Controlling quantum chaos: new platforms for many-body scars and weak ergodicity breaking in synthetic quantum matter

Quantum-many body scarring is a recently discovered paradigm of weak ergodicity breaking that allows specific states to evade thermalisation in chaotic quantum systems. Since its discovery in a Rydberg atom quantum simulator, signatures of quantum many-body scarring have been predicted in numerous theoretical models. However, most of these models do not lend themselves to implementation on the current generation of quantum simulators. In this thesis, we develop theoretical blueprints for realising many-body scarring phenomena in three types of quantum devices beyond Rydberg atom arrays. We start by providing an introduction to quantum thermalisation and weak ergodicity breaking in Chapter 2, focusing on the PXP model - an effective kinetically-constrained model describing Rydberg atoms. In Chapter 3, we illustrate anomalous dynamical properties of the PXP model, such as superdiffusive energy transport, and its possible applications as a resource for quantum metrology. In Chapter 4, we demonstrate how the PXP model can be emulated by ultracold bosonic atoms in a tilted optical lattice. The realisation of quantum many-body scarring in a new experimental platform will allow us to identify a larger set of initial configurations that lead to scarring. In Chapter 5, we employ similar techniques to implement a different type of quantum many-body scarring in a Fermi--Hubbard chain. We explain the distinct scarring mechanism in this model using a graph-based approach. Finally, in Chapter 6 we demonstrate how to create tunable scars in a quantum processor based on superconducting qubits. Overall, these results expand the realm of many-body scarring phenomena to a greater variety of experimental systems and they demonstrate that scarring is a powerful tool for protection of quantum information and entanglement engineering in out-of-equilibrium many-body systems.