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arXiv:1701.01063

Ultracold Atomic Gases in Artificial Magnetic Fields (PhD thesis)

Klaus Osterloh

Published Jan 4, 2017• 0 citations
arXivHTMLPDF

Abstract

A phenomenon can hardly be found that accompanied physical paradigms and theoretical concepts in a more reflecting way than magnetism. From the beginnings of metaphysics and the first classical approaches to magnetic poles and streamlines of the field, it has inspired modern physics on its way to the classical field description of electrodynamics, and further to the quantum mechanical description of internal degrees of freedom of elementary particles. Meanwhile, magnetic manifestations have posed and still do pose complex and often controversially debated questions. This regards so various and utterly distinct topics as quantum spin systems and the grand unification theory. This may be foremost caused by the fact that all of these effects are based on correlated structures, which are induced by the interplay of dynamics and elementary interactions. It is strongly correlated systems that certainly represent one of the most fascinating and universal fields of research. In particular, low dimensional systems are in the focus of interest, as they reveal strongly pronounced correlations of counterintuitive nature. As regards this framework, the quantum Hall effect must be seen as one of the most intriguing and complex problems of modern solid state physics. Even after two decades and the same number of Nobel prizes, it still keeps researchers of nearly all fields of physics occupied. In spite of seminal progress, its inherent correlated order still lacks understanding on a microscopic level. Despite this, it is obvious that the phenomenon is thoroughly fundamental of nature. To resolve some puzzles of this nature is a key topic of this thesis. (excerpt from abstract)

