Magnetic-Monopole Analogues and Topological Textures in Dilute 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. In 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. We 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. The 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.