Rozprawy doktorskie na temat „Dimensioncal crossover”

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2013.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 163-176).
Experiments using ultracold atomic gases address fundamental problems in many-body physics. This thesis describes experiments on strongly-interacting gases of fermionic atoms, with a focus on non-equilibrium physics and dimensionality. One of the fundamental dissipative processes in two-component gases is the transport of spin due to relative motion between the two spin components. We generate spin transport in strongly-interacting Fermi gases using a spin dipole excitation and measure the transport coefficients describing spin drag and spin diffusion. For resonant interactions, we observe strong suppression of spin transport, with the spin transport coefficients reaching quantum-mechanical limits. Dimensionality plays an important role in the formation of bound states between pairs of particles. We tune the dimensionality of a Fermi gas from three to two dimensions (2D) using an optical lattice potential and observe the evolution of the pair binding energy using radio-frequency spectroscopy. The binding energy increases as the lattice depth increases, approaching the 2D limit. Gases with resonant interactions, which have no two-body bound state in three dimensions, show a large binding energy determined by the confinement energy of the lattice wells. The themes of non-equilibrium dynamics and dimensionality come together in the study of soliton excitations in superfluid Fermi gases. We create a planar defect in the superfluid order parameter of an elongated Fermi gas using detuned laser light. This defect moves through the gas as a solitary wave, or soliton, without dispersing. We measure the oscillation period of the soliton and find it to exceed the predictions of mean-field theory by an order of magnitude.
by Ariel T. Sommer.
Ph.D.

One of the most interesting and challenging problems in physics is understanding strongly correlated many-body systems, where strong interactions can yield many remarkable phenomena such as superfluidity in 4He, high-temperature superconductivity, etc. In order to attack these problems, we often need to reduce the complexity of the systems to simple models in hopes of getting better insights into the properties of the systems. The Hubbard model, the focus of this dissertation, is one of the most famous examples of such model, which describes a tunneling of electrons between nearest neighbor sites of a lattice with on-site interactions. This simple model is an important concept in condensed matter physics and provides rich understandings of electronic and magnetic properties of materials. Despite its simplicity, there is no general analytical solution to the Hubbard model beyond 1D.;The discovery of ultracold atoms and optical lattices opens up the possibility of emulating the Hubbard model in experiments. Optical lattices provide an ideal realization of the Hubbard model where relevant parameters can be tuned systematically. It makes theoretical studies of the Hubbard model increasingly attractive since a direct comparison between theoretical calculations and experimental results becomes more and more possible.;In this dissertation, the ground-state properties of the repulsive Hubbard model for weak to intermediate interaction strengths in two, three dimensions and their dimensional crossover are studied within the mean field theory. We show that the system exhibits unidirectional spin-density wave (SDW) order with antiferromagnetic correlations and a long wavelength modulation. The modulating wave is along the [0011-direction at low interaction strength U/t and along the [1111-direction at higher U/t. The evolution of the wavelength of the SDW is determined as a function of U/t, the density, and t⊥/t. With an analysis of the pairing of spins based on nesting and deformation of the Fermi surface, we discuss how these results can be rationalized and how a simple, predictive model can be constructed for the properties of the SDW states.

Un des modèles théoriques les plus susceptibles d'expliquer le fonctionnement des supraconducteurs à haute température critique (SHTC) est le modèle de Hubbard . On comprend de plus en plus ce qui se passe en une dimension (1D) puisque sa solution est connue. Cependant, les calculs de chaleur spécifique montrent que la nature des excitations du modèle en 1D et en 2D (deux dimensions) n'est vraisemblablement pas la même dans les régimes dits de fort et faible couplage. On peut observer ce qui se passe entre les régimes 1D et 2D en introduisant un paramètre d'anisotropie variant continûment, soit: une intégrale de saut interchaîne t[indice]y , telle que 0 ? t[indice]y ? t[îndice]x ; t[indice]x représente ici l'intégrale de saut entre deux atomes voisins d'une même chaîne. On utilise ici la méthode Monte Carlo quantique développée par Blankenbecler, Scalapino et Sugar (MCQ) (BSS), combinée à une nouvelle technique de calcul de la chaleur spécifique dont l'idée de base est de calculer une dérivée aux différences finies en deux points assez peu éloignés l'un de l'autre, de telle sorte que l'on peut utiliser les mêmes configurations de champs de Hubbard-Stratonovich pour ces deux points et ainsi espérer réduire les effets des fluctuations statistiques. Si l'on se sert du nombre de bosses dans la chaleur spécifique comme critère pour discrimer les régime 1D et 2D (une bosse en 1D et deux bosses en 2D), on conclut que le crossover 1D-2D se situe entre t[indice]y ? 0.4t[indice]x et t[indice]y ? 0.6t[indice]x .

