Measuring topological invariants and chiral Meissner currents with ultracold bosonic atoms

Topologische Invarianten sind von zentraler Bedeutung für die Interpretation vieler Phänomene kondensierter Materie. In dieser Arbeit wird die erste Messung einer solchen Invarianten vorgestellt. Dazu wird ein neu entwickeltes Messprotokoll mit ultrakalten bosonischen Atomen in einem eindimensionalen optischen Gitter verwendet. Außerdem wird die Messung chiraler Meissner-Ströme in einer Leitergeometrie in einem künstlichen Magnetfeld sowie die Präparation sogenannter "Resonating Valence Bond"-Zustände (RVB) in vier Gitterplätze umfassenden Plaketten präsentiert. Das Hauptmerkmal des experimentellen Aufbaus ist ein Paar orthogonaler Übergitter-Potentiale, die es ermöglichen eine Vielzahl verschiedener Systeme zu simulieren. Die Modulation des Übergitters mit einem weiteren Paar interferierender Strahlen ermöglicht zu dem die Realisierung eines künstlichen Magnetfelds. Die Zak-Phase ist eine Invariante, welche die topologischen Eigenschaften eines Energiebandes charakterisiert. Sie ist definiert als die Berry-Phase eines Teilchens bei adiabatischem Durchlaufen eines Pfades im Quasiimpulsraum durch die Brillouinzone. Ein einfaches Beispiel für ein System mit zwei verschiedenen topologischen Klassen ist eine eindimensionale Kette mit alternierender Tunnelkopplungsstärke. Im Experiment können diese Klassen durch Messung der Differenz zwischen ihren Zak-Phasen \Deta\Phi_\text{Zak}\approx\pi unter Verwendung von Bloch-Oszillationen und Ramsey-Interferometrie in Übergittern unterschieden werden. Der zweite Teil dieser Arbeit befasst sich mit der Messung chiraler Meissner-Ströme von Bosonen in einer Leitergeometrie mit magnetischem Fluss, welche eines der einfachsten Modelle zur Beobachtung von Orbitaleffekten ist. Obwohl die Atome ladungsneutral sind und daher keine Lorentzkraft auf sie wirkt, kann durch eine externe Modulation im Übergitter ein künstliches Magnetfeld erzeugt werden. Die dadurch hervorgerufenen Wahrscheinlichkeitsströme auf beiden Seiten der Leiter wurden separat mit einer Projektionsmethode gemessen. Beim Ändern der Tunnelkopplung entlang der Leitersprossen wurde, in Analogie zu einem Typ-II Supraleiter, ein Übergang zwischen einer Meissner-artigen Phase mit gesättigtem maximalen chiralen Strom und einer Vortex-Phase mit abnehmendem Strom beobachtet. Dieses System mit ultrakalten Atomen kann auch als Analogon zur Spin-Bahn-Kopplung betrachtet werden. RVB-Zustände gelten als fundamental für das Verständnis von Hochtemperatursupraleitern. Der dritte Teil der Arbeit widmet sich mit der Realisierung eines Minimalbeispiels solcher Zustände auf einer Plakette bei halber Füllung. In diesem System wurden die zwei RVB-Zustände mit s- und d-Wellen-Symmetrie sowie Superpositionen der beiden Zustände präpariert. Die in dieser Arbeit vorgestellten Experimente stellen einen neuen Ansatz dar, die topologischen Eigenschaften von Bloch-Bändern in optischen Gittern zu untersuchen; sie öffnen die Türen zur Erforschung von wechselwirkenden Teilchen in niedrigdimensionalen Systemen in einem homogenen Magnetfeld sowie der Eigenschaften des Grundzustandes des Heisenberg-Modells.The determination of topological invariants is of fundamental importance to interpret many condensed-matter phenomena. This thesis reports on the implementation of a newly developed protocol to measure these invariants for the first time, using ultracold bosonic atoms in one-dimensional optical lattices. In addition, it deals with the measurement of chiral Meissner currents in a ladder-like lattice geometry exposed to an artificial magnetic field, and presents results on the preparation of Resonating Valence Bond (RVB) states on plaquettes. The key feature of the experimental setup is a pair of orthogonal superlattice potentials that permit a rich variety of systems to be simulated, and that when combined with a pair of interfering beams which periodically modulate the lattice allow the realization of artificial magnetic fields. The Zak phase is an invariant that characterizes the topological properties of an energy band, and is defined as the Berry phase that a particle acquires as it adiabatically moves in the quasimomentum space across the Brillouin zone. A dimerized lattice -- a one-dimensional chain with alternating couplings -- is a simple example of a system that possesses two different topological classes. Using a combination of Bloch oscillations and Ramsey interferometry in superlattices we measured the difference of the Zak phase $\approx\pi$ for the two possible polyacetylene phases, which directly indicates that they belong to different topological classes. The second part of this thesis deals with the measurement of chiral Meissner currents in bosonic ladders with magnetic flux, one of the simplest models to observe orbital effects. Although charge neutrality prevents atoms from experiencing the Lorentz force when they are exposed to a magnetic field, employing lattice modulation techniques we implemented an artificial magnetic field on a ladder created with optical lattices. By using a projection technique, we were able to measure the probability currents on each side of the ladder. When changing the coupling strengths along the rungs of the ladder, we found, in analogy to type-II superconductors, a transition between a Meissner-like phase with saturated maximum chiral current and a vortex phase with decreasing currents. Additionally, the flux ladder realizes spin-orbit coupling with ultracold atoms. It is believed that RVB states are fundamental for the understanding of high-T$_c$ superconductivity. The third part of this work describes our measurements on the preparation of minimum instances of RVB states with bosonic atoms in isolated four-site plaquettes at half filling. These small systems possess two RVB states with $s$- and $d$-wave symmetry. Using atom manipulation techniques we prepared these two states, as well as a quantum resonance between them. The experiments in this thesis establish a new general approach for probing the topological structure of Bloch bands in optical lattices. Moreover, they open up the pathway to exploring interacting particles in low dimensions exposed to uniform magnetic fields and to studying ground state properties of the Heisenberg Hamiltonian

