Since the discovery of Bose-Einstein condensation in dilute atomic vapours in 1995, there has been a monumental increase in the research effort in the field of atomic physics due to the unforeseen opportunities and challenges that the degenerate quantum gases present. In particular, quantum gases can emulate complicated models that arise in solid state and high energy physics, allowing realisations of exotic phenomena that have proven to be elusive in their original context. An outstanding example is the existence of various topological defects in degenerate quantum gases with internal degrees of freedom. Topological excitations such as skyrmions and several types of monopoles can be shown to take place in Bose gases with a hyperfine spin degree of freedom as a result of a coupling to an external field or due to thermal fluctuations. A central question in the context of dilute Bose gases is the relation between superfluidity and Bose-Einstein condensation. The dimensionality of the underlying space as well as the internal degrees of freedom have a direct impact on the existence and the nature of the Bose-Einstein condensate. For example, any uniform Bose gas in two spatial dimensions or an antiferromagnetic spinor Bose gas can give rise to a superfluid state which does not involve a conventional Bose-Einstein condensate corresponding to a single macroscopically occupied quantum state. In this Thesis, properties of different topological defects and their relation to superfluidity in dilute Bose gases are investigated. Stability and creation of coreless vortices are first studied and a method to cyclically increase the angular momentum of the condensate is introduced. Subsequently, the properties and creation of different types of monopoles are investigated and an experimentally feasible method to create a Dirac monopole is presented. Finally, finite temperature phase transitions in quasi-two-dimensional Bose gases with a spin degree of freedom are analysed and, as a related subject, the stability of vortex clusters formed by vortices and antivortices is studied.
Since the discovery of Bose-Einstein condensation in dilute atomic vapours in 1995, there has been a monumental increase in the research effort in the field of atomic physics due to the unforeseen opportunities and challenges that the degenerate quantum gases present. In particular, quantum gases can emulate complicated models that arise in solid state and high energy physics, allowing realisations of exotic phenomena that have proven to be elusive in their original context. An outstanding example is the existence of various topological defects in degenerate quantum gases with internal degrees of freedom. Topological excitations such as skyrmions and several types of monopoles can be shown to take place in Bose gases with a hyperfine spin degree of freedom as a result of a coupling to an external field or due to thermal fluctuations. A central question in the context of dilute Bose gases is the relation between superfluidity and Bose-Einstein condensation. The dimensionality of the underlying space as well as the internal degrees of freedom have a direct impact on the existence and the nature of the Bose-Einstein condensate. For example, any uniform Bose gas in two spatial dimensions or an antiferromagnetic spinor Bose gas can give rise to a superfluid state which does not involve a conventional Bose-Einstein condensate corresponding to a single macroscopically occupied quantum state. In this Thesis, properties of different topological defects and their relation to superfluidity in dilute Bose gases are investigated. Stability and creation of coreless vortices are first studied and a method to cyclically increase the angular momentum of the condensate is introduced. Subsequently, the properties and creation of different types of monopoles are investigated and an experimentally feasible method to create a Dirac monopole is presented. Finally, finite temperature phase transitions in quasi-two-dimensional Bose gases with a spin degree of freedom are analysed and, as a related subject, the stability of vortex clusters formed by vortices and antivortices is studied.
Bose–Einstein condensation is a quantum statistical phase transition that occurs in a system consisting of bosons when a single-particle quantum state becomes macroscopically occupied. This peculiar state of matter was first predicted in 1925 and finally realized seventy years later in vapours of weakly-interacting alkali-metal atoms. Since then, Bose–Einstein condensates have been one of the most fascinating research fields in modern physics. \n \nThe gaseous condensates offer a robust platform to accurately study interacting many-particle systems from the first principles. Experimentally, the possibility to precisely control a condensate with external fields and directly image its order parameter provides unforeseen opportunities to obtain deep insight into phenomena across different subfields of physics. In particular, gaseous condensates can emulate complicated models that arise in atomic, condensed-matter, and even particle physics, allowing realizations of exotic phenomena that are elusive in their original contexts. An outstanding example is the existence of various topological defects in ultacold quantum gases with internal degrees of freedom. \n \nIn this thesis, we investigate the creation, stability, and dynamical properties of various topological defects in spinor Bose–Einstein condensates. The majority of the theoretical results is obtained by numerically solving the dynamics using Gross–Pitaevskii equations for spin-1 condensates. Many theoretical predictions are confirmed by the very good agreement with experiments. \n \nThe first experimental observations of a topological point defect in an order parameter describing the quantum gas are presented. Such a point defect is reminiscent to the magnetic monopole particle appearing in grand unified theories. Therefore, the discovery of monopoles in quantum gases further encourages the quest for finding magnetic monopoles in natural electromagnetic fields, a search largely initiated by Paul Dirac almost a century ago. \n \nSubsequently, the fine structure and decay dynamics of the point defect are studied numerically and verified in experiments. The created monopole is gradually destroyed during the polar-to-ferromagnetic quantum phase transition, which results in the spontaneous emergence of a Dirac monopole in synthetic magnetic field. In addition to the singular point defect, the first experimental realization of a knot soliton in the context of quantum field is reported. This thesis lays the foundation for studies of the dynamics and stability of three-dimensional topological structures in quantum systems.