L’exploration de systèmes quantiques à N corps fortement corrélés représente l’un des domaines de recherche les plus stimulants de la physique contemporaine. Au cours des trente dernières années, les vapeurs diluées d’atomes neutres en suspension dans le vide et contrôlées par un laser sont devenues une plate-forme polyvalente et formidable pour l’étude de tels systèmes. L’intérêt principal réside dans la capacité d’ajuster arbitrairement la force de l’interaction atomique au moyen de résonances de Feshbach induites magnétiquement, ainsi que la possibilité de créer une large gamme de potentiels via des champs optiques précisément adaptés. Cette thèse présente les résultats récents de l’expérience FerMix, consacrée à l’étude des systèmes quantiques à plusieurs corps fermioniques à des températures ultra-basses utilisant les atomes alcalins 40K et 6Li. Les principaux résultats présentés dans ce texte sont doubles. Premièrement, nous rapportons la caractérisation expérimentale d’une nouvelle résonance de Feshbach (s,d)-wave du 40K, dont les résultats sont comparés aux prédictions théoriques correspondantes. En particulier, le spectre du taux de perte inélastique est déterminé pour différentes températures et profondeurs de piège, ce qui nous permet d’identifier les pertes en tant que processus à deux corps. De plus, il est confirmé que le canal d’entrée dominant est de type s-wave. À l’aide de modèles d’équation de taux, nous analysons le réchauffement observé de l’ensemble atomique et trouvons que le comportement est cohérent avec l’état lié prévu L = 2 présent dans le canal de sortie. Enfin, nous étudions expérimentalement la dynamique des populations de spin induite par les collisions inélastiques renforcées par résonance dans l’onde d, en observant un bon accord avec nos modèles numériques. En second lieu, nous résumons nos progrès dans l’étude des croisements dimensionnels entre le liquide de Tomonaga-Luttinger en 1D et le liquide de Landau-Fermi en 3D en utilisant les gaz de Fermi de 40K confinés dans un réseau optique à grand pas. Cela inclut à la fois les considérations de conception fondamentales et l’installation du matériel expérimental requis
The exploration of strongly correlated quantum many-body systems represents one of the most challenging fields of research of contemporary physics. Over the past thirty years, dilute vapors of neutral atoms suspended in vacuum and controlled with laser light have become a versatile and powerful platform for the study of such systems. At the very heart lies the ability to arbitrarily tune the interaction strength by means of magnetically induced Feshbach resonances as well as the possibility to create a wide range of potential landscapes via precisely tailored optical fields. This thesis reports on the recent results of the FerMix experiment, which is dedicated to the study of fermionic quantum many-body-systems at ultralow temperatures using the Alkali atoms 40K and 6Li. The main results presented in this text are twofold. First, we report on the experimental characterization of a novel (s,d)-wave Feshbach resonance in 6Li, the results of which are compared to the corresponding theoretical predictions. In particular, the spectrum of the inelastic loss rate is determined for different temperatures and trap depths, which enables us to identify the losses as two-body processes. Moreover, the dominant entrance channel is confirmed to be s-wave in nature. Using rate equation models we analyze the observed heating of the atomic ensemble and find the behavior to be consistent with the predicted L = 2 bound state present in the exit channel. Finally, we investigate experimentally the dynamics of the spin populations driven by resonantly enhanced inelastic collisions in dwave, observing good agreement with our numerical models. Second, we summarize our progress towards the study of dimensional crossovers between the Tomonaga-Luttinger liquid in 1D and the Landau-Fermi liquid in 3D using Fermi gases of 40K confined in a large spacing optical lattice. This includes both the fundamental design considerations as well as the implementation of the required experimental hardware