Measuring topological invariants and chiral Meissner currents with ultracold bosonic atoms

Topologische Invarianten sind von zentraler Bedeutung für die Interpretation vieler Phänomene kondensierter Materie. In dieser Arbeit wird die erste Messung einer solchen Invarianten vorgestellt. Dazu wird ein neu entwickeltes Messprotokoll mit ultrakalten bosonischen Atomen in einem eindimensionalen optischen Gitter verwendet. Außerdem wird die Messung chiraler Meissner-Ströme in einer Leitergeometrie in einem künstlichen Magnetfeld sowie die Präparation sogenannter "Resonating Valence Bond"-Zustände (RVB) in vier Gitterplätze umfassenden Plaketten präsentiert. Das Hauptmerkmal des experimentellen Aufbaus ist ein Paar orthogonaler Übergitter-Potentiale, die es ermöglichen eine Vielzahl verschiedener Systeme zu simulieren. Die Modulation des Übergitters mit einem weiteren Paar interferierender Strahlen ermöglicht zu dem die Realisierung eines künstlichen Magnetfelds. Die Zak-Phase ist eine Invariante, welche die topologischen Eigenschaften eines Energiebandes charakterisiert. Sie ist definiert als die Berry-Phase eines Teilchens bei adiabatischem Durchlaufen eines Pfades im Quasiimpulsraum durch die Brillouinzone. Ein einfaches Beispiel für ein System mit zwei verschiedenen topologischen Klassen ist eine eindimensionale Kette mit alternierender Tunnelkopplungsstärke. Im Experiment können diese Klassen durch Messung der Differenz zwischen ihren Zak-Phasen \Deta\Phi_\text{Zak}\approx\pi unter Verwendung von Bloch-Oszillationen und Ramsey-Interferometrie in Übergittern unterschieden werden. Der zweite Teil dieser Arbeit befasst sich mit der Messung chiraler Meissner-Ströme von Bosonen in einer Leitergeometrie mit magnetischem Fluss, welche eines der einfachsten Modelle zur Beobachtung von Orbitaleffekten ist. Obwohl die Atome ladungsneutral sind und daher keine Lorentzkraft auf sie wirkt, kann durch eine externe Modulation im Übergitter ein künstliches Magnetfeld erzeugt werden. Die dadurch hervorgerufenen Wahrscheinlichkeitsströme auf beiden Seiten der Leiter wurden separat mit einer Projektionsmethode gemessen. Beim Ändern der Tunnelkopplung entlang der Leitersprossen wurde, in Analogie zu einem Typ-II Supraleiter, ein Übergang zwischen einer Meissner-artigen Phase mit gesättigtem maximalen chiralen Strom und einer Vortex-Phase mit abnehmendem Strom beobachtet. Dieses System mit ultrakalten Atomen kann auch als Analogon zur Spin-Bahn-Kopplung betrachtet werden. RVB-Zustände gelten als fundamental für das Verständnis von Hochtemperatursupraleitern. Der dritte Teil der Arbeit widmet sich mit der Realisierung eines Minimalbeispiels solcher Zustände auf einer Plakette bei halber Füllung. In diesem System wurden die zwei RVB-Zustände mit s- und d-Wellen-Symmetrie sowie Superpositionen der beiden Zustände präpariert. Die in dieser Arbeit vorgestellten Experimente stellen einen neuen Ansatz dar, die topologischen Eigenschaften von Bloch-Bändern in optischen Gittern zu untersuchen; sie öffnen die Türen zur Erforschung von wechselwirkenden Teilchen in niedrigdimensionalen Systemen in einem homogenen Magnetfeld sowie der Eigenschaften des Grundzustandes des Heisenberg-Modells.The determination