is also presented which is consistent with our numerical results.

Grâce aux avancées techniques récentes, les physiciens jouent pleinement avec la beauté de la mécanique quantique. Dans ce travail de théorie sur l'effet Josephson mésoscopique, nous exploitons les collaborations avec les expérimentateurs ainsi que les échanges entre les communautés des atomes froids et de la matière condensée. Nous considérons différents systèmes basés sur la jonction Josephson, en commençant par sa description quantique dans le régime sous-amorti. En utilisant le formalisme de Keldysh, nous obtenons les caractéristiques courant-tension du régime classique à la limite de température nulle et l'équation de Smoluchowski quantique dans la limite semi-classique. Nous étudions ensuite la dynamique quantique d'un qubit de phase réalisé avec un SQUID dans une configuration inédite où l'échappement se produit à travers deux barrières quartiques. Le taux d'échappement tunnel dans ce nouveau potentiel, calculé avec la technique des instantons, nous permet de décrire les expériences. L'électrodynamique quantique des circuits prévoit qu'un effet laser apparaît lorsqu'un qubit est couplé à une cavité résonnante. Nous considérons le cas d'un qubit de charge et celui d'un transmon qui exploite l'effet Purcell. Avec le Lindbladien nous obtenons la matrice densité dont nous dérivons le spectre du champ créé. Enfin, nous étudions un gaz d'atomes froids dans un piège circulaire comportant une barrière, créant une jonction de Bose Josephson. La physique à basse énergie est décrite à travers les fonctions de corrélation avec la théorie du liquide de Luttinger. Nous montrons que les fluctuations quantiques dans l'anneau induisent une renormalisation de l'énergie Josephson.