Cette thèse présente la conception et l'implémentation d'une nouvelle génération de puces à atomes, ouvrant de nouvelles perspectives expérimentales dans des micropièges magnétiques très anisotropes. Les propriétés thermiques des puces en nitrure d'aluminium sont étudiées en détail. Le dispositif a été optimisé pour piéger de plus grands nombres d'atomes et améliorer la qualité de l'imagerie, notamment en fabriquant un miroir de planéité sub-λ/10 à la surface de la puce.Nous étudions des gaz quasi-1D grâce à des images in situ de profils fluctuants et des méthodes précises de calibration et d'analyse statistique. Nous mesurons des fluctuations non-gaussiennes, ce qui permet de tester sensiblement la thermodynamique du gaz et donne une mesure de corrélations à trois corps. Nous étudions précisément la transition de quasicondensation et mesurons pour la première fois sa loi d'échelle. En régime 3D, c'est une condensation transverse qui déclenche la quasicondensation longitudinale, tandis qu'en régime 1D, la formation d'un quasicondensat est gouvernée par les interactions répulsives et non par la dégénérescence quantique.Obtenant des températures record pour des gaz 1D, nous observons des fluctuations subpoissoniennes lorsque les corrélations atomiques sont déterminées, au moins localement, par les fluctuations quantiques qui dominent les fluctuations thermiques. Nous discutons également la thermalisation étonnamment rapide mesurée en régime 1D profond qui suggère que des collisions effectives à 3 corps brisent l'intégrabilité du système.

We present the development of a novel, UHV-compatible device fabrication strategy for the realisation of nano- and atomic-scale devices in silicon by harnessing the atomic-resolution capability of a scanning tunnelling microscope (STM). We develop etched registration markers in the silicon substrate in combination with a custom-designed STM/ molecular beam epitaxy system (MBE) to solve one of the key problems in STM device fabrication ??? connecting devices, fabricated in UHV, to the outside world. Using hydrogen-based STM lithography in combination with phosphine, as a dopant source, and silicon MBE, we then go on to fabricate several planar Si:P devices on one chip, including control devices that demonstrate the efficiency of each stage of the fabrication process. We demonstrate that we can perform four terminal magnetoconductance measurements at cryogenic temperatures after ex-situ alignment of metal contacts to the buried device. Using this process, we demonstrate the lateral confinement of P dopants in a delta-doped plane to a line of width 90nm; and observe the cross-over from 2D to 1D magnetotransport. These measurements enable us to extract the wire width which is in excellent agreement with STM images of the patterned wire. We then create STM-patterned Si:P wires with widths from 90nm to 8nm that show ohmic conduction and low resistivities of 1 to 20 micro Ohm-cm respectively ??? some of the highest conductivity wires reported in silicon. We study the dominant scattering mechanisms in the wires and find that temperature-dependent magnetoconductance can be described by a combination of both 1D weak localisation and 1D electron-electron interaction theories with a potential crossover to strong localisation at lower temperatures. We present results from STM-patterned tunnel junctions with gap sizes of 50nm and 17nm exhibiting clean, non-linear characteristics. We also present preliminary conductance results from a 70nm long and 90nm wide dot between source-drain leads which show evidence of Coulomb blockade behaviour. The thesis demonstrates the viability of using STM lithography to make devices in silicon down to atomic-scale dimensions. In particular, we show the enormous potential of this technology to directly correlate images of the doped regions with ex-situ electrical device characteristics.

