We systematically and analytically construct a set of spinor wave functions representing defects and textures that continuously penetrate interfaces between coexisting, topologically distinct magnetic phases in a spin-2 Bose-Einstein condensate. These include singular and nonsingular vortices carrying mass or spin circulation that connect across interfaces between biaxial- and uniaxial nematic, cyclic and ferromagnetic phases, as well as vortices terminating as monopoles on the interface (“boojums”). The biaxial-nematic and cyclic phases exhibit discrete polytope symmetries featuring non-Abelian vortices and we investigate a pair of noncommuting line defects within the context of a topological interface. By numerical simulations, we characterize the emergence of nontrivial defect core structures, including the formation of composite defects. Our results demonstrate the potential of spin-2 Bose-Einstein condensates as experimentally accessible platforms for exploring interface physics, offering a wealth of combinations of continuous and discrete symmetries. Published by the American Physical Society 2024
We systematically and analytically construct a set of spinor wave functions representing defects and textures that continuously penetrate interfaces between coexisting, topologically distinct magnetic phases in a spin-2 Bose-Einstein condensate. These include singular and nonsingular vortices carrying mass or spin circulation that connect across interfaces between biaxial- and uniaxial nematic, cyclic and ferromagnetic phases, as well as vortices terminating as monopoles on the interface (“boojums”). The biaxial-nematic and cyclic phases exhibit discrete polytope symmetries featuring non-Abelian vortices and we investigate a pair of noncommuting line defects within the context of a topological interface. By numerical simulations, we characterize the emergence of nontrivial defect core structures, including the formation of composite defects. Our results demonstrate the potential of spin-2 Bose-Einstein condensates as experimentally accessible platforms for exploring interface physics, offering a wealth of combinations of continuous and discrete symmetries. Published by the American Physical Society 2024
We provide a detailed description of our previously proposed scheme for topological interface engineering with constructed defects and textures perforating across coherent interfaces between different broken symmetries [Borgh and Ruostekoski, Phys. Rev. Lett. 109, 015302 (2012)]. We consider a spin-1 Bose-Einstein condensate, in which polar and ferromagnetic phases are prepared in spatially separated regions. We show that a stable coherent interface is established between the two phases, allowing defects of different topology to connect continuously across the boundary. We provide analytic constructions of interface-crossing defect solutions that could be experimentally phase imprinted using existing technology. By numerically minimizing the energy, we calculate the core structures of interface-crossing defect configurations. We demonstrate nontrivial core deformations to considerably more complex structures, such as the formation of an arch-shaped half-quantum line defect, an Alice arch, at the interface, with the topological charge of a point defect, whose emergence may be understood by the ``hairy ball'' theorem. Another example of an energetically stable object is the connection of a coreless vortex to a pair of half-quantum vortices. We show that rotation leads to spontaneous nucleation of defects in which a coreless vortex continuously transforms to a half-quantum vortex across the interface.
We propose to use spatial control of the Zeeman energy shifts in an ultracold atomic gas to engineer an interface between topologically distinct regions. This provides an experimentally accessible means for studying the interface physics of topological defects and textures. Using the spin-1 Bose–Einstein condensate as an example, we find spinor wave functions that represent defects and textures continuously connecting across the interface between polar and ferromagnetic regions induced by spatially varying Zeeman shifts. By numerical energy-minimization we characterize the defect core structures and determine the energetic stability. The techniques proposed could potentially be used in the laboratory to emulate complex interface physics arising, e.g., in cosmological and condensed-matter contexts in both uniform and lattice systems.
We propose to use spatial control of the Zeeman energy shifts in an ultracold atomic gas to engineer an interface between topologically distinct regions. This provides an experimentally accessible means for studying the interface physics of topological defects and textures. Using the spin-1 Bose–Einstein condensate as an example, we find spinor wave functions that represent defects and textures continuously connecting across the interface between polar and ferromagnetic regions induced by spatially varying Zeeman shifts. By numerical energy-minimization we characterize the defect core structures and determine the energetic stability. The techniques proposed could potentially be used in the laboratory to emulate complex interface physics arising, e.g., in cosmological and condensed-matter contexts in both uniform and lattice systems.
We show that energy relaxation causes a point defect in the uniaxial-nematic phase of a spin-2 Bose-Einstein condensate to deform into a spin-Alice ring that exhibits a composite core structure with distinct topology at short and long distances from the singular line. An outer biaxial-nematic core exhibits a spin half-quantum vortex structure with a uniaxial-nematic inner core. By numerical simulation, we demonstrate a dynamical oscillation between the spin-Alice ring and a split-core hedgehog configuration via the appearance of ferromagnetic rings with associated vorticity inside an extended core region. We further show that a similar dynamics is exhibited by a spin-Alice ring surrounding a spin-vortex line resulting from the relaxation of a monopole situated on a spin-vortex line in the biaxial-nematic phase. In the cyclic phase, similar states are shown instead to form extended phase-mixing cores containing rings with fractional mass circulation or cores whose spatial shape reflects the order-parameter symmetry of a cyclic inner core, depending on the initial configuration. Published by the American Physical Society 2024
Discrete symmetries are spatially ubiquitous but are often hidden in internal states of systems where they can have especially profound consequences. In this work we create and verify exotic magnetic phases of atomic spinor Bose-Einstein condensates that, despite their continuous character and intrinsic spatial isotropy, exhibit complex discrete polytope symmetries in their topological defects. Using carefully tailored spinor rotations and microwave transitions, we engineer singular line defects whose quantization conditions, exchange statistics, and dynamics are fundamentally determined by these underlying symmetries. We show how filling the vortex line singularities with atoms in a variety of different phases leads to core structures that possess magnetic interfaces with rich combinations of discrete and continuous symmetries. Such defects, with their non-commutative properties, could provide unconventional realizations of quantum information and interferometry.
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…