Dissertationen zum Thema „Fermions“

It has been proposed several times in the past that one can obtain an equivalent, but in many aspects simpler description of fermions by first reformulating their first-order (Dirac) Lagrangian in terms of two-component spinors, and then integrating out the spinors of one chirality (e.g.primed or dotted). The resulting new Lagrangian is second-order in derivatives, and contains two-component spinors of only one chirality. The new second-order formulation simplifies the fermion Feynman rules of the theory considerably, e.g. the propagator becomes a multiple of an identity matrix in the field space. The aim of this thesis is to work out the details of this formulation for theories such as Quantum Electrodynamics, and the Standard Model of elementary particles. After having developed the tools necessary to establish the second-order formalism as an equivalent approach to spinor field theories, we proceed with some important consistency checks that the new formulation is required to pass, namely the presence or absence of anomalies in their perturbative and non-perturbative description, and the unitarity of the S-Matrix derived from their Lagrangian. Another aspect which is studied is unification, where we seek novel gauge-groups that can be used to embed all of the Standard Model content: forces and fermionic representations. Finally, we will explore the possibility to unify gravity and the Standard Model when the former is seen as a diffeomorphism invariant gauge-theory.

Ultracold atomic gases have established themselves as quantum systems, which are clean and offer a high degree of control over crucial parameters. They are well isolated from their environment and thus offer the possibility to study coherent many-body dynamics. In this thesis, we address the dynamics of ultracold Fermions with large spin. Fermionic spinor gases differ from the typical situation in condensed matter physics, due to both the presence of the trap and the possibility of having fermions with large (>1/2) spin. Compared to the spin-1/2 case, large spin fermions must have one of two possible new properties. Either they obey an enhanced SU(N) symmetry, or they feature spin-changing collisions and a quadratic Zeeman shift. Here, we address the latter case. In the weakly interacting scenario, there are three different regimes. For very weak interactions, the system is in the collisionless regime and interactions can be taken into account on a mean-field level. For stronger interactions, collisions ensure local equilibrium and the system is described by hydrodynamic equations. For the intermediate regime however, there is no simple description. Moreover, the scattering cross-section for spin-changing and spin-conserving collisions can be different for large-spin fermions and we find a situation, where the system is hydrodynamic with respect to one process but not the other. In this thesis, a semi-classical Boltzmann equation with full spin coherence is developed, which allows to interpolate between the collisionless and hydrodynamic regime in the presence of the trap and for large spins. This approach goes beyond mean-field theory and treats the single-particle dynamics as an open system coupled to an environment given by all other particles. We find good agreement with experiments performed in the group of Klaus Sengstock at Hamburg University, using ultracold Potassium-40. We begin by investigating the effect of the harmonic trap on a collisionless system. We find a dynamical mechanism for spin-segregation, the mean-field driven creation of two domains of opposite magnetization in phase-space. The effect finds a transparent explanation when introducing the concept of dynamically induced long-range interactions, occurring when the fast phase-space rotation induced by a strong parabolic trap effectively smears out the contact interactions. Further results in this thesis have been achieved in collaboration with the experimental group in Hamburg. In the first project, we study the collective excitations of a trapped four-component Fermi gas. Long wavelength spin waves are excited by using a magnetic field gradient to wind up a spin spiral. During the subsequent dynamics, the spin components oscillate in the trap, while the total density remains constant. The dynamics can be understood quantitatively by disentangling it into dipolar, nematic and octupolar configurations. In a further experiment with spin-9/2 fermions, it was found that spin-changing interactions can lead to collective and coherent oscillations of the spin state of the whole Fermi sea with long lifetimes. It is found theoretically, that these giant oscillations are protected from spatial dephasing by dynamically induced long-range interactions. We identify the suppression of such oscillations in the high-density regime as the consequence of incoherent non-forward scattering. In the last project, we study collision processes in ultracold Potassium in greater detail. We find that they can be arranged in 3 categories: Spin-changing vs. spin-conserving collisions, processes depending on density vs. processes depending on density gradients and forward vs. lateral scattering. With this categorization, as well as the exact dependence of each process on scattering lengths and momenta, we can explain and simulate not only the coherent mean-field driven oscillations, but also relaxation effects that appear to be incoherent on the single-particle level
Gases atómicos ultrafríos han establecido como sistemas cuánticos limpias que ofrecen un alto grado de control sobre parámetros cruciales. Están bien aisladas de su entorno y por eso ofrecen la posibilidad de estudiar la dinámica coherente de muchos cuerpos. En esta tesis, estudiamos la dinámica de fermiones ultrafríos con spin largo. Gases espinoriales fermiónicos difieren de la situación típica en la física de materia condensada por la presencia de la trampa y la posibilidad de tener un spin largo (> 1/2). En comparación con el caso de spin 1/2, fermiones de espín largo deben tener una de dos posibles propiedades nuevas. Obedecen a una simetría ampliada SU(N), o muestran colisiones spin-cambiante y un efecto Zeeman cuadrático. Aqui tratamos el segundo caso. En el escenario de interacciónes débiles, hay tres regímenes diferentes. Para interacciones muy débiles, el sistema está en el régimen sin colisiones e interacciones se puede describir en un nivel de campo medio. Para interacciones fuertes, las colisiones garantizan el equilibrio local y el sistema es descrito por ecuaciones hidrodinámicas. Para el régimen intermedio, no hay una descripción sencilla. Ademas, la sección transversa de dispersión para colisiones spin-cambiantes y de spin-conservación puede ser diferente para fermiones de espín largo. Encontramos una situación, donde el sistema es hidrodinámico con respecto a un proceso, pero no a la otra. En esta tesis desarrollamos una ecuación de Boltzmann semi-clásica, que permite interpolar el régimen intermedio, en presencia de la trampa y para espín largo. Este enfoque trata la dinámica de un cuerpo como un sistema abierto, acoplado a un entorno determinado por todas las atomos demás. Encontramos un buen acuerdo con experimentos realizados en el grupo de Klaus Sengstock en la Universidad de Hamburgo, hechos con potasio-40 ultrafrío. Comenzamos investigando el efecto de la trampa armónica en un sistema sin colisiones. Encontramos un mecanismo dinámico par la segregación de spin, la creación de dos dominios de magnetización opuesta en el espacio fásico, impulsada por el campo medio. Encontramos una explicación transparente de este efecto con la introducción del concepto de interacciones de largo alcance inducidos dinámicamente, que se forma cuando una fuerte trampa parabólica desenfoque eficazmente las interacciones de contacto. Otros resultados de esta tesis han sido realizados en colaboración con el grupo experimental en Hamburgo. En el primer proyecto, estudiamos las excitaciones colectivas de un gas de Fermi atrapada, con cuatro componentes de spin. Ondas de spin con larga longitud de onda se excitan mediante un gradiente de campo magnético. Durante la dinámica siguiente, los componentes de spin oscilan en la trampa, mientras que la densidad total permanece constante. Podemos entender esta dinámica cuantitativamente desligandola en configuraciones dipolares, nemáticos y octupolares de espín. En un experimento siguiente con fermiones de spin 9/2, se encontró que las interacciones spin-cambiando pueden activar oscilaciones colectivas y coherentes del estado de spin de todo el mar de Fermi con duración larga. Descubrimos teóricamente, que estas oscilaciones gigantes están protegidos de desfase espacial por las interacciones de largo alcance inducidos dinámicamente. Identificamos la supresión de tales oscilaciones en el régimen de alta densidad como la consecuencia de la dispersión incoherente lateral. En el último proyecto, estudiamos los procesos de colisión en potasio ultrafrío en mas detalle. Podemos organizarlos en tres categorías: Colisiones spin-cambiante vs. spin-conservación, procesos dependiente de la densidad vs. gradientes de densidad y colisiones hacia adelante vs. laterales. Con esta clasificación y la dependencia en la longitud de dispersión y momentos, podemos explicar y simular no sólo las oscilaciones coherentes impulsados por el campo medio, sino también efectos de relajación

The Fermi surface of graphene contains points where the connection between excitation energy and crystal momentum is linear, similar to massless or ultrarelativistic fermions. This is important for the physical properties of this material. In this thesis the candidate has combined a study of the theoretical and experimental literature with his own calculations of the excitation spectra of monolayer, bilayer and multilayer graphene.

