Locally Tuneable Quantum Hamiltonians with Neutral Atoms in Optical Lattices

Abstract

Neutral atoms in optical lattices are powerful and versatile quantum simulators of quantum lattice models with many applications. While they have successfully realised many translationally invariant models, the ability to locally tune all local Hamiltonian parameters remains an outstanding goal that would enable the simulation of a wider range of quantum phenomena. This thesis gives a number of theoretical proposals for generating locally tunable quantum lattice Hamiltonians for neutral atoms. Recent advances in quantum gas microscopes and optical tweezers have allowed for the generation of additional, site-dependent potentials to an underlying optical lattice. This thesis focuses on Hamiltonians generated by incorporating time-periodic implementations of these site-dependent potentials. Time dependence adds a new set of control parameters and allows us to break important symmetries in the system. This can yield qualitatively different behaviours that are fundamentally intractable to static systems. Floquet theory provides effective theoretical machinery to analyse the models that form as a result of periodic driving. Periodically modulating the on-site energy of individual lattice sites provides full individual control over the tunnelling amplitudes in one dimension. Utilising this, this thesis provides various example configurations realising interesting topological models such as extended Su-Schrieffer-Heeger models that would be challenging to realise by other means. Extending to two dimensions, local periodic driving in a Lieb lattice engineers a 2D network with fully controllable tunnelling magnitudes. In a three-site plaquette, full simultaneous control over the relative tunnelling amplitudes and the gauge-invariant flux piercing the plaquette can be achieved. This can be simply extended to realise exotic flux phases in a kagomé lattice and provides a clear stepping stone to building a fully programmable 2D tight-binding model. Utilising laser-assisted tunnelling with locally defined modulations can also be harnessed to yield a magnetic field gradient in 2D. The ability to encode and study Hamiltonians with arbitrary local tunnelling co-efficients will allow optical lattice experiments to simulate an incredibly diverse range of problems and quantum phenomena well beyond solid-state settings. This thesis explores how local driving can generate the same physics as black holes and demonstrates how to experimentally probe their features. This local modulation scheme is applicable to many different lattice geometries and can realise black hole physics in both one and two dimensions.