DOI
10.48550/arxiv.1701.01063

Related papers

Non-Abelian gauge fields

Fabrice Gerbier, Nathan Goldman, Maciej Lewenstein +1 more

Building a universal quantum computer is a central goal of emerging quantum technologies, which has the potential to revolutionize science and technology. Unfortunately, this future does not seem to be very close at hand. However, quantum computers built for a special purpose, i.e. quantum simulators , are currently developed in many leading laboratories. Many schemes for quantum simulation have been proposed and realized using, e.g., ultracold atoms in optical lattices, ultracold trapped ions, atoms in arrays of cavities, atoms/ions in arrays of traps, quantum dots, photonic networks, or superconducting circuits. The progress in experimental implementations is more than spectacular. Particularly interesting are those systems that simulate quantum matter evolving in the presence of gauge fields. In the quantum simulation framework, the generated (synthetic) gauge fields may be Abelian, in which case they are the direct analogues of the vector potentials commonly associated with magnetic fields. In condensed matter physics, strong magnetic fields lead to a plethora of fascinating phenomena, among which the most paradigmatic is perhaps the quantum Hall effect. The standard Hall effect consists in the appearance of a transverse current, when a longitudinal voltage difference is applied to a conducting sample. For quasi-two-dimensional semiconductors at low temperatures placed in very strong magnetic fields, the transverse conductivity, the ratio between the transverse current and the applied voltage, exhibits perfect and robust quantization, independent for instance of the material or of its geometry. Such an integer quantum Hall effect, is now understood as a deep consequence of underlying topological order. Although such a system is an insulator in the bulk, it supports topologically robust edge excitations which carry the Hall current. The robustness of these chiral excitations against backscattering explains the universality of the quantum Hall effect. Another interesting and related effect, which arises from the interplay between strong magnetic field and lattice potentials, is the famous Hofstadter butterfly: the energy spectrum of a single particle moving on a lattice and subjected to a strong magnetic field displays a beautiful fractal structure as a function of the magnetic flux penetrating each elementary plaquette of the lattice. When the effects of interparticle interactions become dominant, two-dimensional gases of electrons exhibit even more exotic behaviour leading to the fractional quantum Hall effect. In certain conditions such a strongly interacting electron gas may form a highly correlated state of matter, the prototypical example being the celebrated Laughlin quantum liquid. Even more fascinating is the behaviour of bulk excitations (quasi-hole and quasi-particles): they are neither fermionic nor bosonic, but rather behave as anyons with fractional statistics intermediate between the two. Moreover, for some specific filling factors (ratio between the electronic density and the flux density), these anyons are proven to have an internal structure (several components) and non-Abelian braiding properties. Many of the above statements concern theoretical predictions—they have never been observed in condensed matter systems. For instance, the fractional values of the Hall conductance is seen as a direct consequence of the fractional statistics, but to date direct observation of anyons has not been possible in two-dimensional semiconductors. Realizing these predictions in experiments with atoms, ions, photons etc, which potentially allow the experimentalist to perform measurements complementary to those made in condensed matter systems, is thus highly desirable! Non-Abelian gauge fields couple the motional states of the particles to their internal degrees of freedom (such as hyperfine states for atoms or ions, electronic spins for electrons, etc). In this sense external non-Abelian fields extend the concept of spin–orbit coupling (Rashba and Dresselhaus couplings), familiar from AMO and condensed matter physics. They lead to yet another variety of fascinating phenomena such as the quantum spin Hall effect, three-dimensional topological insulators, topological superconductors and superfluids of various kinds. One also expects here the appearance of excitations in a form of topological edge states that can support robust transport, or entangled Majorana fermions in the case of topological superconductors or superfluids. Again, while many kinds of topological insulators have been realized in condensed matter systems, a controlled way of creating them in AMO systems and studying quantum phase transitions between various kinds of them is obviously very appealing and challenging. The various systems listed so far correspond to static gauge fields, which are externally imposed by the experimentalists. Even more fascinating is the possibility of generating synthetically dynamical gauge fields, i.e. gauge fields that evolve in time according to an interacting gauge theory, e.g., a full lattice gauge theory (LGT). These dynamical gauge fields can also couple to matter fields, allowing the quantum simulation of such complex systems (notoriously hard to simulate using 'traditional' computers), which are particularly relevant for modern high-energy physics. So far, most of the theoretical proposals concern the simulation of Abelian gauge theories, however, several groups have recently proposed extensions to the non-Abelian scenarios. The scope of the present focused issue of Journal of Physics B is to cover all of these developments, with particular emphasis on the non-Abelian gauge fields. The 14 papers in this issue include contributions from the leading theory groups working in this field; we believe that this collection will provide the reference set for quantum simulations of gauge fields. Although the special issue contains exclusively theoretical proposals and studies, it should be stressed that the progress in experimental studies of artificial Abelian and non-Abelian gauge fields in recent years has been simply spectacular. Multiple leading groups are working on this subject and have already obtained a lot of seminal results. The papers in the special issue are ordered according to the date of acceptance. The issue opens with a review article by Zhou et al [1] on unconventional states of bosons with synthetic spin–orbit coupling. Next, the paper by Maldonado-Mundo et al [2] studies ultracold Fermi gases with artificial Rashba spin–orbit coupling in a 2D gas. Anderson and Charles [3], in contrast, discuss a three-dimensional spin–orbit coupling in a trap. Orth et al [4] investigate correlated topological phases and exotic magnetism with ultracold fermions, again in the presence of artificial gauge fields. The paper of Nascimbène [5] does not address the synthetic gauge fields directly, but describes an experimental proposal for realizing one-dimensional topological superfluids with ultracold atomic gases; obviously, this problem is well situated in the general and growing field of topological superfluids, in particular those realized in the presence of non-Abelian gauge fields/spin–orbit coupling. Graß et al [6] consider in their paper fractional quantum Hall states of a Bose gas with spin–orbit coupling induced by a laser. Particular attention is drawn here to the possibility of realizing states with non-Abelian anyonic excitations. Zheng et al [7] study properties of Bose gases with Raman-induced spin–orbit coupling. Kiffner et al [8] in their paper touch on another kind of system, namely ultracold Rydberg atoms. In particular they study the generation of Abelian and non-Abelian gauge fields in dipole–dipole interacting Rydberg atoms. The behaviour of fermions in synthetic non-Abelian gauge potentials is discussed by Shenoy and Vyasanakere [9]. The paper starts with the study of Rashbon condensates (i.e. Bose condensates in the presence of Rashba coupling) and also introduces novel kinds of exotic Hamiltonians. Goldman et al [10] propose a concrete setup for realizing arbitrary non-Abelian gauge potentials in optical square lattices; they discuss how such synthetic gauge fields can be exploited to generate Chern insulators. Zygelman [11], similarly as Kiffner et al [8], discusses in his paper non-Abelian gauge fields in Rydberg systems. Marchukov et al [12] return to the subject of spin–orbit coupling, and investigate spectral gaps of spin–orbit coupled particles in the realistic situations of deformed traps. The last two papers, in contrast, are devoted to different subjects. Edmonds et al [13] consider a 'dynamical' density-dependent gauge potential, and study the Josephson effect in a Bose–Einstein condensate subject to such a potential. Last, but not least, Mazzucchi et al [14] study the properties of semimetal-superfluid quantum phase transitions in 3D lattices with Dirac points. References [1] Zhou X, Li Y, Cai Z and Wu C 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134001 [2] Maldonado-Mundo D, Öhberg P and Valiente M 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134002 [3] Anderson B M and Clark C W 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134003 [4] Orth P P, Cocks D, Rachel S, Buchhold M, Le Hur K and Hofstetter W 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134004 [5] Nascimbène S 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134005 [6] Graß T, Juliá-Díaz B, Burrello M and Lewenstein M 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134006 [7] Zheng W, Yu Z-Q, Cui X and Zhai H 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134007 [8] Kiffner M, Li W and Jaksch D 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134008 [9] Shenoy V B and Vyasanakere J P 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134009 [10] Goldman N, Gerbier F and Lewenstein M 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134010 [11] Zygelman B 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134011 [12] Marchukov O V, Volosniev A G, Fedorov D V, Jensen A S and Zinner N T 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134012 [13] Edmonds M J, Valiente M and Öhberg P 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134013 [14] Mazzucchi G, Lepori L and Trombettoni A 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134014