We study the chiral anomaly by solving the Dirac equation for fermions in parallel electric and magnetic fields. In such case, only the lowest-energy Landau levels are relevant to the anomaly. Specifically, for massless fermions, the chiral anomaly is a result of the production of particles of one chirality, and no creation of particles of the other chirality. For massive fermions, we find that the chiral anomaly equation can be simply obtained via a proper regularization of the range of the momentum. We extend the method to anomaly cancellation, and conclude that the conservation of the baryon number plus lepton number must be violated as a quantum anomaly in the context of the Standard Model. Accordingly, such baryon number non-conservation can play a vital role during the electroweak transition to achieve the baryon asymmetry of the Universe. Through real-time lattice simulations, we refine the implementation of ensemble fermions for a cold electroweak transition, involving the SU (2) gauge field, Higgs field and one generation of fermions. We find that the dynamics and most observables converge quickly with a reasonable number of fermion realizations, and the method of ensemble fermions for the entire electroweak sector becomes numerically tractable. We apply the method to the computation of the effective preheating temperature during a fast electroweak transition, relevant for Cold Electroweak Baryogenesis. We find that the fermion temperature is never below 20 GeV, and this can indirectly rule out Standard Model CP -violation as the origin of the baryon asymmetry of the Universe, as Standard Model cold baryogenesis requires a temperature of at most of order of 1 GeV. For this reason, new CP -violation source from physics beyond the Standard Model is required in order to explain the baryon asymmetry. We further present a first-principles numerical computation of the baryon asymmetry in electroweak-scale baryogenesis, where the CP -violation is obtained as a consequence of including another Higgs doublet. For one particularly favourable scalar potential that could provide a high sphaleron transition rate, we calculate the asymmetry through large-scale computer simulations. The numerical signal is at the boundary of what is numerically discernible with the available computer resources, but we tentatively find an asymmetry of |η| ≤ 3.5 × 10−7 . We also find it is attainable to include the complete electroweak SU (2) × U (1) gauge fields in the reduced Standard Model that we are using in practical simulations, so that in further studies we can measure the cosmic magnetic field generated during the electroweak phase transition.

"October 2002" Bibliography: p. 129-136. 1. Introduction -- 2. QCD and the standard model -- 3. The Lattice -- 4. Symanzik improvement in the Static Quark Potential -- 5. Scale determination for an improved Gluon Action -- 6. Fat-link Irrelevant Clover Fermion actions -- 7. Excited Baryons in Lattice QCD -- 8. Spin 3/2 Baryons -- 9. Conclusion. This thesis reports work done in conducting numerical simulations of Lattice QCD.

In this Thesis we discussed ultracold Fermi gas with an s-wave interaction and synthetic spin-orbit coupling under a variety of conditions. We considered the system in both three and two spatial dimensions, with equal-Rashba-Dresselhaus type or Rashba-only type of spin-orbit-coupling, and with or without an artificial Zeeman field. We found competing effects on Fermionic superfluidity from spin-orbit coupling and Zeeman fields, and topologically non-trivial states in the presence of both fields. We gave an outlook on the many-body physics in the last.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2013.
Cataloged from PDF version of thesis.
Includes bibliographical references (page 59).
Most materials are either metals or insulators. When they are metals, their electronic properties are usually described by Landau's Fermi liquid theory. That is, they behave more or less like a free Fermi gas, with a few modifications due to electron-electron interactions. However, there exist a few metallic materials whose phenomenology does not fit within Fermi liquid theory. These are quasi-2D metals on the verge of becoming insulators, and they happen to become superconducting at low temperature, by a mechanism different than BCS superconductivity. The physics of these materials calls for a new strongly coupled universality class of interacting electrons, yet to be understood. This work looks at the problem from the novel point of view of gauge/gravity, or holographic, duality.
by Andrea Allais.
Ph.D.

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Defeitos topológicos são soluções de equações diferenciais que conectam configurações distintas de um sistema. Para modelos unidimensionais essas soluções são chamadas de kinks. Com isso, neste trabalho vamos estudar as soluções do tipo torção, denominadas twistons topológicos e também investigaremos o comportamento de fermions na presença de estruturas do tipo kink. Primeiramente estudaremos os twistons topológicos presentes no polietileno cristalino que representam uma torção de 180 na cadeia de CH2 causando também uma contração do comprimento da molécula. Pretendemos então construir um modelo efetivo de dois campos que não contenha degenerescência na energia através da aplicação do chamado Método de Extensão, buscando também obter soluções analíticas desse modelo. Após este estudo, voltaremos nossas investigações para as análises de férmions na presença de kinks com o objetivo de obter um controle da energia de limiar (gap de energia onde residem os estados ligados) usando dois campos escalares.
Topological defects are solutions of differential equations that connect distinct confi gurations of a system. For one-dimensional models these solutions are called kinks. In this work we will study the twist-like solutions, called topological twistons and also investigate the behavior of fermions in the presence of kink-like structures. First we will study the topological twistons present in the crystalline polyethylene which represent a 180 twist in the CH2 chain also causing a contraction of the length of the molecule. We intend to construct an effective model of two elds that does not contain degeneracy in the energy through the application of the so called Extension Method, also seeking to obtain analytical solutions of this model. After this study, we will turn our investigations for fermion analyzes in the presence of kinks in order to control of the threshold energy (energy gap where bound states reside) using two scalar elds.

Cette thèse traite des fermions fortement corrélés. En particulier, nous étudions la possibilité d’observer des transitions de phase quantiques de l’état isolant vers l’état métallique ou vers la phase supraconductrice dans des systèmes de fermions en interaction sur réseaux. Dans un premier chapitre, nous allons introduire le modèle de Hubbard qui permet de décrire le comportement des électrons dans des solides cristallins dans la limite des liaisons fortes. Nous prouverons dans un second chapitre la possibilité d’obtenir des transitions de phase isolant-métal gouvernées par les interactions entre électrons. Ces transitions sont obtenues dans le cadre du modèle de Hubbard ionique où deux types de comportement isolant peuvent être mis en évidence ? L’état métallique est obtenu lorsque les effets de localisation des deux isolants se compensent ? Puis, dans la continuité de cette étude, nous considérerons un système où les électrons peuvent occuper deux plans couplés. Il existe aussi une phase intermédiaire métallique dans ce modèle. Nous étudierons aussi la possibilité d’obtenir une phase supraconductrice grâce à une symétrie particulière dans ce modèle. Finalement, étudiant u modèle de Hubbard dynamique, nous analysons l’effet du couplage des électrons avec les degrés de liberté internes de l’atome. Ce modèle a l’avantage de présenter une dissymétrique particule-trou qui pourrait donner lieu à un diagramme de phase dissymétrique comme observé dans les matériaux supraconducteurs à haute température de transition
We study the possibility of interaction driven insulator to metal transitions and superconductivity in fermionic systems on lattices. We first introduce the Hubbard model which describes fermions in a crystal in the tight-binding limit. Then we show evidence for interaction-driven insulator-metal transitions in the ionic Hubbard model. At half-filling, when the interaction strength or the staggered potential dominates we find Mott and band insulator, respectively. When these two energies are of the same order we find a metallic phase. Then we study a bilayer Hubbard model which exhibits such insulator to metal transitions and shows an interesting superconducting signal. Finally, we study a bilayer Hubaard model which describes interacting fermions on a lattice whose on-site repulsion is modulated by a coupling to fluctuating bosonic field

Nous avons etudie trois systemes a electrons lourds, cecu 2si 2, cepd 2si 2 et uge 2, par des mesures de transport, d'oscillations quantiques (cepd 2si 2) et de diffraction neutronique (uge 2). Les experiences ont ete effectuees dans des conditions extremes : tres basse temperature, champ magnetique eleve et pression hydrostatique. Pour cecu 2si 2, nous avons suivi l'evolution de la phase a magnetique qui s'effondre rapidement sous pression. Nous avons mis en evidence une relation entre la phase a et la presence d'un maximum dans la dependance en temperature de h c 2. Notre analyse a montre qu'a basse pression le signe de l'integrale d'echange doit etre negatif. La supraconductivite est alors renforcee par une augmentation de la susceptibilite paramagnetique comme dans l'effet jaccarino-peter. L'anisotropie de la pente initiale de h c 2 et donc celle de la masse effective change sous pression. Pour cepd 2si 2, l'effet de haas-van alphen a pression ambiante et la resistivite electrique sous pression ont ete etudies. Cette derniere montre un comportement non liquide de fermi a proximite du point critique quantique antiferromagnetique p c27 kbar. L'analyse de h c 2 a p c prouve que l'etat supraconducteur est bien decrit par le modele du couplage faible en limite propre, avec une limite paramagnetique fortement anisotrope. Uge 2 presente une coexistence de ferromagnetisme et de supraconductivite, se developpant juste en dessous du point critique quantique ferromagnetique p c16 kbar. Les mesures de resistivite sous pression montrent l'existence possible d'une autre ligne de transition et d'un autre point critique quantique, p x12 kbar, dans l'etat ferromagnetique. Le diagramme de phase p-t incluant p c et p x a ete trace, et une relation possible entre p x et le developpement de supraconductivite a ete discutee. La dependance en temperature de h c 2 montre une variete de comportements nouveaux, ne pouvant pas etre compris dans les modeles conventionnels de la supraconductivite.