of topological invariants is of fundamental importance to interpret many condensed-matter phenomena. This thesis reports on the implementation of a newly developed protocol to measure these invariants for the first time, using ultracold bosonic atoms in one-dimensional optical lattices. In addition, it deals with the measurement of chiral Meissner currents in a ladder-like lattice geometry exposed to an artificial magnetic field, and presents results on the preparation of Resonating Valence Bond (RVB) states on plaquettes. The key feature of the experimental setup is a pair of orthogonal superlattice potentials that permit a rich variety of systems to be simulated, and that when combined with a pair of interfering beams which periodically modulate the lattice allow the realization of artificial magnetic fields. The Zak phase is an invariant that characterizes the topological properties of an energy band, and is defined as the Berry phase that a particle acquires as it adiabatically moves in the quasimomentum space across the Brillouin zone. A dimerized lattice -- a one-dimensional chain with alternating couplings -- is a simple example of a system that possesses two different topological classes. Using a combination of Bloch oscillations and Ramsey interferometry in superlattices we measured the difference of the Zak phase $\approx\pi$ for the two possible polyacetylene phases, which directly indicates that they belong to different topological classes. The second part of this thesis deals with the measurement of chiral Meissner currents in bosonic ladders with magnetic flux, one of the simplest models to observe orbital effects. Although charge neutrality prevents atoms from experiencing the Lorentz force when they are exposed to a magnetic field, employing lattice modulation techniques we implemented an artificial magnetic field on a ladder created with optical lattices. By using a projection technique, we were able to measure the probability currents on each side of the ladder. When changing the coupling strengths along the rungs of the ladder, we found, in analogy to type-II superconductors, a transition between a Meissner-like phase with saturated maximum chiral current and a vortex phase with decreasing currents. Additionally, the flux ladder realizes spin-orbit coupling with ultracold atoms. It is believed that RVB states are fundamental for the understanding of high-T$_c$ superconductivity. The third part of this work describes our measurements on the preparation of minimum instances of RVB states with bosonic atoms in isolated four-site plaquettes at half filling. These small systems possess two RVB states with $s$- and $d$-wave symmetry. Using atom manipulation techniques we prepared these two states, as well as a quantum resonance between them. The experiments in this thesis establish a new general approach for probing the topological structure of Bloch bands in optical lattices. Moreover, they open up the pathway to exploring interacting particles in low dimensions exposed to uniform magnetic fields and to studying ground state properties of the Heisenberg Hamiltonian

Experimental realization of strong effective magnetic fields in an optical lattice