Journal of Physics B Atomic Molecular and Optical Physics•Jun 24, 2013•11 citations

Hydrodynamics of Bose gases with internal degrees of freedom

J. Armaitis

Just a couple decades ago bosonic low-temperature physics was synonymous with one particular liquid at a temperature of several degrees Kelvin. This liquid, helium-4, and its famous Helium-II phase, has revealed remarkable quantum properties such as quantized vortices and second sound. Yet, despite many things learned by investigating helium, its study has certain limitations. On the one hand, helium is a strongly interacting liquid, which makes first-principles theoretical research challenging. To name one example, establishing a connection between the non-interacting condensate state described by Bose and Einstein, and the helium properties observed in the lab took decades. Furthermore, helium is a specific chemical element, and hence there is no surprise that its physical properties are fixed by nature. However, every particular chemical element has particular physical properties, so for a long time it seemed that it was as good as it gets. The picture has changed drastically when the first Bose-Einstein condensate (BEC) was observed in an ultracold atomic gas. “Low temperature” has become synonymous with “ultracold”, and the latter implies temperatures on the order of nanokelvins. Most strikingly, the relationship between what is fixed by nature and what is experimentally changeable has evolved. In particular, systems of different particle statistics, spin, and interactions have been engineered using ultracold vapours of various alkali atoms. This versatile manipulation not only makes emulating various condensed-matter physics models in a controlled system without impurities possible, but also opens a path towards novel phenomena that are at present not achievable in any other manner. In this thesis, we have explored some of the novel phenomena that arise in systems of bosonic particles with internal degrees of freedom, such as (pseudo)spin and electric dipole moment. In the introduction, we describe a ferromagnetically coupled spin-1/2 Bose gas with contact interactions in the mean- field approximation. In particular, we compute and discuss the phase diagram of this gas, since it is a simple system which nevertheless has two order parameters. In the chapters that follow, the ideas touched upon in the introduction are developed in more detail. In Chapter 2 we develop a hydrodynamic description of the ferromagnetic spin-1/2 Bose gas at arbitrary temperatures. We study magnetization relaxation and geometric forces. In particular, we consider the topological Hall effect due to the presence of a skyrmion. In Chapter 3 we investigate the miscible (non-ferromagnetic) spin-1/2 Bose gas at arbitrary temperatures, construct its hydrodynamic description, calculate the thermodynamic properties, and study the collective modes of this system. In Chapter 4 we discuss the influence of the off-diagonal Berry curvature on the Bose-Einstein condensation temperature. Finally, in Chapter 5 we study a Bose-Einstein condensate of dipolar molecules in a weak electric field and find it to be described by a quantum rotor model. Moreover, we show that the molecular Bose-Einstein condensate is a ferroelectric material that is fully disordered by quantum fluctuations.

•Jun 3, 2015•0 citations

Low dimensional magnetism

Jonas A. Kjäll

Magnetism is a subject that has fascinated mankind for countless generations. With the development of quantum mechanics around a century ago a fundamental understanding of many of the underlying causes of magnetism were obtained. However, the long range interaction combined with the complex systems magnetism appears in makes it very hard to investigate it. In our days this research area is more active than ever, mainly due to future demand of the electronic industry for components engineered down to the atomic level. Quantum effects gets more important at short scales, especially in lower dimensional materials like sheets and wires. The rapidly increasing amount of computational power available makes the numerical techniques a more important part of the research effort. Many of these are especially well suited to analyze lower dimensional quantum problems. 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In a recent experiment on CoNb2O6, Coldea et. al. found for the first time experimental evidence of the exceptional Lie algebra E8. The emergence of this symmetry was theoretically predicted long ago for the transverse quantum Ising chain in the presence of a weak longitudinal field. We consider an accurate microscopic model of CoNb2O6 incorporating additional couplings and calculate numerically the dynamical structure function using a recently developed matrix-product-state method. The excitation spectra show bound states characteristic of the weakly broken $textrm{E}_8$ symmetry. We compare the observed bound state signatures in this model to those found in the transverse Ising chain in a longitudinal field and to experimental data.Finally, we investigate the ground state phase diagram of a related quantum spin chain, the S=2 XXZ chain with single-ion anisotropy. 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•Jan 1, 2012•0 citations

Spin-Motion Coupling in Cold Atomic Gases

Andrew Koller

The interplay between spin and motional degrees of freedom in interacting electron systems has been a long-standing research topic in condensed matter physics. Interactions can modify the behavior of individual electrons and give rise to emergent collective phenomena such as superconductivity and colossal magnetoresistance. Theoretical understanding of non-equilibrium dynamics in interacting fermionic matter is limited, however, and many open questions remain. Ultracold atomic Fermi gases, with precisely controllable parameters, offer an outstanding opportunity to investigate the emergence of collective behavior in out-of-equilibrium settings. In this thesis we will describe how an optical lattice clock operated with neutral Fermionic atoms can be turned into a quantum simulator of charged particles in a strong magnetic field. We will then discuss the counterintuitive notion that weak interactions in a Fermi gas can lead to large scale collective behavior and global correlations. These ideas are being tested experimentally at JILA and the University of Toronto. We also investigate in detail the so-called spin model approximation which is used extensively throughout this thesis.