Das Ziel dieser Doktorarbeit ist die Berechnung, aus ersten Prinzipien, von Niedrigenenergiekonstanten (NEK), welche die chirale Störungsheorie (ChST) parametrisieren, durch Simulationen auf dem Gitter. Diese Arbeit ist eine Pilotstudie und will deshalb nicht zu definitiven und präzisen quantitativen Vorhersagen führen, sondern wir möchten qualitative Leitlinien für zukünftige genauere Erforschungen der epsilon-Entwicklung der ChST geben. Letztere ist ein Gebiet in dem die chirale Symmetrie wiederhergestellt ist und wo die Compton-Wellenlänge der leichtesten Mesonen grösser als die lineare Dimension des endlichen Volumens ist. Die epsilon-Region ist weiterhin durch die wichtige Rolle der topologischen Ladung, nu, charakterisiert, so dass die Untersuchung der mesonischen Zweipunkt-Korrelationsfunktionen in definierten topologischen Sektoren vorzunehmen ist. Aus diesem Grunde haben wir chirale Fermionen auf dem Gitter simuliert, wobei der overlap Formalismus für den Dirac Operator, mit dem gewöhnliches Wilson Dirac Operator als Kern, in der quenched Approximation genommen wurde. Wir demonstrieren dass der Sektor mit neutraler topologischer Ladung, nu = 0, numerisch sehr schwierig zu untersuchen ist, weil die Daten von erheblichen Spitzen beeinflusst werden, die aufgrund sehr kleiner, nicht verschwindender Eigenwerte herrühren. Diese Beobachtung findet eine Übereinstimmung in einer Studie der Random Matrix Theory (RMT), die besagt, dass man eine Statistik von mehr als 10000 Konfigurationen benötigt, falls man auf kleine Eigenwerte empfindlich reagierende physikalische Grössen, im triviale topologische Sektoren simulieren möchte. Weniger Probleme ergeben sich in dem nicht-trivialen Sektoren |nu| > 0: wir präsentieren deshalb unsere Ergebnisse aus dem topologisches Sektor nu = 1 und den Daten aus das Sektor mit nu = 2 nur als Gegenprobe. Wir zeigen die Existenz einer unteren Schranke für das physikalisches Volumen bei V > 1 fm zur vierten Potenz für die Gültigkeit der ChST, übereinstimmend mit einer vorherigen Beobachtung aus der RMT. Wir beschränken deshalb unsere Untersuchung auf ein grösseres Gitter, wo wir die Daten des axialen Korrelators mit den Vorhersagen der ChST in der Valenzquark-Approximation fitten und eine stabile Bestimmung der gequenchten Pionen-Zerfallskonstante, F, erhalten. Die skalaren und pseudoskalaren Korrelationsfunktionen sind durch mehrere NEK parametrisiert. Dadurch ist der Vergleich mit den Vorhersagen der ChST schwieriger, und deshalb präsentieren wir nur einige Abschätzungen, die mit der entsprechenden Literatur verglichen werden. Zum Schluss präsentieren wir mögliche Implementierungen von verbesserten Algorithmen für die Inversion des overlap Operators, die die Simulationkosten reduzieren.
The aim of this thesis is the computation of Low Energy Constants (LEC) which parameterise Chiral Perturbation Theory (ChPT) from a first principles analysis via lattice simulations. The thesis provides a pilot study and will not give definitive and precise quantitative predictions, but rather our aim is to provide qualitative hints for future accurate investigations of the epsilon-expansion of ChPT, where chiral symmetry is restored and the Compton wavelength of the lightest meson is larger than the linear size of the finite volume. One of the property characterising the epsilon-regime is the important role played by the topological charge, nu, leading to the investigation of the two-point meson correlation functions in distinct topological sectors. To this end, we simulate chiral fermions on the lattice adopting the overlap formalism for the Dirac operator in the quenched approximation, with the kernel provided by the usual Wilson Dirac operator. We demonstrate that the neutral topological sector, nu = 0, is very difficult to explore numerically, as the data are affected by large spikes due to the presence of very small, non-zero eigenvalues. This observation is in agreement with a study of Random Matrix Theory (RMT), which indicates that a statistic of more than 10000 configurations is required when physical quantities sensitive to small eigenvalues are investigated in the neutral topological sector. Therefore, we present our results corresponding to the topological sector nu = 1. Due to the modest statistic, we only use the nu = 2 data as a crosscheck. We find a lower bound on the physical volume V > 1 fm to the four for ChPT to be used, in agreement with a previous observation using RMT. Restricting our attention to a larger lattice, we fit the data of the axial correlation function with the predictions of quenched ChPT, obtaining a stable determination of the quenched pion decay constant, F. The scalar and pseudoscalar correlation functions are parameterised by a larger number of LEC, rendering the comparison with ChPT predictions much more difficult and hence we present only some estimates that are compared with other determinations in the literature. Finally, we present possible implementations of improved algorithms used in the ``inversion'''' of the overlap operator, whose aim is to reduce the computational cost of the simulations.

Dans cette thèse, nous étudions d'un point de vue théorique différents aspects de la matière topologique. Ces systèmes présentent des propriétés résistantes aux éventuelles perturbations grâce à une topologie non-triviale de leur structure de bandes. En particulier, des excitations exotiques, par exemple des fermions de Majorana, peuvent apparaitre à leurs bords.L'entropie d'intrication, ainsi que le spectre d'intrication ont été fondamentaux dans l'étude théorique de ces systèmes, et plus généralement des phases libres. Il est cependant difficile de les mesurer expérimentalement. L'étude des fluctuations de charge bipartites a été proposée afin de remédier à ce problème, et celles-ci permettent une mesure faible de l'intrication, en particulier pour des modèles unidimensionnels libres. Nous généralisons les précédents travaux sur les Liquides de Luttinger à des familles génériques de supraconducteurs et isolants topologiques en une et deux dimensions, systèmes dans lesquels la charge observée n'est plus conservée. Nous montrons que les transitions de phases topologiques sont caractérisées par certains coefficients universels dans les fluctuations et les fonctions de corrélations. Les systèmes bidimensionnels que nous étudions présentent des cônes de Dirac, et ces coefficients dépendent de leur enroulement. Cela nous permet de caractériser la topologie de ces points critiques. Dans tous les cas, les fluctuations suivent une loi de volume, qui a un comportement non-analytique aux transition de phase.Dans un second temps, nous nous intéressons aux systèmes en interactions. Nous montrons tout d'abord que certaines des signatures des transitions topologiques survivent en leur présence, dans les supraconducteurs topologiques. Nous étudions ensuite le diagramme de phase de deux fils supraconducteurs couplés par une interaction Coulombienne. Celle-ci mène à la création de phases exotiques grâce à la compétition avec la supraconductivité non-conventionnelle. Nous montrons en particulier l'apparition de phases de Mott brisant spontanément la symétrie de renversement du temps et présentant des courant orbitaux non-triviaux, ainsi que celle d'une phase de fermions libres, qui est l'extension de deux chaînes de Majorana critiques en interaction.Enfin, nous nous intéressons aux effets de la présence de fermions de Majorana sur le transport électronique. Nous étudions un îlot supraconducteur où plusieurs de ces fermions existent. Ce système pourrait être l'un des composants élémentaires d'un éventuel ordinateur quantique. Les fermions de Majorana changent les statistiques d'échange des porteurs de charges, ce qui se traduit par une fractionnalisation de la conductance. Celle-ci se révèle très robuste face aux anisotropies et autres perturbations. Nous étendons les études précédentes au cas où le nombre d'électrons dans la boîte peut fluctuer, et montrons l'équivalence de ce problème avec le modèle Kondo à plusieurs canaux. Nous réinterprétons alors ce modèle en terme du déplacement d'une particule dans un réseau fictif dissipatif
In this thesis, we study theoretically different aspects of topological systems. These models present resilient properties due to a non-trivial topology of their band structures, and in particular exotic edge excitations such as Majorana fermions.Entanglement entropy and entanglement spectrum have been fundamental to the study of these systems and of gapless systems in general, but are difficult to measure experimentally. Bipartite charge fluctuations were proposed as a weak measurement of this entanglement, in particular for one-dimensional gapless phases. We extend previous results on standard Luttinger Liquids to generic families of one- and two-dimensional non-interacting topological systems. Through exact computations, we show that their critical points are characterized by universal coefficients that reveal the topological aspect of the transitions. In two dimensions, the Dirac cones give quantized contributions to the fluctuations and various correlation functions. These contributions depend on their winding numbers, allowing for a precise determination of the topological structure of the gapless points. A volume law is also present and linked to the Quantum Fisher information, with characteristic non-analyticities at the phase transitions.In a second time, we include interactions and show that some of these signatures are preserved in topological superconductors even in their presence. Through analytical (bosonization, renormalization group) and numerical (exact diagonalization and DMRG) methods, we study the phase diagram of two Coulomb-coupled topological superconducting wires. We are interested in their behavior when the interactions are strong enough to break the topological protection: the interplay between unconventional superconductivity and interactions leads to exotic phases. We show the appearance of phases spontaneously breaking the time-reversal symmetry, with non-trivial orbital currents, and of an unusual gapless phase that is the extension of two critical interacting Majorana modes.Finally, we are interested in electronic transport mediated by Majorana fermions. We study a floating superconducting island carrying several such impurities. This device is thought to be a potential building block for a quantum computer. The Majorana fermions affect the statistics of the charge carriers, which leads to very resilient fractionalized transport. We extend previous studies to the charge degenerate case, where the total number of fermions in the island is not fixed, and map it to the well-known Multi-Channel Kondo model at large interaction. We reinterpret this standard model in terms of a particle moving in a highly dimensional, dissipative lattice

