Higgs bosons, half-quantum vortices, and Q-balls : an expedition in the ³He universe

For several decades, superfluid helium has provided an almost unparalleled frontier of quantum physics research, especially in topics related to macroscopic quantum phenomena. While nowadays systems studied in quantum physics are becoming increasingly artificially engineered - the quest for quantum computers and quantum technology in general being one of the driving forces of this development - traditionally both superfluid 4He and 3He have provided a natural but versatile window to their quantum nature. Superfluid 3He, the subject of this thesis, is a quantitatively understood macroscopic quantum system of considerable yet manageable mathematical complexity. In this thesis I show how such versatility translates into a variety of emergent phenomena, touching many seemingly distant fields in physics such as cosmology. Approaching superfluid helium-3 experimentally requires sophisticated cooling and probing methodology. We have used a rotating ultra-low-temperature refrigerator, where the superfluid sample is cooled down by a nuclear demagnetisation stage and probed using nuclear magnetic resonance spectroscopy (NMR). One particularly useful NMR instrument can be constructed by trapping a Bose-Einstein condensate (BEC) of magnon quasiparticles within the superfluid. We have used such condensates in probing a variety of delicate phenomena such as other spin wave modes, including Higgs modes. We have also observed propagation of self-trapped Q-ball solitons making use of magnon BECs. These achievements required careful experimental and numerical studies of the magnon BEC. The spectrum of the magnon BEC is controlled by the profile of the external magnetic field and by the spatial variation of the superfluid order parameter. The main part of the relaxation is due to temperature dependent spin transport in the normal component of the liquid, which allows translating the magnon BEC read-out into in-situ thermometer. As perhaps the most pubilicized topic of this thesis, I explain how we discovered half-quantum vortices in superfluid helium-3, a manifestation of the topological versatility of this system. Nobel laureate Anthony Leggett recently listed finding these vortices the most important remaining open problem in the ultra-low-temperature superfluid physics. In general, the very name of quantum physics refers to the observation that fundamental concepts such as energy and momentum are quantised in the microscopic world, that is, changes in the quantities describing a physical system can only occur in finite steps, integer multiples one quantum. Therefore finding vortices carrying only half-a-quantum of circulation is not only intriguing, but manifests deep understanding of the underlying physics and quantum physics in general.