Topological Quantum Matter: Bridging Theory and Experiment

Abstract

Quantum many-body systems host a variety of exotic phases which can be described as the deconfined phase of an emergent gauge theory. Such phases in the context of spin systems go by the name Quantum Spin Liquids (QSLs). Often, the same features that make them interesting also make them hard to detect experimentally. This thesis is a collection of works aimed at connecting the defining theoretical properties of such phases to experimentally accessible observables, both in the setting of solid state materials and quantum devices. The main theme of the first part of the thesis is magnetic monopoles of emergent compact U(1) gauge theories that describe certain QSLs, namely Quantum Spin Ice and Dirac Spin Liquid in three and two spatial dimensions respectively. The condensation of monopoles drives a deconfinement-confinement phase transition in the gauge theory, and in the context of spin systems, drives transitions from QSL to ordered phases. We exploit this understanding to propose a ``Monopole Josephson Junction" scheme to test if a candidate material is a Dirac Spin Liquid. A key component of our detection scheme is Raman Scattering. Next, we provide a proposal to prepare and diagnose Quantum Spin Ice (deconfined phase of U(1) gauge theory in three spatial dimensions) in Rydberg atom arrays. In the second part of the thesis, we explore quantum optics techniques to probe correlated quantum materials. In optical experiments, the photonic observable measured is usually the intensity or photon number operator of inelastically scattered light. We ask a general question -- what can we learn about a material, given access to other photonic observables like quadrature and correlation between pairs of photons (G2)? We develop a general formalism to map such photonic correlation functions to electronic ones. Focusing on the Hubbard model at half-filling, we show that such correlators can be used to probe spin-charge correlations, and to detect QSLs by detecting spin chirality and existence of fractional statistics.