The electric (EDM) and magnetic (g-2) dipole moments are static properties sensitive to quantum corrections induced by the virtual particles that populate the vacuum. Indeed, they are well suited to test the Standard Model of Elementary of particle physics and to unveil unknown New Physics (NP) hidden at high energy. The electron and muon g-2 have been measured with the wonderful precision of 0.24 ppb and 0.54 ppm, respectively, and thus they represent one of the strongest confirmation of the SM and greatest achievement in Quantum Field Theory. Nonetheless the SM deficiencies, the explanation of dark matter and dark energy, cosmological inflaton, neutrino oscillations and masses, the strong CP problem and the origin of matter-antimatter asymmetry, call for new physics beyond the SM. Since NP contribution to the dipole moments of a fermion f is expected to be proportional to m_f^2, dipole moments of heavy fermions, such as the top quark or the tau lepton, are much more sensitive to NP effects than the electron or muon ones. However the very short lifetime of these unstables particle makes it impossible to directly measure their electromagnetic properties. Therefore, indirect information must be obtain by precisely measuring cross sections and decay rates in processes involving the emission of a real photon by the heavy fermion. In this thesis, we investigate the possibility to measure the anomalous magnetic moment and the electric dipole moment of the top quark at the LHC and tau lepton at future high luminosity B-factories.
I momenti di dipolo magnetico ed elettrico sono proprietà sensibili alle fluttuazioni quantistiche indotte dalle particelle visuali che popolano il vuoto. Per questo motivo, essi sono particolarmente adatti a testare il Modello Standard della fisica delle particelle e a svelare Nuova Fisica nascosta ad alta energia. I g-2 dell’elettrone e del muon sono stati misurati, rispettivamente, con la meravigliosa precisione di 0.24 ppb e 0.54 ppm: essi rappresentano una delle maggiori conferme del Modello Standard e uno delle più grandi conquiste della Teoria dei Campi. Tuttavia, il Modello Standard non spiega materia oscura ed energia oscura, l’inflazione cosmologica, il problema di strong-CP e l’origine dell’asimmetria materia-antimateria, e dunque richiede nuova fisica oltre il Modello Standard. Poiché contributi di nuova fisica ai momenti di dipolo di una particella f sono stimati essere proporzionai alla m_f^2, i momenti di dipolo di fermioni pesanti, come il leptone tau e il quark top, sono molto più sensibili ad effetti di nuova fisica rispetto quelli dell’elettrone o del muone. Tuttavia, la breve vita media di queste particelle instabili rende impossibile la misurazione diretta delle loro proprietà elettromagnetiche. Quindi, informazioni su di esse devono essere ottenute indirettamente a partire dalla misurazione di sezioni d’urto e larghezze di decadimento in processi che coinvolgono l’emissione di un fotone reale da parte del fermione pesante. In questa tesi si analizza la possibilità di misurare il momento magnetico anomalo e il momento di dipolo elettrico del quark top, a LHC, e del leptone tau alle future B-factory ad alta luminosità.

Les gaz ultrafroids permettent d'étudier sous un angle nouveau des hamiltoniens complexes issus de la matière condensée, tels le modèle de Fermi-Hubbard. Cette thèse présente une nouvelle méthode de mesure de l'équation d'état d'un gaz ultrafroid, autorisant une comparaison directe avec la théorie. Elle repose sur une mesure de la pression à l'intérieur d'un gaz à partir de son image in situ. Nous appliquons cette méthode à l'étude d'un gaz de fermions en interaction résonnante, un gaz de 7Li en interaction faible servant de thermomètre. De manière surprenante, aucune des théories à N corps du gaz unitaire ne rend compte intégralement de l'équation déduite de cette analyse. Le développement du viriel extrait des données à haute température est en accord avec la résolution du problème à trois corps. A basse température nous montrons, contrairement à un certain nombre d'études antérieures, que la phase normale se comporte comme un liquide de Fermi. Enfin, nous obtenons la température critique de superfluidité grâce à une signature claire sur l'équation d'état. Nous avons aussi mesuré la pression de l'état fondamental en fonction du déséquilibre de spin et de la force des interactions - mesure directement utile à la description de la croûte des étoiles à neutrons. Nos données valident les simulations Monte-Carlo et sont en accord avec les corrections Lee-Huang-Yang au champ moyen pour un superfluide fermionique ou bosonique. Nous observons que, dans presque tous les cas, la phase partiellement polarisée peut être décrite comme un liquide de Fermi de polarons. La masse effective du polaron déduite de l'équation d'état est en accord avec une étude de modes collectifs.

Recently, a large amount of effort has gone towards using the AdS/CFT conjecture in condensed matter physics. First, we present a review of the conjecture, then we use the conjecture to model 2+1-dimensional fermions. We find three kinds of solutions with different kinds of discrete symmetries. We show that Chern-Simons- like electric responses, computed using a holographic model appear with the right quantized coefficients.

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Bachelors
Arts and Sciences
Physics

En utilisant la technique de la renormalisation constructive, nous avons developpe une technique rigoureuse pour la renormalisation des systemes fermioniques. Apres l'avoir testee sur un probleme deja bien connu (la limite ultraviolette du modele de gross-neveu massif a deux dimensions) nous l'avons etendue a la physique du solide. Dans ce contexte nous avons considere un modele simple decrivant la phase normale d'un supraconducteur en deux dimensions spatiales. En particulier nous avons donne la premiere preuve rigoureuse d'une relation, entre la constante de couplage et la temperature critique, qui a ete prevue par les theories phenomenologiques.

Quantum states of Dirac fermions at zero or finite temperature are investigated using the point-splitting method in Minkowski and anti-de Sitter space-times undergoing rotation about a fixed axis. In the Minkowski case, analytic expressions presented for the thermal expectation values (t.e.v.s) of the fermion condensate, parity violating neutrino current and stress-energy tensor show that thermal states diverge as the speed of light surface (SOL) is approached. The divergence is cured by enclosing the rotating system inside a cylinder located on or inside the SOL, on which spectral and MIT bag boundary conditions are considered. For anti-de Sitter space-time, renormalised vacuum expectation values are calculated using the Hadamard and Schwinger-de Witt methods. An analytic expression for the bi-spinor of parallel transport is presented, with which some analytic expressions for the t.e.v.s of the fermion condensate and stress-energy tensor are obtained. Rotating states are investigated and it is found that for small angular velocities Ω of the rotation, there is no SOL and the thermal states are regular everywhere on the space-time. However, if Ω is larger than the inverse radius of curvature of adS, an SOL forms and t.e.v.s diverge as inverse powers of the distance to it.