Since their experimental discovery in 1995, dilute Bose–Einstein condensates have proven to be excellent platforms for studying interacting many-body quantum systems. The gaseous condensates can be conveniently controlled in space and time with lasers and magnetic fields. Theoretically, these low-temperature systems can be described starting from first principles, and their dynamics is accurately captured by the mean-field approach. Dilute condensates with internal spin degrees of freedom may host various topological defects including vortices, monopoles, and skyrmions. Precise external control fields can be used to engineer and study these topological states. \n \nIn this thesis, we investigate the creation, stability, and dynamics of various topological defects in spinor Bose–Einstein condensates. A combination of numerical and analytical methods is used and a part of the research is carried out in collaboration with an experimental research group. The majority of the research involves numerically solving the mean-field Gross–Pitaevskii equation for a spin-1 condensate. The computations are accelerated with graphics processing units. \n \nWe find that the ground state of a ferromagnetic spin-1 condensate supports a Dirac monopole in its synthetic magnetic field in the presence of a quadrupole magnetic field. The energetics of various stationary states of spin-orbit coupled condensates are analyzed and a robust method to observe these exotic states in experiments is proposed. The creation of topological skyrmions is simulated and a very good quantitative agreement with a recent experiment is obtained. Importantly, the first experimental observations of both, Dirac monopoles and topological point defects in a system governed by a quantum field are presented. Subsequently, the decay dynamics of the point defect is studied, revealing the decay into a ferromagnetic state supporting the Dirac monopole. \n \nThe impact of the research conducted in this thesis is not limited to gaseous Bose–Einstein condensates, but due to the universality of quantum mechanics and topological defects, our work provides knowledge, ideas, and inspiration across research fields.
Bose-Einstein condensation is a quantum statistical phase transition which was theoretically predicted almost a hundred years ago. After years of seminal research, physicists realized the first almost ideal Bose-Einstein condensates in ultracold dilute atomic gases in 1995. Since then, the theoretical and experimental methods concerning such systems have been developing rapidly, and many fascinating phenomena have been found in these novel quantum systems.\n\nBose-Einstein condensation occurs in a system consisting of massive bosons when a single quantum state becomes macroscopically occupied as the temperature is lowered below the transition temperature. In general, condensates consisting of repulsively interacting bosons exhibit superfluidity: Particle currents can flow in the system without dissipation and viscosity. Moreover, the velocity fields of condensates have to be irrotational, which severely restricts the rotational characteristics of these systems. Apart from the center of mass motion, the system may carry angular momentum in the form of elementary excitations or so-called quantized vortices.\n\nThis Thesis is a theoretical study of subjects related to stability and dynamics of quantized vortices in dilute atomic Bose-Einstein condensates. The precession and instability of off-centered vortices in trapped condensates is investigated both in the zero-temperature limit and at finite temperatures. Dynamical stability of multiply quantized vortices and vortex clusters is studied in axisymmetric trap geometries. Splitting of energetically and dynamically unstable multiply quantized vortices into singly quantized vortices is also studied. Finally, as a separate subject, tunneling of a condensate through a potential barrier is investigated. Majority of this work relies on numerical methods for solving the Gross-Pitaevskii and Bogoliubov equations, which are of central importance in the study of dilute atomic Bose-Einstein condensates.
Topology provides deep conceptual links between the various branches of physics. Bose–Einstein condensates with spin degrees of freedom are among the most accessible quantum systems available for studying topological structures. A wide range of topological defects and textures available in condensates, such as vortices, monopoles, knots, and skyrmions, are analogous to those predicted in electromagnetism, high-energy physics, and cosmology.
In this dissertation, we numerically and experimentally investigate novel creation methods for topological structures and study their dynamical properties. Specifically, we experimentally observe the evolution of an isolated monopole into a Dirac monopole in the presence of a quadrupole magnetic field. The Dirac monopole appears in the synthetic magnetic field of the condensate and is accompanied by spontaneously emerging nodal lines. We observe the decay of a quantum knot into a polar-core spin vortex in the presence of a uniform magnetic field. Furthermore, we observe that a decaying coreless-vortex state gives rise to a pair of singular SO(3) vortices.
Many of the studied creation methods for topological structures in the condensate rely on adiabatic control of the external magnetic field. The counterdiabatic protocol offers a way to speed up the otherwise slow magnetic field driving required for adiabatic dynamics with a correcting magnetic field. Using this method, we numerically implement a scheme for fast vortex pumping which leads to the vortex with highest angular momentum reported to date in Bose–Einstein condensates with experimentally feasible methods. We further use the counterdiabatic protocol in a novel way to create quantum knots in the condensate.
Another focal point of this dissertation is the study on different types of skyrmions in spinor condensates. Our simulations of two-dimensional skyrmions are in a quantitative agreement with an experiment carried out elsewhere, explaining the experimentally observed instabilities. We numerically analyze the exotic spin-2 skyrmions available in the cyclic and biaxial nematic phases. Importantly, we present the first experimental observations of Shankar skyrmions in spin-1 condensates and analyze their synthetic electromagnetic properties.