We studied the structural instabilities of one-dimensional (1D) and quasi-one-dimensional (Q1D) electron-phonon systems at low temperature through two models, SuSchrieffer-Heeger (SSH) and molecular crystal (CM) with and without spin. The phase diagrams are obtained using a Kadanoff-Wilson renormalization group approach (GR). For the 1D half-filled system the study of the frequency dependence of the electronic gap allowed us to connect continuously the two limits, adiabatic and non-adiabatic. The Peierls and Cooper channels interference and the quantum fluctuations reduce the gap. A regime change occurs when the frequency becomes of the order of mean field gap, marking a quantum-classical crossover that is the Kosterlitz-Thouless type. At this level, the effective coupling behaves in power law function on frequency. For the case with spin, a gapped Peierls state is maintained in the non-adiabatic limit, while for the case without spin, the system transits to ungapped disordered state, namely the Luttinger liquid stat (LL). For the SSH model without spin, the GR confirms the existence of a threshold phonon coupling beyond which the gap is restored. The study of the rigidities of the two models without spin allowed us to trace the main features of the LL state predicted by the bosonization method. The study of the Holstein-Hubbard model has allowed us not only to reproduce the phase diagrams already obtained by the Monte Carlo method, but to highlight two additional phases, namely, free fermions phase and the bond charge-density-wave phase. We have extended this study to the quarter-filled Q1D Peierls systems at finite temperature. Within the SSH model, an unconventional superconducting phase with spin singlet symmetry SS-s emerges at low temperature when the deviation to the perfect nesting of the Fermi surface is strong enough. Peierls-SS transition is characterized by the presence of a quantum critical point at low frequency and by a power law behavior of the transition temperature as a function of frequency with an exponent identical to one of 1D system. This exponent which universality has been verified contrasts with the BCS result. Coulomb interactions have been introduced through the study of the extended SSH-Hubbard model. The extension of this work to half-filled SSH and CM cases was also performed.

碩士
國立臺灣大學
機械工程學研究所
105
In recent years, the biochip technology is flourishing as the demand for medical laboratory has been increasing. However, the phenomenon of dielectrophoresis (DEP) plays an indispensable role in the biochip for many biological and colloidal science application. We can easily manipulate the motion of micro particle with non-contact by changing the alternating current (AC) electric field frequency, the kinds of medium and electrode shape, to separate different properties and size of particle. Then we can reach a variety of biomedical purposes. In dielectrophoresis research, the general calculation of the crossover frequency method include the dipole model and numerical simulations based on Maxwell stress tensor (MST). The dipole model is high computation efficiency but cannot predict the crossover frequency for larger particles or large medium conductivity accurately and the situation of no crossover frequency. The MST method is accuracy but time-consuming and may lack predictive understanding of the interplay between key parameters. Here, we present a mathematical model using Buckingham pi theorem and predict the crossover frequency of different parameter sets and the situation of no crossover frequency. The first research process is dimensional analysis using Buckingham pi theorem. Secondly, we establish a database of electrophoretic parameters using MST simulation and insert them to dimensional parameter set. Third, we can find the relationship between the crossover frequency and five import parameters (medium conductivity, medium permittivity, particle permittivity, particle size and particle surface conductivity) and built mathematical model to predict the crossover frequency of different situations and the situation of no crossover frequency. Finally we compare the results with previous experiment, dipole model and MST. In addition, we explore the reasons for dipole model error and provide physical insights through our mathematic model our research establish.