Quantenchromodynamik mit zwei leichten Quarks wird in der Gitterregularisierung mit verbesserten Wilson Fermionen betrachtet. Die chirale Symmetrie in dieser Formulierung wird von Gitterartefakten, die linear im Gitterabstand a sind, explizit gebrochen. Daher erfordern die axialen Isospin Ströme Verbesserung (im Symanzik Sinn), sowie eine endliche Renormierung, wenn sie die Ward--Takahashi Identitäten des Kontinuums bis auf kleine Gitterkorrekturen proportional zu a^2 erfüllen sollen. Algorithmische Probleme bei großen Gitterabständen machen die numerischen Simulationen der Gittertheorie schwierig. Der Hybrid Monte Carlo Algorithmus leidet unter einem verformten Dirac Spektrum in Form unphysikalisch kleiner Eigenwerte. Es wird gezeigt, daß dies ein Gitterartefakt ist, welches schnell verschwindet, wenn der Gitterabstand verringert wird. Ein alternativer Algorithmus, der polynomische Hybrid Monte Carlo Algorithmus, zeigt erheblich bessere Eigenschaften im Umgang mit den außergewöhnlich kleinen Eigenwerten. Durch Erweiterung und Verbesserung vorher verwendeter Methoden wird die nicht-perturbative Verbesserung und Renormierung des Axialstroms durch Korrelationsfunktionen im Schrödinger Funktional implementiert. In beiden Fällen wird dies erzielt, indem man Ward Identitäten des Kontinuums bei endlichem Gitterabstand erzwingt. Zusammen stellt dies die chirale Symmetrie bis zur quadratischen Ordnung im Gitterabstand wieder her. Mit wenig zusätzlichem Aufwand wird auch der Normierungsfaktor des lokalen Vektorstroms berechnet. Die Methoden, die hier entwickelt und implementiert wurden, können leicht auch für andere Wirkungen verwendet werden, die im Schrödinger Funktional formuliert werden können. Dies umfaßt verbesserte Eichwirkungen sowie Theorien mit mehr als zwei dynamischen Quarks.
Quantum Chromodynamics with two light quark flavors is considered in the lattice regularization with improved Wilson fermions. In this formulation chiral symmetry is explicitly broken by cutoff effects linear in the lattice spacing a. As a consequence the isovector axial currents require improvement (in the Symanzik sense) as well as a finite renormalization if they are to satisfy the continuum Ward-Takahashi identities associated with the isovector chiral symmetries up to small lattice corrections of order a^2. In exploratory numerical simulations of the lattice theory algorithmic difficulties were encountered at coarse lattice spacings. There the hybrid Monte Carlo algorithm used suffers from a distorted Dirac spectrum in the form of unphysically small eigenvalues. This is shown to be a cutoff effect, which disappears rapidly as the lattice spacing is decreased. An alternative algorithm, the polynomial hybrid Monte Carlo algorithm, is found to perform significantly better in the presence of exceptionally small eigenvalues. Extending previously used methods both the improvement and the renormalization of the axial current are implemented non-perturbatively in terms of correlation functions formulated in the framework of the Schrödinger functional. In both cases this is achieved by enforcing continuum Ward identities at finite lattice spacing. Together, this restores the isovector chiral symmetry to quadratic order in the lattice spacing. With little additional effort the normalization factor of the local vector current is also obtained. The methods developed and implemented here can easily be applied to other actions formulated in the Schrödinger functional framework. This includes improved gauge actions as well as theories with more than two dynamical quark flavors.

This thesis presents a study of two-dimensional electron systems in GaAs-(Al,Ga)As heterojunctions and quasi-two-dimensional electron and hole systems in graphite within the quantum Hall effect regime of low temperature and high magnetic field. This thesis covers three main sets of experimental work as well as details of the experimental methods (chapter 2) used and the background theory behind the observed results (chapter 1). The first experimental results presented in this thesis in chapter 3 focus on contactless measurement of the equilibrium magnetisation of sample A2268, a ten layer multiple quantum well sample. Fitting the shape of dHvA oscillations at various temperatures to different models for the density of states, various properties of the system can be estimated, such as the shape of the disorder-broadened density of states and the presence of a background density of states between the Landau levels. Chapter 4 focuses on measurements of the decay of induced circulating currents in the quasi-dissipationless quantum Hall regime in two samples, V0049 and T73. The induced current is measured via contactless measurement of the associated magnetic moment. The magnitude of the induced current is found to be affected by the sweep rate of the magnetic field and also the distance of approach. The decay of the induced currents is observed at several temperatures and for different magnetic field sweep rates and distances of approach. Decays are observed for up to several days at time, far longer than previously possible. Information about the rate of decay can be used to build a picture of the decay mechanisms present in the quantum Hall regime. The presence of a power-law decay regime indicates many decay mechanisms contribute to the decay of a circulating current in the quasi-dissipationless quantum Hall regime. Chapter 5 focuses on both contactless magnetometry and transport experiments carried out on a graphite sample. The experiments aim to confirm or dispute recent claims of Dirac fermions in graphite. Experiments are carried out at temperatures in the range 30 mK to ~4 K and at two different angles to the applied magnetic field. Phase analysis of both Shubnikov de Haas and de Haas van Alphen oscillations is used to distinguish between normal and Dirac fermions. Observation of quantum Hall effect displays the presence of a half-integer quantum Hall staircase similar to that observed in graphene.

Ce mémoire de thèse est divisé en deux parties. La première est consacrée à l'étude de la superfluidité dans un gaz de fermions ultra-froids. En utilisant un gaz dégénéré de lithium 6 au voisinage d'une résonance de Feshbach nous avons obtenu un superfluide fermionique et étudié son évolution en fonction de l'énergie de liaison des paires. Afin de caractériser la transition BEC-BCS entre un condensat de Bose-Einstein de molécules et un état BCS de paires de Cooper faiblement liées, nous avons étudié l'expansion du nuage en absence ou en présence d'interactions. Nous avons ainsi extrait la distribution en impulsion du système et sondé son caractère hydrodynamique. La seconde partie concerne la conception et la réalisation d'un montage expérimental de seconde génération. Par rapport à l'ancien dispositif, ses principaux atouts sont un gain d'un ordre de grandeur sur le nombre d'atomes piégés, un bon accès optique, une grande stabilité et reproductibilité ainsi qu'un taux de répétition cinq fois supérieur. La nouvelle expérience a déjà permis d'atteindre le seuil de dégénérescence quantique du lithium 7 avec des performances très satisfaisantes et donne accès à la simulation de hamiltoniens de matière condensée avec des fermions ultra-froids.

Recently a new outlook on dealing with dipolar ultracold fermions based on density functional methods has received attention. A Thomas-Fermi treatment coupled with a variational approach has been developed for a collection of fermions trapped in a harmonic potential interacting via dipole-dipole forces. In this thesis, firstly our alternative formalism for Thomas-Fermi method by performing some calculations based on the Kohn-Sham formalism which is one of the main idea of density functional theory is investigated. Furthermore, density distributions are obtained dependent to the parameters
rescaled interaction strength, dipole-dipole energy and the trap parameter which determine the trap geometry based on this theory. The thesis starts with a brief outline of the density functional theory and theory of our system, continues with calculations based on this theory, which are free of any variational assumptions for the density profile. Moreover, results of density graphics for harmonic trap will be followed by discussion of comparison and contrast with Thomas-Fermi method based on the paper of Goral et al.. These discussions are mainly about the shape of the density distribution, variation of the cloud parameters and energy behaviours according to the rescaled interaction strength. The thesis concludes with an analysis of contribution of density functional theory to this fermionic system.

The present thesis is divided into three parts. In Part I we address a problem within Higher-Spin Gauge Theory in dimension three: namely, that of computing the asymptotic symmetry algebra of supersymmetric models, describing an infinite spectrum of integer and half-integer higher-spin fields. In Part II we investigate higher-spin theories in dimension four or greater, where we classify the consistent cross interactions between free gauge fermions of arbitrary spin and a photon or a graviton. A third part supplements the bulk of the manuscript with technical appendices.

Part I is concerned with the Higher-Spin Theory extending the anti-de Sitter orthosymplectic Supergravity in three dimensions. After recalling the construction of the latter we exhibit the structure of the former, and then explain how to generalize the boundary conditions for Supergravity to the higher-spin case. Following the usual procedure, we compute the form of the residual gauge parameter and then identify the Poisson-bracket algebra governing the asymptotic dynamics. It is found to be a nonlinear, supersymmetric algebra of the W-infinity type with same central charge as pure Gravity in the Virasoro sector, which is a subalgebra thereof. The simply supersymmetric case is treated explicitly whereas the details of the extended cases are relegated to the appendices.

