Classical electromagnetism and quantum mechanics are both central to the modern understanding of the physical world and its ongoing technological development. Quantum simulations of electromagnetic forces have the potential to provide information about materials and systems that do not have conveniently solvable theoretical descriptions, such as those related to quantum Hall physics, or that have not been physically observed, such as magnetic monopoles. However, quantum simulations that simultaneously implement all of the principal features of classical electromagnetism have thus far proved elusive. We experimentally realize a simulation in which a charged quantum particle interacts with the knotted electromagnetic fields peculiar to a topological model of ball lightning. These phenomena are induced by precise spatiotemporal control of the spin field of an atomic Bose-Einstein condensate, simultaneously creating a Shankar skyrmion-a topological excitation that was theoretically predicted four decades ago but never before observed experimentally. Our results reveal the versatile capabilities of synthetic electromagnetism and provide the first experimental images of topological three-dimensional skyrmions in a quantum system.
Classical electromagnetism and quantum mechanics are both central to the modern understanding of the physical world and its ongoing technological development. Quantum simulations of electromagnetic forces have the potential to provide information about materials and systems that do not have conveniently solvable theoretical descriptions, such as those related to quantum Hall physics, or that have not been physically observed, such as magnetic monopoles. However, quantum simulations that simultaneously implement all of the principal features of classical electromagnetism have thus far proved elusive. We experimentally realize a simulation in which a charged quantum particle interacts with the knotted electromagnetic fields peculiar to a topological model of ball lightning. These phenomena are induced by precise spatiotemporal control of the spin field of an atomic Bose-Einstein condensate, simultaneously creating a Shankar skyrmion-a topological excitation that was theoretically predicted four decades ago but never before observed experimentally. Our results reveal the versatile capabilities of synthetic electromagnetism and provide the first experimental images of topological three-dimensional skyrmions in a quantum system.
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.
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…
Single topological defects and related structures have been experimentally created inside clouds of Bose-Einstein condensates. However, a practical protocol for creating multiple defects inside a single cloud—a prerequisite for studying defect interactions—has been lacking. Here we propose, and theoretically analyze, a practical protocol for the creation of configurations of topological monopoles, quantum knots, and skyrmions in Bose-Einstein condensates by employing fictitious magnetic fields induced by the interaction of the atomic cloud with coherent light fields. It is observed that a single coherent field is not enough for this purpose, but instead we find incoherent superpositions of several coherent fields that introduce topological point charges. We numerically estimate the experimentally achievable strengths and gradients of the induced fictitious magnetic fields and find them to be adjustable at will to several orders of magnitude greater than those of the physical magnetic fields employed in previous experimental studies. This property together with ultrafast control of the optical fields paves the way for advanced engineering of topological defects in quantum gases. Published by the American Physical Society 2024
We report the first experimental realization of a synthetic Hall torus using a spinor Bose-Einstein condensate confined in a ring-shaped trap with in situ imaging. By cyclically coupling three hyperfine spin states via Raman and microwave fields, we impose a periodic boundary condition in the synthetic dimension, which, together with a real-space ring trap, realizes a toroidal geometry with synthetic magnetic flux penetrating the surface. This flux induces azimuthal density modulations whose periodicity is uniquely determined by the quantized toroidal flux, a hallmark of the Hall torus. We then implement a topological charge pump by adiabatically varying an axial flux through the torus, inducing quantized azimuthal transport of the atoms. We further investigate the onset of these modulations as the system transitions from cylindrical to toroidal topology. Our results establish a versatile platform for exploring quantum Hall physics and topological phenomena in synthetic curved spaces.
Knots are familiar entities that appear at a captivating nexus of art, technology, mathematics, and science. As topologically stable objects within field theories, they have been speculatively proposed as explanations for diverse persistent phenomena, from atoms and molecules to ball lightning and cosmic textures in the universe. Recent experiments have observed knots in a variety of classical contexts, including nematic liquid crystals, DNA, optical beams, and water. However, no experimental observations of knots have yet been reported in quantum matter. We demonstrate here the controlled creation and detection of knot solitons in the order parameter of a spinor Bose-Einstein condensate. The experimentally obtained images of the superfluid directly reveal the circular shape of the soliton core and its accompanying linked rings. Importantly, the observed texture corresponds to a topologically non-trivial element of the third homotopy group and demonstrates the celebrated Hopf fibration, which unites many seemingly unrelated physical contexts. Our observations of the knot soliton establish an experimental foundation for future studies of their stability and dynamics within quantum systems.
We propose a new scheme for creating three-dimensional Skyrmions in a ferromagnetic spin-1 Bose-Einstein condensate by manipulating a multipole magnetic field and a pair of counter-propagating laser beams. The result shows that a three-dimensional Skyrmion with topological number Q = 2 can be created by a sextupole magnetic field and the laser beams. Meanwhile, the vortex ring and knot structure in the Skyrmion are found. The topological number can be calculated analytically in our model, which implies that the method can be extended to create Skyrmions with arbitrary topological number. As the examples, three-dimensional Skyrmions with Q = 3, 4 are also demonstrated and are distinguishable by the density distributions with a specific quantization axis. These topological objects have the potential to be realized in ferromagnetic spin-1 Bose-Einstein condensates experimentally.