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Superfluid helium is a quantum liquid that exhibits a range of counter-intuitive phenomena such as frictionless flow. Quantized vortices are a particularly important feature of superfluid helium, and all superfluids, characterized by a circulation that can only take prescribed integer values. However, the strong interactions between atoms in superfluid helium prohibit quantitative theory of vortex behaviour. Experiments have similarly not been able to observe coherent vortex dynamics. This thesis resolves this challenge, bringing microphotonic techniques to bear on two-dimensional superfluid helium, observing coherent vortex dynamics for the first time, and achieving this on a silicon chip. This represents a major scientific contribution, as it opens the door not only to providing a better understanding of this esoteric quantum state of matter, but also to building new quantum technologies based upon it, and to understanding the dynamics of astrophysical superfluids such as those thought to exist in the core of neutron stars.

Condensed matter. --- Quantum physics. --- Chemistry. --- Materials science. --- Condensed Matter Physics. --- Quantum Physics. --- Chemistry/Food Science, general. --- Materials Science, general. --- Material science --- Physical sciences --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Quantum liquids. --- Liquids, Quantum --- Low temperatures --- Quantum statistics

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This thesis presents an exact theoretical study of dynamical correlation functions in different phases of a two-dimensional quantum spin liquid. By calculating the dynamical spin structure factor and the Raman scattering cross section, this thesis shows that there are salient signatures—qualitative and quantitative—of the Majorana fermions and the gauge fluxes emerging as effective degrees of freedom in the exactly solvable Kitaev honeycomb lattice model. The model is a representative of a class of spin liquids with Majorana fermions coupled to Z2 gauge fields. The qualitative features of the response functions should therefore be characteristic for this broad class of topological states.

Electricity & Magnetism --- Physics --- Physical Sciences & Mathematics --- Quantum theory. --- Quantum liquids. --- Liquids, Quantum --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Low temperatures --- Quantum statistics --- Mechanics --- Thermodynamics --- Magnetism. --- Strongly Correlated Systems, Superconductivity. --- Magnetism, Magnetic Materials. --- Quantum Field Theories, String Theory. --- Mathematical physics --- Electricity --- Magnetics --- Superconductivity. --- Superconductors. --- Magnetic materials. --- Quantum field theory. --- String theory. --- Models, String --- String theory --- Nuclear reactions --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Materials --- Superconducting materials --- Superconductive devices --- Cryoelectronics --- Electronics --- Solid state electronics --- Electric conductivity --- Critical currents --- Superfluidity