Part II deals with the interaction problem for gauge fermions coupled to Electromagnetism and Gravity in flat spacetime of arbitrary dimension. First we recall the so-called BRST-Antifield techniques, which reformulate the deformation problem as a cohomological one, recasting the familiar Noether procedure for finding out interactions in a mathematically systematic way. We then use these methods to classify and obtain expressions for the gauge-invariant cubic couplings between a symmetric tensor-spinor and a spin-1 and spin-2 gauge field. With no input from previous works, we find the complete list of interaction terms with minimal assumptions and in particular shed light on the quartic obstructions to full consistency.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

Geometric quantization is a subject of finding irreducible representations of certain group or algebra and identifying those equivalent representations by geometric means. Geometric quantization of even dimensional fermionic system has been constructed based on the spinor representation of even dimensional Clifford algebras. Although geometric quantization of odd dimensional fermionic system has not been done, the existence of spinor representations in odd dimension indicates that the geometric quantization is possible. In quantum field theory, charge conjungation can be defined on complex bosons and fermions. Without interaction, the particles and anti-particles essentially have same physical properties. In this thesis, we will first recall the setup of geometric quantization of even dimensional fermion and bosons. Then we will show how to quantize odd dimensional fermion. After that, charge conjungation on complex fermion and boson will be defined and the remaining effort will be put on how to identify the Hilbert spaces produced by different charge conjungations.
published_or_final_version
Mathematics
Master
Master of Philosophy

In this work, we derive the time-dependent Hartree(-Fock) equations as an effective dynamics for fermionic many-particle systems. Our main results are the first for a quantum mechanical mean-field dynamics for fermions; in previous works, the mean-field limit is usually either coupled to a semiclassical limit, or the interaction is scaled down so much, that the system behaves freely for large particle number N. We mainly consider systems with total kinetic energy bounded by const N and long-range interaction potentials, e.g., Coulomb interaction. Examples for such systems are large molecules or certain solid states. Our analysis also applies to attractive interactions, as, e.g., in fermionic stars. The fermionic Hartree(-Fock) equations are a standard tool to describe, e.g., excited states or chemical reactions of large molecules (like proteins). A deeper understanding of these equations as an approximation to the time evolution of a many body quantum system is thus highly relevant. We consider the fermionic Hatree equations (i.e., the Hartree-Fock equations without exchange term) in this work, since the exchange term is subleading in our setting. The main result is that the fermionic Hartree dynamics approximates the Schrödinger dynamics well for large N. This statement becomes exact in the thermodynamic limit N to infinity. We give explicit values for the rates of convergence. We prove two types of results. The first type is very general and concerns arbitrary free Hamiltonians (e.g., relativistic, non-relativistic, with external fields) and arbitrary interactions. The theorems give explicit conditions on the solutions to the fermonic Hartree equations under which a derivation of the mean-field dynamics succeeds. The second type of results scrutinizes situations where the conditions are fulfilled. These results are about non-relativistic free Hamiltonians with external fields, systems with total kinetic energy bounded by const N and with long-range interactions of the form x^(-s), with 0 < s < 6/5 (sometimes, for technical reasons, with a weaker or cut off singularity). We prove our main results by using a new method for deriving mean-field dynamics developed by Pickl in [Lett. Math. Phys., 97(2):151-164, 2011]. This method has been applied successfully in quantum mechanics for deriving the bosonic Hartree and Gross-Pitaevskii equations. Its application to fermions in this work is new. The method is based on a functional that "counts the number of particles outside the condensate", i.e., in the case of fermions, it measures those parts of the Schrödinger wave function that are not in the antisymmetric product of the Hartree states. We show that convergence of the functional to zero (which means that the mean-field equations approximate the dynamics well) is equivalent to convergence of the corresponding reduced one-particle density matrices in trace norm and in Hilbert-Schmidt norm. Finally, we show how also the recently treated semiclassical mean-field limits can be derived with this method.
In dieser Arbeit werden die zeitabhängigen Hartree(-Fock) Gleichungen als effektive Dynamik für fermionische Vielteilchen-Systeme hergeleitet. Die Hauptresultate sind die ersten für eine quantenmechanische Mean-Field Dynamik ("Mittlere-Feld Dynamik") für Fermionen; in vorherigen Arbeiten ist der Mean-Field Limes üblicherweise entweder mit einem semiklassischen Limes gekoppelt oder die Wechselwirkung wird so stark runterskaliert, dass sich das System für große Teilchenzahl N frei verhält. Wir betrachten hauptsächlich Systeme, deren kinetische Energie durch konst N beschränkt ist, und langreichweitige Wechselwirkungen, wie z.B. Coulomb Wechselwirkung. Beispiele für solche Systeme sind große Moleküle oder bestimmte Festkörper. Unsere Analyse gilt auch für anziehende Wechselwirkungen, wie z.B. in fermionischen Sternen. Die fermionischen Hartree(-Fock) Gleichungen sind ein Standardwerkzeug um z.B. angeregte Zustände oder chemische Reaktionen in großen Molekülen (wie Proteinen) zu beschreiben. Ein tieferes Verständnis dieser Gleichungen als Näherung der Zeitentwicklung eines quantenmechanischen Vielteilchen-Systems ist daher äußerst relevant. Wir betrachten in dieser Arbeit die fermionischen Hartree Gleichungen (d.h., die Hartree-Fock Gleichungen ohne Austauschterm), da der Austauschterm in unserem Fall von niedriger Ordnung ist. Das Hauptresultat ist, dass die fermionische Hartree Dynamik die Schrödinger Dynamik für große N gut annähert. Diese Aussage wird im thermodynamischen Limes N gegen unendlich exakt. Wir geben explizite Konvergenzraten an. Es werden zwei Arten von Resultaten bewiesen. Die erste Art ist sehr allgemein und betrifft beliebige freie Hamiltonians (z.B. relativistisch, nicht-relativistisch, mit externen Feldern) und beliebige Wechselwirkungen. Die Theoreme geben explizite Bedingungen an die Lösungen der fermionischen Hartree-Gleichungen an, unter denen eine Herleitung der Mean-Field Dynamik funktioniert. In der zweiten Art von Resultaten wird untersucht für welche Situationen diese Bedingungen erfüllt sind. Diese Resultate sind über nicht-relativistische freie Hamiltonians mit externen Feldern, Systeme mit kinetischer Energie beschränkt durch konst N und mit langreichweitiger Wechselwirkung der Form x^(-s), mit 0 < s < 6/5 (aus technischen Gründen, manchmal mit abgeschnittener oder abgeschwächter Singularität). Die Hauptresultate werden mit einer neuen Methode zur Herleitung von Mean-Field Limiten bewiesen, die von Pickl in [Lett. Math. Phys., 97(2):151-164, 2011] entwickelt wurde. Diese Methode wurde in der Quantenmechanik erfolgreich zur Herleitung der bosonischen Hartree und Gross-Pitaevskii Gleichungen angewandt. Die Anwendung auf Fermionen in dieser Arbeit ist neu. Die Methode basiert auf einem Funktional, das die "Anzahl der Teilchen außerhalb des Kondensats zählt", d.h. im Falle von Fermionen misst es die Anteile der Schrödinger Wellenfunktion, die nicht im antisymmetrisierten Produkt der Hartree-Zustände sind. Wir zeigen, dass die Konvergenz des Funktionals gegen Null (was bedeutet, dass die Mean-Field Gleichungen die Dynamik gut annähern) äquivalent zur Konvergenz der zugehörigen Einteilchen-Dichtematrizen in Spur-Norm und Hilbert-Schmidt-Norm ist. Wir zeigen außerdem wie die kürzlich behandelten semiklassischen Mean-Field Limiten mit dieser Methode hergeleitet werden können.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2017.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 239-251).
This thesis describes experiments on ultracold fermionic atoms, and can be divided into two areas. The first concerns spin-orbit coupling; the second concerns quantum gas microscopy. With the use of Raman transitions, ID spin-orbit coupling of ultracold 6Li was realized. Using a novel type of spectroscopy, spin-injection spectroscopy, where the spin, energy, and momentum are all resolved, we directly observed the spinful dispersions of the spin-orbit bands. In addition, we demonstrated selective adiabatic loading of the spin-orbit bands, which can be used to create a spinless Fermi gas with effective p-wave interactions. Spin-injection spectroscopy was further applied to a novel spinful lattice system created using Raman and radio-frequency coupling, which allowed for state tomography of spinful bands. The second part of this thesis describes quantum gas microscopy of ultracold fermions. This enables one to simulate the Fermi-Hubbard model, a prototypical strongly correlated model, with site-resolved detectioi and control capablities. A new apparatus that can detect fermionic 40K in a square lattice with single-site resolution was constructed. High-fidelity site-resolved imaging was achieved using Raman imaging, which allowed for the direct observation of the band-insulating, the metallic, and the Mott-insulating states of the Hubbard model. The interactiondriven Mott insulator, where doubly occupied sites are highly suppressed, illustrates the strongly correlated nature of the Hubbard model. Harnessing the capability to measure the occupations of individual lattice sites with the microscope, we explored spatial correlations of both spin and charge in the Hubbard model as a function of doping. For the spin correlations, we observed weakening of antiferromagnetic correlations away from half-filling. However, in the charge correlations between local magnetic moments, non-monotonic behavior was observed. This can be understood as arising from competition between Pauli-blocking, dominant at low fillings, and doublon-holon bunching, which arises from superexchange and is strongest at half-filling. The anti-bunching correlations at low filling can be interpreted as the first direct real-space observation of the interaction-enhanced Pauli hole.
by Lawrence W. Cheuk.
Ph. D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2007.
Includes bibliographical references (p. 131-138).
Two sets of studies are described in this thesis. The first describes studies conducted with sodium Bose-Einstein condensates (BEC) while the second focuses on the pairing of fermionic lithium-6 pairs in an optical lattice within the strongly interacting BEC-BCS regime. Common to both sets of studies is the use of a magnetically tunable Feshbach resonance to manipulate interactions between the atoms. In the first experiment, we destabilize a sodium BEC by switching its interactions from repulsive to attractive and studied the resulting dynamics. A local amplification of low momentum energetic instabilities was observed and the measured rate of amplification agreed well with theoretical predictions. For large condensates, this process depleted the condensate faster than the global inward collapse. Subsequently, I describe the major construction effort that was undertaken to convert our BEC machine to a two-species machine capable of cooling fermionic lithium-6. Upon its completion, we obtained a resonance superfluid of loosely bound 6Li pairs in the BECBCS crossover. When placed in a shallow optical lattice, long range phase coherence of this resonance superfluid was inferred from the presence of sharp interference peaks after ballistic expansion. With this observation we have obtained the first evidence of superfluidity of fermions in an optical lattice. A loss in phase coherence occurred when the lattice depth was increased past a critical value, possibly signaling a transition to an insulating state. Further preliminary explorations of this novel system is described followed by an outline of its potential for studying condensed matter phenomena like high temperature superconductivity.
by Jit Kee Chin.
Ph.D.