We use Raman-assisted tunneling in an optical superlattice to generate large tunable effective magnetic fields for ultracold atoms. When hopping in the lattice, the accumulated phase shift by an atom is equivalent to the Aharonov-Bohm phase of a charged particle exposed to a staggered magnetic field of large magnitude, on the order of one flux quantum per plaquette. We study the ground state of this system and observe that the frustration induced by the magnetic field can lead to a degenerate ground state for non-interacting particles. We provide a measurement of the local phase acquired from Raman-induced tunneling, demonstrating time-reversal symmetry breaking of the underlying Hamiltonian. Furthermore, the quantum cyclotron orbit of single atoms in the lattice exposed to the magnetic field is directly revealed.Comment: 6 pages, 5 figure

Perturbación escalar en Reissner-Nordström

Tesis (Lic. en Física)--Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física, 2010.Este trabajo trata sobre perturbaciones alrededor de Reissner-Nordström. La perturbación genérica de este sistema, admite un desacoplamiento en armónicos esféricos, y a su vez, en dos modos: escalar y vectorial. El modo vectorial ha sido ya estudiado en forma covariante, no así el escalar. En este trabajo se realiza la formulación covariante del modo escalar, llegando a obtener un conjunto de dos ecuaciones a partir de las cuales se pueden reconstruir las componentes de la métrica y del campo electromagnético perturbado.Marcos Exequiel Atal

Controlling Correlated Tunneling and Superexchange Interactions with AC-Driven Optical Lattices

The dynamical control of tunneling processes of single particles plays a major role in science ranging from Shapiro steps in Josephson junctions to the control of chemical reactions via light in molecules. Here we show how such control can be extended to the regime of strongly interacting particles. Through a weak modulation of a biased tunnel contact, we have been able to coherently control single particle and correlated two-particle hopping processes. We have furthermore been able to extend this control to superexchange spin interactions in the presence of a magnetic-field gradient. We show how such photon assisted superexchange processes constitute a novel approach to realize arbitrary XXZ spin models in ultracold quantum gases, where transverse and Ising type spin couplings can be fully controlled in magnitude and sign.Comment: 10 pages, 9 figure

Direct measurement of the Zak phase in topological Bloch bands

Geometric phases that characterize the topological properties of Bloch bands play a fundamental role in the band theory of solids. Here we report on the measurement of the geometric phase acquired by cold atoms moving in one-dimensional optical lattices. Using a combination of Bloch oscillations and Ramsey interferometry, we extract the Zak phase—the Berry phase gained during the adiabatic motion of a particle across the Brillouin zone—which can be viewed as an invariant characterizing the topological properties of the band. For a dimerized lattice, which models polyacetylene, we measure a difference of the Zak phase δφZak = 0.97(2)π for the two possible polyacetylene phases with different dimerization. The two dimerized phases therefore belong to different topological classes, such that for a filled band, domain walls have fractional quantum numbers. Our work establishes a new general approach for probing the topological structure of Bloch bands inoptical lattices

The cost of type 1 diabetes: a nationwide multicentre study in Brazil

Objective To determine the direct medical costs of type 1 diabetes mellitus (T1DM) to the National Brazilian Health-Care System (NBHCS) and quantify the contribution of each individual component to the total cost.Methods A retrospective, cross-sectional, nationwide multicentre study was conducted between 2008 and 2010 in 28 public clinics in 20 Brazilian cities. the study included 3180 patients with T1DM (mean age 22 year's +/- 11.8) who were surveyed while receiving health care from the NBHCS. the mean duration of their diabetes was 10.3 years (+/- 8.0). the costs of tests and medical procedures, insulin pumps, and supplies for administration, and supplies for self-monitoring of blood glucose (SMBG) were obtained from national and local health system sources for 2010-2011. Annual direct medical costs were derived by adding the costs of medications, supplies, tests, medical consultations, procedures and hospitalizations over the year preceding the interview.Findings the average annual direct medical cost per capita was 1319.15 United States dollars (US$). Treatment-related expenditure - US$ 1216.33 per patient per year represented 92.20% of total direct medical costs. Insulin administration supplies and SMBG (US$696.78 per patient per year) accounted for 52.82$ 75.64 per patient per year) of direct medical costs. Consultations accounted for 1.94% of direct medical costs (US$ 25.62 per patient per year).Conclusion Health technologies accounted for most direct medical costs of T1DM. These data can serve to reassess the distribution of resources for managing T1DM in Brazil's public health-care system.Farmanguinhos/Fundacao Oswaldo Cruz/National Health MinistryBrazilian Diabetes SocietyFundacao do Amparo a Pesquisa do Estado do Rio de JaneiroConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)State Univ Hosp Rio de Janeiro, BR-20551030 Rio de Janeiro, BrazilUniversidade Federal de São Paulo, São Paulo, BrazilBauru Diabet Assoc, Bauru, BrazilJoinville Endocrinol & Diabet Inst, Joinville, BrazilUniversidade Federal de São Paulo, São Paulo, BrazilWeb of Scienc

