Quantum Simulation seeks to gain fundamental insight into the behaviour of complex quantum systems, which underlie diverse fields ranging from materials science to chemistry and biology. New understanding can now be gained by modelling (or simulating) this behaviour with experiments that are controllable on a microscopic, quantum-mechanical level.
Within this PhD project, we will use ultracold atom in optical lattices in a quantum-gas microscope setup, with the capabilities of single-site-resolved atom detection. We will will build on new experimental capabilities in our setup able to generate arbitrary light potentials by spatial light modulators that are projected onto the atoms with a high-resolution microscope [1,2].
Within the first part of this PhD project we will apply our dynamically programmable light potentials in a new context: the study of Mott insulating states in quasi one-dimensional quantum systems. Our goal is to observe ‘rung’ Mott insulating states, which form in ladder systems at exactly half filling [3,4]. In such a state, atoms delocalize over each rung of the lattice while the overall many-body quantum state remains insulating.
We will create these quantum states using our unique dynamically controlled potentials. Initially, we will prepare a Mott insulating state in a one-dimensional chain between potential barriers. We will then move the potential barriers parallel to the chain by one site, effectively doubling the number of lattice sites while maintaining the same initial atom number. By adjusting the strength of the optical lattice lasers perpendicular to the chain, we can control the tunneling between the ladder rungs. Meanwhile, the strength of the optical lattice along the rungs will alter the ratio of tunneling to on-site interaction. This will allow us to map out a phase diagram and compare it with theoretical predictions [3,4]. Theoretical studies have already been conducted in our group and show the feasibility of these experiments within our setup.

In the second part of this PhD project, we will aim to laser cool and trap the 85Rb isotope instead of 87Rb. As 85Rb has a Feshbach resonance of the F=2, mF=-2 ground state at 155 G, we will be able to tune the scattering length and control the interatomic interactions. This will allow us to realise a two-component Bose-Hubbard Model, with different inter- and intra-species interactions, to study richer physics in the abovementioned ladder system. It is also predicted to exhibit an x-y ferromagnetic phase [5]. Control of the scattering length, in a way that it remains positive at all stages of the experiment including the transport is critical to avoid heating and losses of 85Rb during the multi-stage cooling and loading process. The experimental setup has been specifically designed maintain a suitable magnetic field during the transport. We will then employ the programmable light potentials to perform spin flips of atoms on selected lattice sites, enabling us to generate arbitrary initial distributions of the atomic spins. It will allow us to study out-of-equilibrium dynamics and perform local quenches. Further studies will include lattice geometries of a higher complexity such as Lieb-lattice systems and diamond chains.