•Jan 1, 2017•1 citation

Ultracold atoms in artificial gauge fields

Tobias Graß

The present thesis studies a variety of cold atomic systems in artificial gauge fields. In the first part we focus on fractional quantum Hall effects, asking whether interesting topological states can be realized with cold atoms. We start by making a close connection to solid-state systems and first consider fermionic atoms with dipolar interactions. Assuming the system to be in the Laughlin state, we evaluate the energy gap in the thermodynamic limit as a measure for the robustness of the state. We show that it can be increased by additionally applying a non-Abelian gauge field squeezing the Landau levels. We then switch to bosonic systems with repulsive contact interactions. Artificial magnetic fields for cold bosons have extensively been discussed before in the context of rotating Bose gases. We follow a different approach where the gauge field is due to an atom-laser coupling. Thus, transitions between different dressed states have to be included. They are shown to break the cylindrical symmetry of the system. Modifying the Laughlin state and the Moore-Read state accordingly, we determine the parameter regimes where they are good representations for the ground state of the system obtained via exact diagonalization. One of the most interesting feature of fractional quantum Hall states is the anyonic behavior of their excitations. We therefore also study quasiholes in the Laughlin state and the modified Laughlin state. They are shown to posses anyonic properties, which become manifest even in small systems. Moreover, the dynamics of a single quasihole causes visible traces in the density of the system which allow to clearly distinguish the Laughlin regime from less correlated phases. In the latter, a sequence of collapses and revivals of the quasihole can be observed, which is absent in the Laughlin regime. Extending our study to bosonic systems with a pesudospin-1/2 degree of freedom, we discuss the formation of strongly correlated spin singlets. Strikingly, at filling v=4/3, the system is described by a state with non-Abelian excitations, which is constructed as the zero-energy ground state of repulsive three-body contact interactions. Systems with internal degrees of freedom also allow for implementing artificial spin-orbit coupling. It is shown to give rise to a variety of incompressible states. In the second part of the thesis, we concentrate on condensed system. Bose-Einstein condensates with spin-orbit coupling are shown to have a degeneracy on the mean-field level, which is lifted by quantum and thermal fluctuations. The system becomes experimentally feasible in three dimensions, where the condensate depletion remains finite, and thus allow for an experimental observation of this order-by-disorder mechanism. Finally, we study the influence of Abelian and non-Abelian gauge fields on the quantum phase transitions of bosons in a square optical lattice. Re-entrant superfluid phases and superfluids at finite momenta are interesting properties featured by such systems.

•Apr 23, 2013•3 citations

Strongly Correlated States in Low Dimensions (Thesis)

Dmitry Green

This thesis is a theoretical analysis of sample two- and one-dimensional systems. The two-dimensional examples are the quantum Hall liquid and anomalous paired states. The most widely accepted effective theory of the quantum Hall liquid is based on the so-called Chern Simons Lagrangian, but it is not entirely satisfactory. We obtain the first derivation of an alternative effective theory from microscopic principles. Our formulation allows for a first principles derivation of physical quantities such as the effective mass and compressibility and contains the first analytical observation of the magnetoroton. The formalism developed along the way is also applied to paired states in anomalous supeconductors, a topic of much recent interest. The one-dimenisonal system is the carbon nanotube. Gas uptake in nanotube bundles is currently attracting a wealth of research with both applied and fundamental implications. We propose adsorption of gases on the surface of a single tube, finding strong correlations and symmetries that have not been observed yet. The properties of these states are directly relevant to other one-dimensional structures such as spin ladders and stripes and raise interesting and open questions.