Nationwide multicenter study on the prevalence of overweight and obesity in type 2 diabetes mellitus in the Brazilian population

AIM: To evaluate the prevalence of overweight and obesity in type 2 diabetic (DM2) outpatients from different regions of Brazil. PATIENTS AND METHODS: We studied 2,519 randomly selected patients, from 11 hospitals, 2 endocrine and one general public care clinics from 10 cities. Overweight was defined as body-mass index (BMI) > 25 and obesity as BMI > 30 kg/m². Glycemic control (GC) was evaluated by GC index (GCI= patient's HbA1 or HbA1c/upper limit of normal for the method x 100). RESULTS: 39% of the population studied was male, the mean age was 58.8 ± 11.6 y, the duration from clinical diagnosis of DM2 was 9.0 ± 7.3y, and BMI was 28.3 ± 5.2 kg/m². No measurements of BMI were recorded from 265 patients (10.5%). Patients from the Northeast presented lower BMI as compared with those from the Midwest, Southeast and South areas, respectively (26.4 ± 4.7 vs. 27.9 ± 4.8 vs. 29.2 ± 5.1 vs. 29.4 ± 5.4 kg/m²; p 25 e obesidade um IMC > 30 kg/m². O controle glicêmico (CG) foi avaliado pelo índice de CG [ICG= HbA1 e ou HbA1c do paciente/limite superior de normalidade do método x 100]. RESULTADOS: Os pacientes tinham idade de 58,8 ± 11,6 anos, tempo de diagnóstico clínico de DM de 9,0 ± 7,3 anos, IMC de 28,3 ± 5,2 kg/m², e 39% eram do sexo masculino. Do total da amostra, 265 pacientes (10,5%) não apresentavam avaliação do IMC. Os pacientes da região Nordeste apresentaram menor IMC em comparação com os das regiões Centro-Oeste, Sudeste e Sul, respectivamente (26,4 ± 4,7 vs. 27,9 ± 4,8 vs. 29,2 ± 5,1 vs. 29,4 ± 5,4 kg/m²; p< 0,001). Houve maior prevalência de obesidade na região Sudeste e Sul em comparação à região Nordeste (p< 0,001) e nos pacientes do sexo feminino, respectivamente (69 vs. 31%; p< 0,001). Os pacientes com peso normal apresentaram menor ICG. Aqueles em tratamento com associação de duas ou mais drogas orais e associação de insulina + droga oral apresentaram maior IMC do que aqueles em tratamento com dieta, hipoglicemiante oral e insulina; p< 0,001. O IMC não diferiu entre os pacientes assistidos ou não por especialistas. CONCLUSÕES: Da população estudada, 75% não estava na faixa de peso ideal, sendo que um terço tinha obesidade. Nossos dados indicam que o sobrepeso e a obesidade já atingem um percentual de pacientes com DM2 no Brasil semelhante ao relatado em estudos europeus, mas ainda menor do que o observado nos EUA. A prevalência de obesidade nos pacientes diabéticos foi três vezes maior do que a observada na população brasileira em geral de acordo com os dados do IBGE.UERJUSPUNIFESP-EPMUNICAMPUNIFEUniversidade Federal do MaranhãoCEDEBVA Serviço de Endocrinologia e DiabetesHospital Agamenon Magalhães Serviços de EndocrinologiaSanta Casa Serviços de EndocrinologiaIAPSEB Serviços de EndocrinologiaHospital Geral Serviços de EndocrinologiaPAM Jaguaribe Serviços de EndocrinologiaSanta Casa Serviço de DiabetesSecretaria Municipal de SaúdeUNIFESP, EPMSciEL