Dynamics and vortex structures in topological superfluid ³He at ultra-low temperatures and under confinement

Symmetry and its breaking are central to the modern understanding of the physical world. In conjunction with a handful of judiciously chosen experiments and topological reasoning, they have guided us to formulating fundamental laws in the context of relativistic quantum field theory as well as the theory of possible states of matter, their phase transitions and universal behavior. Topological defects, such as quantized vortices, affect the behavior at macroscopic scales. The range of possible defects is governed by the broken symmetries and topology of the system. The symmetries contained by the normal phase of ³He are exceptionally rich, and support a variety of symmetry-breaking phase transitions to macroscopically coherent, superfluid, states. Due to the existence of these symmetry-breaking phase transitions and the zoo of topological and nontopological defects allowed by the different superfluid phases, ³He can be used as a model system for a wide range of research topics ranging from turbulence and topological quantum computing to cosmology and grand unification scenarios. This thesis focuses on experimental studies on properties of linear topological defects born due to breaking of the U(1) symmetry at the superfluid transition - quantized vortices. At ultra-low temperatures in the superfluid B phase we quantify the interpretation of vortex imaging techniques based on Andreev scattering of thermal quasiparticles and study the response of an equilibrium vortex array to perturbations, namely to a rapid spin-down of the rotating drive. Superfluid B phase of ³He provides a unique platform to study non-equilibrium hydrodynamics as the ratio of the inertial and viscous forces may be tuned by orders of magnitude by changing the temperature. Recent advances in experimental techniques have demonstrated that under engineered confinement the topology of the superfluid may be altered, resulting in novel superfluid phases. These phases provide experimental access to new types of topological and nontopological defects, which are also studied in this thesis. We demonstrate that a new type of vortex - the half-quantum vortex (HQV), is stabilized in the superfluid polar phase. Taking advantage of the phase diagram of ³He under confinement, we demonstrate that HQVs may be transferred to superfluid phases with polar distortion - with striking consequences. In the polar-distorted A phase the HQVs have been predicted to harbor isolated Majorana fermions that in 2D systems obey non-Abelian statistics, while in the polar-distorted B phase the HQVs survive as "walls bounded by strings" - composite defects predicted in cosmological context decades ago.