arXiv:cond-mat/0202455•Feb 26, 2002•1 citation
A phenomenon can hardly be found that accompanied physical paradigms and theoretical concepts in a more reflecting way than magnetism. From the beginnings of metaphysics and the first classical approaches to magnetic poles and streamlines of the field, it has inspired modern physics on its way to the classical field description of electrodynamics, and further to the quantum mechanical description of internal degrees of freedom of elementary particles. Meanwhile, magnetic manifestations have posed and still do pose complex and often controversially debated questions. This regards so various and utterly distinct topics as quantum spin systems and the grand unification theory. This may be foremost caused by the fact that all of these effects are based on correlated structures, which are induced by the interplay of dynamics and elementary interactions. It is strongly correlated systems that certainly represent one of the most fascinating and universal fields of research. In particular, low dimensional systems are in the focus of interest, as they reveal strongly pronounced correlations of counterintuitive nature. As regards this framework, the quantum Hall effect must be seen as one of the most intriguing and complex problems of modern solid state physics. Even after two decades and the same number of Nobel prizes, it still keeps researchers of nearly all fields of physics occupied. In spite of seminal progress, its inherent correlated order still lacks understanding on a microscopic level. Despite this, it is obvious that the phenomenon is thoroughly fundamental of nature. To resolve some puzzles of this nature is a key topic of this thesis. (excerpt from abstract)
Building a universal quantum computer is a central goal of emerging quantum technologies, which has the potential to revolutionize science and technology. Unfortunately, this future does not seem to be very close at hand. However, quantum computers built for a special purpose, i.e. quantum simulators , are currently developed in many leading laboratories. Many schemes for quantum simulation have been proposed and realized using, e.g., ultracold atoms in optical lattices, ultracold trapped ions, atoms in arrays of cavities, atoms/ions in arrays of traps, quantum dots, photonic networks, or superconducting circuits. The progress in experimental implementations is more than spectacular. Particularly interesting are those systems that simulate quantum matter evolving in the presence of gauge fields. In the quantum simulation framework, the generated (synthetic) gauge fields may be Abelian, in which case they are the direct analogues of the vector potentials commonly associated with magnetic fields. In condensed matter physics, strong magnetic fields lead to a plethora of fascinating phenomena, among which the most paradigmatic is perhaps the quantum Hall effect. The standard Hall effect consists in the appearance of a transverse current, when a longitudinal voltage difference is applied to a conducting sample. For quasi-two-dimensional semiconductors at low temperatures placed in very strong magnetic fields, the transverse conductivity, the ratio between the transverse current and the applied voltage, exhibits perfect and robust quantization, independent for instance of the material or of its geometry. Such an integer quantum Hall effect, is now understood as a deep consequence of underlying topological order. Although such a system is an insulator in the bulk, it supports topologically robust edge excitations which carry the Hall current. The robustness of these chiral excitations against backscattering explains the universality of the quantum Hall effect. Another interesting and related effect, which arises from the interplay between strong magnetic field and lattice potentials, is the famous Hofstadter butterfly: the energy spectrum of a single particle moving on a lattice and subjected to a strong magnetic field displays a beautiful fractal structure as a function of the magnetic flux penetrating each elementary plaquette of the lattice. When the effects of interparticle interactions become dominant, two-dimensional gases of electrons exhibit even more exotic behaviour leading to the fractional quantum Hall effect. In certain conditions such a strongly interacting electron gas may form a highly correlated state of matter, the prototypical example being the celebrated Laughlin quantum liquid. Even more fascinating is the behaviour of bulk excitations (quasi-hole and quasi-particles): they are neither fermionic nor bosonic, but rather behave as anyons with fractional statistics intermediate between the two. Moreover, for some specific filling factors (ratio between the electronic density and the flux density), these anyons are proven to have an internal structure (several components) and non-Abelian braiding properties. Many of the above statements concern theoretical predictions—they have never been observed in condensed matter systems. For instance, the fractional values of the Hall conductance is seen as a direct consequence of the fractional statistics, but to date direct observation of anyons has not been possible in two-dimensional semiconductors. Realizing these predictions in experiments with atoms, ions, photons etc, which potentially allow the experimentalist to perform measurements complementary to those made in condensed matter systems, is thus highly desirable! Non-Abelian gauge fields couple the motional states of the particles to their internal degrees of freedom (such as hyperfine states for atoms or ions, electronic spins for electrons, etc). In this sense external non-Abelian fields extend the concept of spin–orbit coupling (Rashba and Dresselhaus couplings), familiar from AMO and condensed matter physics. They lead to yet another variety of fascinating phenomena such as the quantum spin Hall effect, three-dimensional topological insulators, topological superconductors and superfluids of various kinds. One also expects here the appearance of excitations in a form of topological edge states that can support robust transport, or entangled Majorana fermions in the case of topological superconductors or superfluids. Again, while many kinds of topological insulators have been realized in condensed matter systems, a controlled way of creating them in AMO systems and studying quantum phase transitions between various kinds of them is obviously very appealing and challenging. The various systems listed