This dissertation addresses an extensive amount of topological structures available in the condensate, but many different structures await future studies. In addition, the precise computational characterization of the elementary excitations of monopoles, knots, and skyrmions is of great interest. The results of this dissertation form a sturdy basis for future experimental studies on the dynamics of topological structures in spinor condensates.; Topologia tarjoaa syvallisia kasitteellisia yhteyksia fysiikan eri haarojen valilla. Bosen–Einsteinin kondensaatit spin-vapausasteilla ovat yksia monipuolisimmista systeemeista topologisten rakenteiden tutkimukseen. Laaja kirjo kondensaatissa esiintyvia topologisia rakenteita, kuten kvanttipyorteet, monopolit, solmut ja skyrmionit, ovat…
The condensation of weakly interacting alkali atom gases observed in 1995 is a manifestation of the macroscopic quantum phenomenon called Bose-Einstein condensation. In contrast to superconductivity and Helium superfluids, the dilute alkali atom condensates are directly observable using optical imaging techniques and they constitute highly controllable quantum systems. Hence, they offer an ideal test bench to investigate the applicability of quantum field theories and to predict the properties of the condensates starting from the first principles.\n\nSince the first experimental realizations of dilute Bose-Einstein condensates, a great interest has been focused on this field, resulting in numerous experimental studies concerning, for example, nonlinear dynamics and the elementary excitations of these many-particle quantum systems. The existence of topological phase singularities, quantized vortices, first predicted theoretically and finally observed experimentally in 1999, led to another series of pioneering theoretical and experimental studies.\n\nSeveral methods to create single-quantum vortices were realized already in 2001 but, however, the puzzle of creating multiply quantized vortices still remained. In this thesis, the so-called topological method to create two and four times quantized vortices is studied in detail. Since the instrumentation required for the experimental realization of the topological method had already been installed in many laboratories, the theoretical predictions of this thesis were experimentally verified shortly after their publication. Multiply quantized vortices are energetically unstable and tend to split into singly quantized vortices. However, the dissipation of energy in the condensates is minimal at low temperatures and, consequently, can lead to long lifetimes for the multiquantum vortices. Nevertheless, one prediction of this thesis is that the lifetimes of doubly quantized vortices are relatively short, owing to the known dynamical instability of the state. The splitting of the doubly quantized vortex has recently been observed experimentally.\n\nThe stability of vortices in dilute Bose-Einstein condensates is intimately related to the excitation spectrum of the stationary vortex state. However, developing an accurate, computationally feasible finite-temperature quantum field theory remains an open problem. In this thesis, we study the elementary excitations of an irrotational condensate within a recently developed systematic second order perturbation theory. The collapse and revival of certain elementary excitations is discovered.\n\nThe most recent studies of this thesis are devoted to stationary, but rotationally asymmetric vortex states. In weakly interacting condensates, a novel stationary state, a vortex tripole holding finite angular momentum is presented. Also the lowest elementary excitations of the so-called vortex dipole, tripole, and quadrupole states are studied.
In 1995, atomic physics took a quantum leap with the experimental discovery of almost ideal Bose-Einstein condensation in dilute gases of alkali atoms. The gaseous condensates offer a rare chance to study an interacting many-particle system accurately from first-principles theories, and they can be used to simulate many seminal models that have proven elusive in their original context of, e.g., solid-state or high-energy physics. An important topic in the research has been the quantized vortex, which was experimentally realized in 1999 and whose existence is intimately related to the concepts of quantum phase coherence and superfluidity.\nIn this dissertation, unconventional vortex structures are investigated in the dilute condensates at ultralow temperatures. A combination of analytical and numerical methods is used to examine the structure, stability, and dynamical behavior of multiquantum vortices and vortex-antivortex pairs in spin-polarized condensates, unusual vortex lattices in two-species condensates, and spin textures in condensates with dipolar interactions. In studying the properties of the multiquantum vortices, particular emphasis is placed on exploring the practical limits of producing them through adiabatic pumping of vorticity. The majority of the research is conducted by solving the mean-field Gross-Pitaevskii and Bogoliubov equations.\nVarious original, experimentally verifiable results concerning the exotic vortex structures are presented. Novel splitting patterns of vortices with large quantum numbers are introduced, and it is shown that such vortices can be feasibly stabilized by piercing them with a focused laser beam. A recent experiment on vortex-antivortex pairs is simulated, and an excellent quantitative agreement with the experimental data is obtained. Unconventional ground-state vortex lattices, such as ones having a square geometry or consisting of two-quantum vortices, are shown to exist in rotating two-species condensates. Dipolar interactions are found to support helical spin-vortex states, and the energies of spin-wave excitations are observed to increase rapidly with the dipolar coupling strength.\nThis dissertation contributes to the understanding of superfluid phenomena in Bose-Einstein condensates and has significant implications for the prospects of detecting novel vortex structures in current experiments.