Etude de divers aspects des theories de jauge sur reseau. Etude de l'ecriture des champs de fermions due a kogut et susskind. Cette formulation reproduit une partie de la symetrie chirale de la theorie continue. Presentation des resultats relatifs aux effets de taille finie agissant sur le parametre d'ordre de cette symetrie et le mode de goldstone associe. Examen de la limite continue d'une modele de theorie des champs bidimensionnelle en interactions dit de gross-neveu. Ceci permet d'etablir que la discretisation de kogut-susskind a le bon comportement necessaire pour reproduire une theorie continue. Cette meme etude explicite la nature des symetries discretes du reseau en terme d'operations du continu. La partie suivante traite de modeles integrables de mecanique statistique presentant une structure analogue aux fermions de kogut-susskind. L'utilisation de methodes de commutation de matrices de transfert nous permet de conclure sur l'integrabilite de tels modeles. La derniere partie etudie les anomalies non-abeliennes des theories de jauge sur reseau. Demonstration de l'absence d'anomalies dans le cas des symetries rigides associees a un groupe compact ou semi-simple. Ceci permet de montrer que le formalisme sur reseau reproduit bien l'anomalie de bardeen

Ce mémoire de thèse est divisé en deux parties. La première est consacrée à l’étude de la superfluidité dans un gaz de fermions ultra-froids. En utilisant un gaz dégénéré de 6Li au voisinage d’une résonance de Feshbach nous avons obtenu un superfluide fermionique et étudié son évolution en fonction de l’énergie de liaison des paires. Afin de caractériser la transition BEC-BCS entre un condensat de Bose-Einstein de molécules et un état BCS de paires de Cooper faiblement liées, nous avons étudié l’expansion du nuage en absence ou en présence d’interactions. Nous avons ainsi extrait la distribution en impulsion du système et sondé son caractère hydrodynamique. La seconde partie concerne la conception et la réalisation d’un montage expérimental de seconde génération. Par rapport à l’ancien dispositif, ses principaux atouts sont un gain d’un ordre de grandeur sur le nombre d’atomes piégés, un bon accès optique, une grande stabilité et reproductibilité ainsi qu’un taux de répétition cinq fois supérieur. La nouvelle expérience a déjà permis d’atteindre le seuil de dégénérescence quantique du 7Li avec des performances très satisfaisantes et donne accès à la simulation de hamiltoniens de matière condensée avec des fermions ultra-froids.

Charge carriers in graphene mimic two-dimensional massless Dirac fermions with linear energy dispersion, resulting in unique optical and electronic properties. They exhibit high mobility and strong interaction with electromagnetic radiation over a broad frequency range. Interband transitions in graphene give rise to pronounced optical absorption in the mid-infrared to visible spectral range, where the optical conductivity is close to a universal value $\sigma_0 = \pi e^2/2h$. Free-carrier intraband transitions, on the other hand, cause low-frequency absorption, which varies significantly with charge density and results in strong light extinction at high carrier density. These properties together suggest a rich variety of possible optoelectronic applications for graphene. In this thesis, we investigate the optoelectronic properties of graphene by measuring transient photoconductivity with optical pump-terahertz probe spectroscopy. We demonstrate that graphene exhibits semiconducting positive photoconductivity near zero carrier density, which crosses over to metallic negative photoconductivity at high carrier density. These observations are accounted for by the interplay between photoinduced changes of both the Drude weight and carrier scattering rate. Our findings provide a complete picture to explain the opposite photoconductivity behavior reported in (undoped) graphene grown epitaxially and (doped) graphene grown by chemical vapor deposition. Our measurements also reveal the non-monotonic temperature dependence of the Drude weight in graphene, a unique property of two-dimensional massless Dirac fermions.
Physics

The constituents of a quantum many-body system can be inextricably linked, a phenomenon known as quantum entanglement. Entanglement can be used as a resource for quantum computing, quantum communication and detecting phase transitions, among others. The amount of entanglement can be quantified via the von Neumann and Rényi entropies, which have their origins in information theory. In this work, the quantum entanglement between subsystems of a one dimen- sional lattice model of fermions is quantified. The von Neumann and Rényi entropies were calculated for two types of subsystems. In the first study, the subsystems were treated as two subsets of particles, and in the second, as two spatial subregions. Finally, by considering particle superselection rules, the amount of entanglement that can actually be accessed as a resource was calcu- lated. In all cases, the quantum entanglement served to detect phase transitions in the model.

The present thesis is devoted to the study of physical phenomena emerging from strong correlations in strongly interacting quantum many-body systems with several components. Hubbard models are widely used as minimal models which take into account the interactions between particles and they have been studied in relation to phenomena such as Mott localization, unconventional superconductivity, quantum magnetism and many others. All of these striking phenomena share their origin from the strong correlations among fermions induced by their mutual interactions. Furthermore, condensed matter models are usually realized only in an approximate fashion in actual solid-state systems, making the situation all the more puzzling and hard to be treated analytically or numerically. Therefore, a great effort has been performed to simulate Hubbard models in a system of atoms cooled down to ultra low temperatures and trapped in optical lattices. The most peculiar feature of cold atoms experiments consists in the possibility of tuning relevant physical parameters of the systems, as the density or the interactions among atoms, using laser and/or magnetic fields. This paved the way to the observation of fundamental quantum states of matter as the weakly interacting Bose-Einstein condensate, the super fluid to Mott insulator transition, the super fluid BEC-BCS crossover, the Mott transition in systems of composite fermions and so on. Hence, it is considered of great interest establishing connections between the quantum simulations cold atomic toolbox and systems realized in solid-state physics...

Ce travail s'intéresse au calcul de la masse des baryons à partir de la théorie décrivant l'interaction forte : la chromodynamique quantique (QCD). Cette théorie régit l'interaction entre les quarks et l es gluons et a pu durant ces dernières décennies être vérifiée à haute énergie grâce à l'une de ses propriétés : la liberté asymptoti que. Celle-ci prédit que les calculs perturbatifs sont valides à haute énergie car la constante de couplage tend vers zéro. Les quantités physiques régissant la physique à basse énergie nécessitent quant à elles un traitement non pertubatif et font l'objet de ce travail. La seule approche con nue permettant de calculer ces observables en contrôlant tous les effets systématiques est la QCD sur réseau. Le C hapitre 1 est une introduction au formalisme de la QCD et à sa formulation discrétisée. Le second chapitre est dédié à la discréti sation particulière utilisée au sein de la collaboration Europan Twisted Mass (ETM). Le Chapitre 3 met en place la technologie nécessaire au calcul des masses des hadrons. L'estimation des intégrales fonctionnelles en utilisant le calcul massi vement parallèle sur des Super Calculateurs est décrite dans le Chapitre 4. La production de configurations de jauge sur ce type d'architecture constitue une part importante du travail effectué durant cette thèse. Le Chapitre 5 est dédié à la formulation des théories effectives dites de pertubations chirales. Les Chapitres 6 et 7 sont consacrés aux baryons légers et étranges. Les eff ets systématiques ainsi que les extrapolations chirales sont largement discutés.