Ultracold atomic systems have provided an ideal platform to study the physics of strongly interacting many body systems in an unprecedentedly controlled and clean environment. And, since fermions are the building blocks of visible matter, being naturally motivated we focus on the physics of ultracold fermionic systems in this thesis. There have been many recent experimental developments in these systems such as the creation of synthetic gauge fields, realization of dimensional crossover and realization of systems with synthetic dimensions. These developments pose many open theoretical questions, some of which we address in this thesis. We start the discussion by studying the spectral function of an ideal spin-12 Fermi gas in a harmonic trap in any dimensions. We discuss the performance of the local density approximation (LDA) in calculating the spectral function of the system by comparing it to exact numerical results. We show that the LDA gives better results for larger number of particles and in higher dimensions. Fermionic systems with quasi two dimensional geometry are of great importance because of their connections to the high-Tc superconducting cuprate materials. Keeping this in mind, we consider a spin-12 fermionic system in three dimensions interacting with a contact interaction and confined by a one dimensional optical potential in one direction. Using the Bogoliubov-de Gennes formalism, we show that with increasing the depth of the optical potential the three dimensional superfluid evolves into a two dimensional one by looking at the shifts in the radio-frequency spectrum of the system and the change in the binding energy of the pairs that are formed. The next topic of interest is studying the effect of synthetic gauge fields on the ultracold fermionic systems. We show that a synthetic non-Abelian Rashba type gauge field has experimentally observable signatures on the size and shape of a cloud of a system of non-interacting spin-12 Fermi system in a harmonic trap. Also, the synthetic gauge field in conjunction with the harmonic potential gives rise to ample possibilities of generating novel quantum Hamiltonians like the spherical geometry quantum Hall, magnetic monopoles etc. We then address the physics of fermions in “synthetic dimensions”. The hyperfine states of atoms loaded in a one dimensional optical lattice can be used as an extra dimension, called the synthetic dimension (SD), by using Raman coupling. This way a finite strip Hofstadter model is realized with a tunable flux per plaquette. The experimental realization of the SD system is most naturally possible in systems which also have SU(M) symmetric interactions between the fermions. The SU(M) symmetric interactions manifest as long-ranged along the synthetic dimension and is the root cause of all the novel physics in these systems. This rich physics is revealed by a mapping of the Hamiltonian of the system to a system of particles interacting via an SU(M) symmetric interaction under the influence of an SU(M) Zeeman field and a non-Abelian SU(M) gauge field. For example, this equivalence brings out the possibility of generating a non-local interaction between the particles at different sites; while the gauge filed mitigates the baryon (SU(M) singlet M-body bound states) breaking effect of the Zeeman field. As a result, the site localized SU(M) singlet baryon gets deformed and forms a “squished baryon”. Also, finite momentum dimers and resonance like states are formed in the system. Many body physics in the SD system is then studied using both analytical and numerical (Density Matrix Renormalization Group) techniques. This study reveals fascinating possibilities such as the formation of Fulde-Ferrell-Larkin-Ovchinnikov states even without any “imbalance” and the possibility to evolve a “ferromagnet” to a “superfluid” by the application of a magnetic field. Other novel fermionic phases with quasi-condensates of squished baryons are also demonstrated. In summary, the topics addressed in this thesis demonstrate the possibilities and versatilities of the ultracold fermionic systems used in conjunction with synthetic gauge fields and dimensions

When a liquid is cooled below its equilibrium freezing temperature, it becomes supercooled and the molecular motions slow down until the system becomes kinetically arrested, forming a glass, at the glass transition temperature. These amorphous materials have the mechanical properties of a solid while retaining the structural properties of a liquid, but do not exhibit the usual features of a thermodynamic phase transition. As such, they present a number of important challenges to our understanding of the dynamics and thermodynamics of condensed phases. For example, supercooled liquids are classified on the basis of the temperature dependence of their transport properties and structural relaxations times. Strong liquids display an Arrhenius behavior, with the logarithm of their viscosity growing linearly with inverse temperature. Fragile liquids behave in a super-Arrhenius manner, where the viscosity appears to diverge at temperatures above absolute zero, suggesting the possibility of an underlying thermodynamic origin to the glass transition. Some complex, network forming liquids, such as water and silica have also been shown to have a dynamical crossover from fragile to strong liquid behavior as the temperature is decreased. The potential energy landscape paradigm, combined with inherent structure formalism, provide a framework for connecting the way particles pack together with the thermodynamics and dynamics of the liquid and glassy phases. However, the complexity of this multi-dimensional surface makes it difficult to fully characterize and rigorous relationships between the nature of particle packing and glass forming properties have not been established. The goal of this thesis is to study some of the general features of glass transition and find the connection between the dynamics and the thermodynamics of glass forming liquids. To this end, the packing landscapes of quasi-one-dimensional hard discs and hard spheres are studied. A two dimensional system of hard discs with diameter σ, confined between two hard walls (lines) of length L, separated by a distance 1