O presente trabalho apresenta o estudo das propriedades da condensação de Bose-Einstein e da superfluidez em um sistema bosônico disposto em um arranjo unidimensional de potenciais periódicos em formato de anel. O Hamiltoniano efetivo usual em termos dos operadores de campo é implementado na representação construída em termos das funções de Bloch da primeira banda e o problema é resolvido por meio da sua diagonalização através de métodos numéricos. No limite de hopping pequeno, este modelo é essencialmente equivalente à representação usual do modelo de Bose-Hubbard, mas incorpora efeitos adicionais através das energias de Bloch de partícula independente e dos elementos da matriz de dois corpos na situação em que o hopping é grande [19]. Através da inclusão de rotação no sistema, as energias de partícula independente são forçadas a depender da velocidade angular. Isto implica, correspondentemente, uma dependência da velocidade angular nas funções de onda de partícula independente e nos resultados de muitos corpos obtidos através da diagonalização do Hamiltoniano. Com o objetivo de estudar a superfluidez, o critério de dois fluidos é empregado e através de resultados numéricos obtêm-se a variação da fração de superfluido com o quadrado da velocidade angular. Ainda, considera-se aqui uma expressão perturbativa para o parâmetro inercial do sistema expresso em termos das excitações do sistema sem rotação, o que permite relacionar as energias do sistema com rotação com aquelas do sistema sem rotação. Isto é particularmente interessante para obter a fração de superfluido em termos da informação espectral do sistema sem rotação. Resultados semelhantes podem ser encontrados através da definição de superfluido baseada na resposta do sistema a uma variação de fase, imposta através de condições de contorno torcidas [30, 33], mas com a diferença de que os desenvolvimentos aqui não fazem uso da hipótese do modo condensado. De maneira geral, os resultados numéricos obtidos indicam, que pelo menos para este sistema, as frações de superfluido e condensado são quantidades sem relação direta, sugerindo então que mesmo para sistemas gasosos diluídos a idéia de que a superfluidez é uma consequência da condensação de Bose-Einstein deve ser considerada com mais cuidado. / In this work we study the properties of Bose-Einstein condensation and superfluidity in a finite bosonic system in a 1-dimensional ring with a periodic potential under rotation. The usual field effective Hamiltonian is implemented in a representation constructed in terms of the first band Bloch functions and the problem is solved by numeric diagonalization. In the limit of small hopping, this model is essentially equivalent to the quasi-momentum representation of the usual Bose-Hubbard model but incorporates additional effects via Bloch single particle energies and two-body matrix elements in the case of large hopping [19]. By including rotation in the system we force the single particle energies to be a function of the angular velocity. This implies a corresponding angular velocity dependence of the single particle wavefunctions and many-body diagonalization results. In order to study superfluidity, we consider the two fluid criterion. Numerical results for the superfluid fraction involving the change of in rinsic ground state energy with the square of the angular velocity are obtained. We also consider a perturbative expression for the system inertial parameter expressed in terms of the excitation spectrum of the non rotating system, which enables us to relate the energies in the rotating system to the ones in the system without rotation. This is particularly interesting for obtaining superfluid fraction in terms of spectral information of the non rotating system. Similar results can be found by using the definition of superfluid fraction based on the response of the system to a phase variation imposed by means of twisted boundary conditions [30, 33], but with the difference that our developments do not assume the hypothesis of a condensate mode. Our numerical results indicate that in this system condensate and superfluid fractions are quite unrelated in terms of parameter values, indicating that even for dilute gases the concept that superfluidity is a consequence of Bose-Einstein condensation should be considered more carefully.

A three-level system can be used in a Λ-type configuration in order to construct auniversal set of non-adiabatic quantum gates through the use of non-Abelian non-adiabatic geometrical phases. Such construction allows for high-speed operation times which diminish the effects of decoherence. This might be, however, accompanied by a breakdown of the validity of the rotating wave approximation (RWA) due to the comparable timescale between the counter-rotating terms and the pulse length, which greatly affects the dynamics. Here we investigate the trade-off between dissipative effects and the RWA validity, obtaining the optimal regime for the operation of the holonomic quantum gates.