so far correspond to static gauge fields, which are externally imposed by the experimentalists. Even more fascinating is the possibility of generating synthetically dynamical gauge fields, i.e. gauge fields that evolve in time according to an interacting gauge theory, e.g., a full lattice gauge theory (LGT). These dynamical gauge fields can also couple to matter fields, allowing the quantum simulation of such complex systems (notoriously hard to simulate using 'traditional' computers), which are particularly relevant for modern high-energy physics. So far, most of the theoretical proposals concern the simulation of Abelian gauge theories, however, several groups have recently proposed extensions to the non-Abelian scenarios. The scope of the present focused issue of Journal of Physics B is to cover all of these developments, with particular emphasis on the non-Abelian gauge fields. The 14 papers in this issue include contributions from the leading theory groups working in this field; we believe that this collection will provide the reference set for quantum simulations of gauge fields. Although the special issue contains exclusively theoretical proposals and studies, it should be stressed that the progress in experimental studies of artificial Abelian and non-Abelian gauge fields in recent years has been simply spectacular. Multiple leading groups are working on this subject and have already obtained a lot of seminal results. The papers in the special issue are ordered according to the date of acceptance. The issue opens with a review article by Zhou et al [1] on unconventional states of bosons with synthetic spin–orbit coupling. Next, the paper by Maldonado-Mundo et al [2] studies ultracold Fermi gases with artificial Rashba spin–orbit coupling in a 2D gas. Anderson and Charles [3], in contrast, discuss a three-dimensional spin–orbit coupling in a trap. Orth et al [4] investigate correlated topological phases and exotic magnetism with ultracold fermions, again in the presence of artificial gauge fields. The paper of Nascimbène [5] does not address the synthetic gauge fields directly, but describes an experimental proposal for realizing one-dimensional topological superfluids with ultracold atomic gases; obviously, this problem is well situated in the general and growing field of topological superfluids, in particular those realized in the presence of non-Abelian gauge fields/spin–orbit coupling. Graß et al [6] consider in their paper fractional quantum Hall states of a Bose gas with spin–orbit coupling induced by a laser. Particular attention is drawn here to the possibility of realizing states with non-Abelian anyonic excitations. Zheng et al [7] study properties of Bose gases with Raman-induced spin–orbit coupling. Kiffner et al [8] in their paper touch on another kind of system, namely ultracold Rydberg atoms. In particular they study the generation of Abelian and non-Abelian gauge fields in dipole–dipole interacting Rydberg atoms. The behaviour of fermions in synthetic non-Abelian gauge potentials is discussed by Shenoy and Vyasanakere [9]. The paper starts with the study of Rashbon condensates (i.e. Bose condensates in the presence of Rashba coupling) and also introduces novel kinds of exotic Hamiltonians. Goldman et al [10] propose a concrete setup for realizing arbitrary non-Abelian gauge potentials in optical square lattices; they discuss how such synthetic gauge fields can be exploited to generate Chern insulators. Zygelman [11], similarly as Kiffner et al [8], discusses in his paper non-Abelian gauge fields in Rydberg systems. Marchukov et al [12] return to the subject of spin–orbit coupling, and investigate spectral gaps of spin–orbit coupled particles in the realistic situations of deformed traps. The last two papers, in contrast, are devoted to different subjects. Edmonds et al [13] consider a 'dynamical' density-dependent gauge potential, and study the Josephson effect in a Bose–Einstein condensate subject to such a potential. Last, but not least, Mazzucchi et al [14] study the properties of semimetal-superfluid quantum phase transitions in 3D lattices with Dirac points. References [1] Zhou X, Li Y, Cai Z and Wu C 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134001 [2] Maldonado-Mundo D, Öhberg P and Valiente M 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134002 [3] Anderson B M and Clark C W 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134003 [4] Orth P P, Cocks D, Rachel S, Buchhold M, Le Hur K and Hofstetter W 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134004 [5] Nascimbène S 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134005 [6] Graß T, Juliá-Díaz B, Burrello M and Lewenstein M 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134006 [7] Zheng W, Yu Z-Q, Cui X and Zhai H 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134007 [8] Kiffner M, Li W and Jaksch D 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134008 [9] Shenoy V B and Vyasanakere J P 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134009 [10] Goldman N, Gerbier F and Lewenstein M 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134010 [11] Zygelman B 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134011 [12] Marchukov O V, Volosniev A G, Fedorov D V, Jensen A S and Zinner N T 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134012 [13] Edmonds M J, Valiente M and Öhberg P 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134013 [14] Mazzucchi G, Lepori L and Trombettoni A 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134014