Ce travail s'intéresse au calcul de la masse des baryons à partir de la théorie décrivant l'interaction forte : la chromodynamique quantique (QCD). Cette théorie régit l'interaction entre les quarks et l es gluons et a pu durant ces dernières décennies être vérifiée à haute énergie grâce à l'une de ses propriétés : la liberté asymptoti que. Celle-ci prédit que les calculs perturbatifs sont valides à haute énergie car la constante de couplage tend vers zéro. Les quantités physiques régissant la physique à basse énergie nécessitent quant à elles un traitement non pertubatif et font l'objet de ce travail. La seule approche con nue permettant de calculer ces observables en contrôlant tous les effets systématiques est la QCD sur réseau. Le C hapitre 1 est une introduction au formalisme de la QCD et à sa formulation discrétisée. Le second chapitre est dédié à la discréti sation particulière utilisée au sein de la collaboration Europan Twisted Mass (ETM). Le Chapitre 3 met en place la technologie nécessaire au calcul des masses des hadrons. L'estimation des intégrales fonctionnelles en utilisant le calcul massi vement parallèle sur des Super Calculateurs est décrite dans le Chapitre 4. La production de configurations de jauge sur ce type d'architecture constitue une part importante du travail effectué durant cette thèse. Le Chapitre 5 est dédié à la formulation des théories effectives dites de pertubations chirales. Les Chapitres 6 et 7 sont consacrés aux baryons légers et étranges. Les eff ets systématiques ainsi que les extrapolations chirales sont largement discutés
The aim of this work is an ab initio computation of the baryon masses starting from quantum chromodynamics (QCD). This theory describe the interaction betw een quarks and gluons and has been established at high energy thanks to one of its fundamental properties : the asymptotic freedom. This property predicts th at the running coupling constant tends to zero at high energy and thus that perturbative expansions in the coupling constant are justified in this regime. On the contrary the low energy dynamics can only be understood in terms of a non perturbative approach. To date, the only known method that allows the computat ion of observables in this regime together with a control of its systematic effects is called lattice QCD. It consists in formulating the theory on an Eucl idean space-time and to evaluating numerically suitable functional integrals. The chapter 1 and 2 are an introduction to the QCD in the continuum and on a discrete space time. The chapter 3 deals with the techniques needed to build hadronic correlator starting from gauge configuration. We then discuss how we determine hadron masses and their statistical errors. The numerical estimation of functional integral is explained in chapter 4. It is stressed that it requires sophisticated algorithm and massive parallel computating on BlueGene type architecture. Gauge configuration production is an important part of the work realized during my Ph. D. Chapter 5 is a critical review on chiral perturbation theory in the baryon sector. Th e chapters 6 and 7 are devoted to the analyze in the light and strange baryon sector. Systematics and chiral extrapolation are extensively discussed

Recently the discoveries of graphene, Weyl semi-metal and Dirac semi-metal are drawing more and more people’s attentions back to the topological characteristics of Fermi surfaces, which may be tracked back to the pair of Weyl points observed experimentally in the phase A of Helium three in 80s in the last century. Based on the pioneer works by Volovik and Hořava, we classify all kinds of Fermi surfaces with respect to anti-unitary symmetries and codimensions of Fermi surfaces. The first chapter of this thesis is attributed to develop symmetry-dependent topological invariants to characterize topological properties of Fermi surfaces, and map out the periodic classification tables of Fermi surfaces. Compared with the existing classification of topological insulators (TIs) and superconductors (TSCs), it is observed that there exists a two-step dimension shift from our classification of Fermi surfaces. Actually the two classifications can both be derived rigorously in the framework of K-theory, a mathematical algebraic topology theory for stable fiber bundles, where the dimension shift can also be derived rigorously by constructing maps between Fermi surfaces and TIs/TSCs. This unified treatment of the two classifications is of mathematical elegance, even providing us deeper understandings of these topological phenomena, and is the subject of chapter II of this thesis. In the beginning of chapter III, when applying our theory of topological Fermi surfaces on the boundary of TIs/TSCs, a general index theory is conjectured describing a faithful boundary-bulk correspondence of TIs/TSCs, which is motivated by the dimension shift in the two classifications. Then we construct all kinds of TIs/TSCs and Fermi surfaces by Dirac matrices, which is actually a physical interpretation of the Atiyah-Bott-Shapiro construction as a mathematical theory, and provides us a rigorous proof of our general index theorem. We also provide applications of our theory and its connections to nonlinear sigma models of disordered systems. The last chapter of this thesis may be regarded as a collection of applications of the boundary-bulk correspondence described by the general index theorem for spatially one-dimensional systems. Specifically one-dimensional superconductor models in the other three nontrivial cases are constructed as generalizations of the Kitaev’s model that is one of four nontrivial cases, and every model is solved in detail by methods similar to that provided by Kitaev. Then we analyze each model in the framework of the general index theorem, focusing on the topological properties of Majorana zero-modes with codimension zero at the ends of these models under the open boundary condition. The possible applications of these models to universal quantum manipulations are also discussed.
published_or_final_version
Physics
Doctoral
Doctor of Philosophy

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Nous etudions les fluctuations magnetiques et les proprietes a une particule (1p) du modele de hubbard a 2d, en decrivant les fluctuations de spin par un modele sigma non lineaire (msnl) effectif. Notre theorie suppose l'existence d'un ordre antiferromagnetique (af) a courte portee. Elle est valable pour toute valeur de l'interaction coulombienne u, en dessous d'une temperature de cross-over, ou s'etablit l'ordre af local. Au demi-remplissage, nous traÇons le diagramme de phases magnetique nous montrons qu'a temperature nulle (t=0) l'ordre af existe quelle que soit la valeur de u. Le fondamental evolue continument entre un regime caracteristique de l'af de slater a faible u et un comportement de type mott-heisenberg a grand u. A t>0, l'ordre af disparait, en accord avec le theoreme de mermin-wagner. Cependant, la longueur de correlation af reste tres grande par rapport a la maille du reseau, nous developpons une nouvelle methode de calcul des proproetes a 1p, qui tient compte de la nature non gaussienne des fluctuations de spin. Nous rendons compte d'une transition entre un regime de faible u ou un pseudogap apparait dans le spectre des fermions et un regime de grand u ou les excitations a 1p sont gappees. Nous etudions l'evolution des quasi particules (qp) de bogoliubov a t=o en precurseurs incoherents a t>0. Dans le cas dope, nous presentons une nouvelle technique de derivation de l'action effective de basse energie, celle-ci fait intervenir des qp de bogoliubov au voisinage de la surface de fermi couplees a un msnl decrivant les fluctuations de spin. L'action de basse energie est comparee aux modeles phenomenologiques connus de fermions couples a un msnl
We study magnetic and one-particle properties of the 2d hubbard model within the framework of a non-linear sigma model (nlsm) description of spin fluctuations the theory rests upon the assumption of local antiferromagnetic (af) ordering. It is valid at all coulom interaction strengths, below a cross-over temperature marking the onset of af short-range order. At half-filling, we derive the magnetic phase diagram and compute the fermion spectral function. At zero temperature, long-range af order is shown to be present for all values of the coulomb repulsion. The ground-state exhibits a smooth transition from a slater-like behavior at weak coupling, to a mott-heisenberg-like behavior at strong coupling. At finite temperatures the af order is suppressed, in agreement with the mermin-wagner theorem, but the af correlation length remains exponentially large with respect to the lattice spacing, we develop a new technique for calculating the spectral function and the density of states, which takes into account the highly non-gaussian nature of magnetic fluctuations. We establish the existence of a transition between a weak-coupling regime exhibiting a pseudogap at finite temperatures, and a strong-coupling regime where one-particle excitations are gapped. The properties of bogoliubov quasi particles at zero temperature and of their precursors at finite temperatures are analyzed. Away from half filling, a new method for deriving the low-energy effective action is proposed. The effective model involves low-energy bogoliubov quasi particles coupled to a nlsm. The low-energy action is critically compared to known phenomenological nlsm-fermion theories