In the past decade we have seen fast development of new quantum technologies that promise to revolutionise communications and computing. Many different routes are explored to physically implement such quantum technologies. Among others, we can mention superconducting circuits, spin-based devices and photonic devices.  An active area of research concerns hybrid quantum systems, which aim at combining the best properties of these different implementations. Recently quantum acoustics has been gaining interest as a potential intermediate in such hybrid systems. Indeed, phonons can couple to many different degrees of freedom and could therefore form an interface between different quantum systems.One method to convert microwaves to an acoustic signal relies on the exploitation of the piezoelectric effect. However, for transducer devices based on the piezoelectric effect, the operating bandwidth has remained limited. By using tunable matching circuits, we propose a device capable of performing piezoelectric transduction over large bandwidths. The tunability is achieved by using SQUID transmission lines. This work reports some preliminary studies towards the creation of such a platform. We conduct measurements at cryogenic temperatures on suspended lithium niobate delay lines. These allow us to characterise the dependence of the IDT response on various parameters such as the number of fingers and the angle relative to the underlying crystal. We show that certain angles favour transduction into a single acoustic mode. In parallel, we characterise transmission lines consisting of one-dimensional arrays of SQUIDs. By applying magnetic flux to these lines, we show that it is possible to tune their impedance. These experiments improved our understanding of both IDTs and SQUID transmission lines and pave the way for the implementation of our experimental platform. / Under det senaste decenniet har vi sett en snabb utveckling av ny kvantteknologi som kommer att revolutionera telekommunikation och databehandling. Många olika vägar utforskas för att fysiskt realisera sådan kvantteknologi. Bland annat kan vi nämna supraledande kretsar, spinbaserade anordningar och fotoniska anordningar.  Ett aktivt forskningsområde är hybrida kvantsystem som kombinera de bästa egenskaperna hos dessa olika tillämpningar. På senare tid har kvantakustik fått ökat intresse som en potentiell mellansteg i sådana hybridsystem. Fononer kan kopplas till många olika frihetsgrader och skulle därför kunna fungera som ett gränssnitt mellan olika kvantsystem.En metod för att omvandla mikrovågor till en akustisk signal bygger på utnyttjandet av den piezoelektriska effekten. För transduceranordningar som bygger på den piezoelektriska effekten har dock den operativa bandbredden fortfarande varit liten. Genom att använda avstämbara anpassningskretsar föreslår vi en anordning som kan utföra piezoelektrisk transduktion över stora bandbredder. Avstämbarheten uppnås med hjälp av SQUID-överföringsledningar. I detta arbete rapporteras några preliminära studier för att skapa en sådan plattform. Vi utför mätningar vid kryogena temperaturer på upphängda fördröjningsledningar av litiumniobat. Dessa gör det möjligt för oss att karakterisera IDT-svarets beroende av olika parametrar, t.ex. antalet fingrar och vinkeln i förhållande till den underliggande kristallen. Vi har visat att vissa vinklar gynnar transduktion till ett enda akustiskt läge. Parallellt karakteriserar vi transmissionsledningar som består av endimensionella matriser av SQUIDs. Genom att applicera magnetiskt flöde på dessa linjer visar vi att det är möjligt att ställa in deras impedans. Dessa experiment förbättrade vår förståelse av både IDT:er och SQUID-överföringslinjer och banar väg för genomförandet av vår experimentella plattform.

