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 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 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 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 propose an experimentally feasible scheme for topological interface engineering and show how it can be used for studies of dynamics of topologically nontrivial interfaces and perforation of defects and textures across such interfaces. The method makes use of the internal spin structure of the atoms together with locally applied control of interaction strengths to create many-particle states with highly complex topological properties. In particular, we consider a constructed coherent interface between topologically distinct phases of spinor Bose-Einstein condensates.
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 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.