Just a couple decades ago bosonic low-temperature physics was synonymous with one particular liquid at a temperature of several degrees Kelvin. This liquid, helium-4, and its famous Helium-II phase, has revealed remarkable quantum properties such as quantized vortices and second sound. Yet, despite many things learned by investigating helium, its study has certain limitations. On the one hand, helium is a strongly interacting liquid, which makes first-principles theoretical research challenging. To name one example, establishing a connection between the non-interacting condensate state described by Bose and Einstein, and the helium properties observed in the lab took decades. Furthermore, helium is a specific chemical element, and hence there is no surprise that its physical properties are fixed by nature. However, every particular chemical element has particular physical properties, so for a long time it seemed that it was as good as it gets. The picture has changed drastically when the first Bose-Einstein condensate (BEC) was observed in an ultracold atomic gas. “Low temperature” has become synonymous with “ultracold”, and the latter implies temperatures on the order of nanokelvins. Most strikingly, the relationship between what is fixed by nature and what is experimentally changeable has evolved. In particular, systems of different particle statistics, spin, and interactions have been engineered using ultracold vapours of various alkali atoms. This versatile manipulation not only makes emulating various condensed-matter physics models in a controlled system without impurities possible, but also opens a path towards novel phenomena that are at present not achievable in any other manner. In this thesis, we have explored some of the novel phenomena that arise in systems of bosonic particles with internal degrees of freedom, such as (pseudo)spin and electric dipole moment. In the introduction, we describe a ferromagnetically coupled spin-1/2 Bose gas with contact interactions in the mean- field approximation. In particular, we compute and discuss the phase diagram of this gas, since it is a simple system which nevertheless has two order parameters. In the chapters that follow, the ideas touched upon in the introduction are developed in more detail. In Chapter 2 we develop a hydrodynamic description of the ferromagnetic spin-1/2 Bose gas at arbitrary temperatures. We study magnetization relaxation and geometric forces. In particular, we consider the topological Hall effect due to the presence of a skyrmion. In Chapter 3 we investigate the miscible (non-ferromagnetic) spin-1/2 Bose gas at arbitrary temperatures, construct its hydrodynamic description, calculate the thermodynamic properties, and study the collective modes of this system. In Chapter 4 we discuss the influence of the off-diagonal Berry curvature on the Bose-Einstein condensation temperature. Finally, in Chapter 5 we study a Bose-Einstein condensate of dipolar molecules in a weak electric field and find it to be described by a quantum rotor model. Moreover, we show that the molecular Bose-Einstein condensate is a ferroelectric material that is fully disordered by quantum fluctuations.
Magnetism is a subject that has fascinated mankind for countless generations. With the development of quantum mechanics around a century ago a fundamental understanding of many of the underlying causes of magnetism were obtained. However, the long range interaction combined with the complex systems magnetism appears in makes it very hard to investigate it. In our days this research area is more active than ever, mainly due to future demand of the electronic industry for components engineered down to the atomic level. Quantum effects gets more important at short scales, especially in lower dimensional materials like sheets and wires. The rapidly increasing amount of computational power available makes the numerical techniques a more important part of the research effort. Many of these are especially well suited to analyze lower dimensional quantum problems. Three of the most important techniques, (classical) Monte Carlo, Exact Diagonalization (ED) and matrix product states (MPS) based techniques, like density renormalization group (DMRG) and time evolving block decimation (TEBD) will be described in some detail and put to use later in this dissertation.With the rapid development of experimental techniques for ultracold gases in optical traps a new approach to investigate magnetic properties that are hard achieve or control in the solid state has emerged. We first study the ground-state phase diagram of a spin-1 condensate trapped in an optical trap when the magnetic dipole interaction between the atoms is taken into account along with confinement and spin precession. The boundaries between the regions of ferromagnetic and polar phases move as the dipole strength is varied and the ferromagnetic phases can be modulated. The magnetization of the ferromagnetic phase perpendicular to the field becomes modulated as a helix winding around the magnetic field direction, with a wavelength inversely proportional to the dipole strength. This modulation should be observable for current experimental parameters in 87Rb. Hence the much-sought supersolid state, with broken continuous translation invariance in one direction and broken global U(1) invariance, occurs generically as a metastable state in this system as a result of dipole interaction. The ferromagnetic state parallel to the applied magnetic field becomes striped in a finite system at strong dipolar coupling.The development of artificial gauge fields, that can mimic magnetic fields, in ultracold gases suggests that atomic realization of fractional quantum Hall physics will become experimentally practical in the near future. While it is known that bosons on lattices can support quantum Hall states, the universal edge excitations that provide the most likely experimental probe of the topological order have not been obtained. We find that the edge excitations of an interacting boson lattice model are surprisingly sensitive to interedge hybridization and edge-bulk mixing for some confining potentials. With properly chosen potentials and fluxes, the edge spectrum is surprisingly clear even for small systems with strong lattice effects such as bandwidth. Various fractional quantum Hall phases for bosons can be obtained, and the phases ν=1/2 and ν=2/3 have the edge spectra predicted by the chiral Luttinger liquid theory.Also, some of the traditional experimental techniques for detecting magnetic order and dynamics in solid state materials, like neutron scattering has had somewhat of a renaissance lately. In a recent experiment on CoNb2O6, Coldea et. al. found for the first time experimental evidence of the exceptional Lie algebra E8. The emergence of this symmetry was theoretically predicted long ago for the transverse quantum Ising chain in the presence of a weak longitudinal field. We consider an accurate microscopic model of CoNb2O6 incorporating additional couplings and calculate numerically the dynamical structure function using a recently developed matrix-product-state method. The excitation spectra show bound states characteristic of the weakly broken textrmE8textrm{E}_8textrmE8​ symmetry. We compare the observed bound state signatures in this model to those found in the transverse Ising chain in a longitudinal field and to experimental data.Finally, we