Thesis advisor: Ilija Zeljkovic / We used spectroscopic-imaging scanning tunneling microscopy (SI-STM) and spin-polarized STM (SP-STM) to unveil new electronic phenomena in several different quantum systems. We explored: (1) a potential topological superconductor heterostructure Bi₂Te₃/Fe(Te, Se), (2) high-Tc superconductors − Bi₂Sr₂CaCu₂O₈₊ₓ and Fe(Te, Se), and (3) doped spin-orbit Mott insulators Sr₂IrO₄ and Sr₃Ir₂O₇. In Bi₂Te₃/Fe(Te, Se), we observed superconductivity (SC) on the surface of Bi₂Te₃ thin film, induced by the iron-based superconductor substrate. By annealing the optimally-doped cuprate superconductor Bi₂Sr₂CaCu₂O₈₊ₓ, we drastically lowered the surface hole doping concentration to detect a unidirectional charge stripe order, the first reported charge order on an insulating (defined by the spectral gap with zero conductance spanning the Fermi level) cuprates surface. In the high-Tc SC Fe(Te, Se) single crystal, we found local regions of electronic nematicity, characterized by C₂ quasiparticle interference (QPI) induced by Fermi surface anisotropy and inequivalent spectral weight of dyz and dxz orbitals near Fermi level. Interestingly, the nematic order is locally strongly anti-correlated with superconductivity. Finally, utilizing SP-STM, we observed a short-range antiferromagnetic (AF) order near the insulator-metal transition (IMT) in spin-orbital Mott insulators Sr₂IrO₄ and Sr₃Ir₂O₇. The AF order inhomogeneity is found not to be strongly correlated with the charge gap. Interestingly, the AF order in the bi-layered Sr₃Ir₂O₇ shows residual memory behavior with temperature cycling. Overall, our work revealed new phenomena in a range of today’s most intriguing materials and set the stage for using SP-STM in other complex oxides. / Thesis (PhD) — Boston College, 2020. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Quantum annealing represents an essential milestone towards the goal of adiabatic quantum computing. In quantum annealing, the computation involves finding the ground state of a classical Ising-like Hamiltonian realized as interactions between qubits. Quantum fluctuations are introduced to allow the wavefunction of the qubits to explore the energy landscape, the hope being that the wavefunction finds a minimum energy configuration and possibly giving the result of the computation. While quantum annealing likely may not be as powerful as adiabatic quantum computing, it is possible that it may be better at optimization compared to analogous classical algorithms. In physical realizations of quantum annealing, there are still questions as to the role of quantum fluctuations in the operation of a device given the short coherence times of the individual qubits. These questions have consistently posed a serious theoretical challenge making it difficult to verify experimental results. Here we simplify the problem by considering a system of qubits with ferromagnetic interactions, modeling the decoherence effects as classical noise in the transverse-field of each qubit. We compare the calculations to data collected from a system of manufactured qubits produced by D-wave Systems by performing a finite-size scaling analysis that captures the competition between quantum fluctuations of the transverse-field and bit-flip errors from the noise. We argue that on time-scales larger than the single-qubit decoherence time, the device produces the expected quantum fluctuations for the many-body system. Using this finite-size scaling, one can diagnose sources of noise in the system. Hopefully, in the near future, these devices will not only be realizing coherent quantum annealing but will likely be useful as another example of synthetic quantum matter.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21548号 / 理博第4455号 / 新制||理||1640(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川上 則雄, 教授 田中 耕一郎, 教授 前野 悦輝 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

付記する学位プログラム名: 京都大学卓越大学院プログラム「先端光・電子デバイス創成学」 / 京都大学 / 新制・課程博士 / 博士(理学) / 甲第24402号 / 理博第4901号 / 新制||理||1700(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川上 則雄, 教授 佐々 真一, 教授 高橋 義朗 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The purpose of this thesis is the theoretical study of interference and correlation effects in multimode and continuum mode quantum systems. We are concerned with interference effects in multiport devices which in a sense are generalised Mach-Zehnder interferometers. It is shown how these multimode devices can be employed for the study of negative result and interaction free measurements. Interference and coherence effects are also studied in relation to the radiation fields generated by atoms through the process of spontaneous emission. Besides first order interference, higher order coherence effects are investigated with the aid of Glauber's photodetection theory and it is found that detectors that lie in spacelike regions may display nonclassical correlations under certain conditions. It is well known that the vanishing of field commutators between regions that cannot be connected by subluminal signals reflects the locality of quantum field theory. But is it possible that these spacelike regions exhibit correlations that violate Bell type inequalities? This is the main question and principal concern of the thesis and the answer is affirmative, nonclassical correlations between spacelike regions are indeed possible. A scheme of four detectors that lie in spacelike points was also studied. In this case we do not consider the radiation field but a free scalar field in vacuum state. Nevertheless the virtual quanta of this field may induce nonclassical correlations if the intervals between the detectors are spacelike but small enough. The fundamental reason for this fact is the nonvanishing of the Feynman propagator outside the light cone. Since this propagator is decaying expotentially with the distance it is demonstrated that for large spacelike intervals field correlations obey classical inequalities. We should also note that different inertial observers will agree on the violation or not of these inequalities since the results are manifestly Lorentz invariant.

Quantum systems in the d-dimensional Hilbert space are considered. The mutually unbiased bases is a deep problem in this area. The problem of finding all mutually unbiased bases for higher (non-prime) dimension is still open. We derive an alternate approach to mutually unbiased bases by studying a weaker concept which we call weak mutually unbiased bases. We then compare three rather different structures. The first is weak mutually unbiased bases, for which the absolute value of the overlap of any two vectors in two different bases is 1/√k (where k∣d) or 0. The second is maximal lines through the origin in the Z(d) × Z(d) phase space. The third is an analytic representation in the complex plane based on Theta functions, and their zeros. The analytic representation of the weak mutually unbiased bases is defined with the zeros examined. It is shown that there is a correspondence (triality) that links strongly these three apparently different structures. We give an explicit breakdown of this triality.

In this Bachelor thesis project, the Lindblad master equation is derived, both as the most general way of modeling interaction with an environment that lacks memory, and through microscopic derivations focused on assumptions about the way the system interacts with its environment (weak-coupling, Born-Markov and rotating wave approximations). It is then applied to a two-level system (qubit).