investigate the ground state phase diagram of a related quantum spin chain, the S=2 XXZ chain with single-ion anisotropy. The interest in this system comes mainly from connecting the highly quantum mechanical spin-1 phase diagram with the classical S=∞ phase diagram. While most of these questions where believed to have been satisfactorily answered mainly with DMRG, some recent studies have questioned some of the conclusions. We use several of the recent advances within DMRG and perform a detailed analysis of the whole phase diagram. We extend the phase diagram by considering different types of single ion anisotropies which help us to answer two important questions: First we show that one can adiabatically move from the isotropic Heisenberg point to the so-called large-D phase with a continuous change of the Hamiltonian. Second, we can tune the model into a predicted intermediate phase which is equivalent to the topologically non-trivial spin-1 Haldane phase. Furthermore, we study the spin-3 XXZ chain to help explaining the development of the classical phase diagram.
The interplay between spin and motional degrees of freedom in interacting electron systems has been a long-standing research topic in condensed matter physics. Interactions can modify the behavior of individual electrons and give rise to emergent collective phenomena such as superconductivity and colossal magnetoresistance. Theoretical understanding of non-equilibrium dynamics in interacting fermionic matter is limited, however, and many open questions remain. Ultracold atomic Fermi gases, with precisely controllable parameters, offer an outstanding opportunity to investigate the emergence of collective behavior in out-of-equilibrium settings. In this thesis we will describe how an optical lattice clock operated with neutral Fermionic atoms can be turned into a quantum simulator of charged particles in a strong magnetic field. We will then discuss the counterintuitive notion that weak interactions in a Fermi gas can lead to large scale collective behavior and global correlations. These ideas are being tested experimentally at JILA and the University of Toronto. We also investigate in detail the so-called spin model approximation which is used extensively throughout this thesis.
The present thesis studies a variety of cold atomic systems in artificial gauge fields. In the first part we focus on fractional quantum Hall effects, asking whether interesting topological states can be realized with cold atoms. We start by making a close connection to solid-state systems and first consider fermionic atoms with dipolar interactions. Assuming the system to be in the Laughlin state, we evaluate the energy gap in the thermodynamic limit as a measure for the robustness of the state. We show that it can be increased by additionally applying a non-Abelian gauge field squeezing the Landau levels. We then switch to bosonic systems with repulsive contact interactions. Artificial magnetic fields for cold bosons have extensively been discussed before in the context of rotating Bose gases. We follow a different approach where the gauge field is due to an atom-laser coupling. Thus, transitions between different dressed states have to be included. They are shown to break the cylindrical symmetry of the system. Modifying the Laughlin state and the Moore-Read state accordingly, we determine the parameter regimes where they are good representations for the ground state of the system obtained via exact diagonalization. One of the most interesting feature of fractional quantum Hall states is the anyonic behavior of their excitations. We therefore also study quasiholes in the Laughlin state and the modified Laughlin state. They are shown to posses anyonic properties, which become manifest even in small systems. Moreover, the dynamics of a single quasihole causes visible traces in the density of the system which allow to clearly distinguish the Laughlin regime from less correlated phases. In the latter, a sequence of collapses and revivals of the quasihole can be observed, which is absent in the Laughlin regime. Extending our study to bosonic systems with a pesudospin-1/2 degree of freedom, we discuss the formation of strongly correlated spin singlets. Strikingly, at filling v=4/3, the system is described by a state with non-Abelian excitations, which is constructed as the zero-energy ground state of repulsive three-body contact interactions. Systems with internal degrees of freedom also allow for implementing artificial spin-orbit coupling. It is shown to give rise to a variety of incompressible states. In the second part of the thesis, we concentrate on condensed system. Bose-Einstein condensates with spin-orbit coupling are shown to have a degeneracy on the mean-field level, which is lifted by quantum and thermal fluctuations. The system becomes experimentally feasible in three dimensions, where the condensate depletion remains finite, and thus allow for an experimental observation of this order-by-disorder mechanism. Finally, we study the influence of Abelian and non-Abelian gauge fields on the quantum phase transitions of bosons in a square optical lattice. Re-entrant superfluid phases and superfluids at finite momenta are interesting properties featured by such systems.
This thesis is a theoretical analysis of sample two- and one-dimensional systems. The two-dimensional examples are the quantum Hall liquid and anomalous paired states. The most widely accepted effective theory of the quantum Hall liquid is based on the so-called Chern Simons Lagrangian, but it is not entirely satisfactory. We obtain the first derivation of an alternative effective theory from microscopic principles. Our formulation allows for a first principles derivation of physical quantities such as the effective mass and compressibility and contains the first analytical observation of the magnetoroton. The formalism developed along the way is also applied to paired states in anomalous supeconductors, a topic of much recent interest. The one-dimenisonal system is the carbon nanotube. Gas uptake in nanotube bundles is currently attracting a wealth of research with both applied and fundamental implications. We propose adsorption of gases on the surface of a single tube, finding strong correlations and symmetries that have not been observed yet. The properties of these states are directly relevant to other one-dimensional structures such as spin ladders and stripes and raise interesting and open questions.