Programmable Local Tunnelling in Ultracold Atomic Gases

Ultracold atoms in optical lattices represent powerful quantum simulators with large system sizes and long coherence times. Their programmability, however, is traditionally very limited. While on-site energies can be controlled in quantum gas microscopes with single-site resolution, local control over tunnelling elements remains a challenge. In this work, we demonstrate theoretically that periodically modulating individual on-site energies can provide local, flexible control over the tunnelling elements in a tight-binding model. We explore the functionality of this technique on a three-site plaquette and show we can access models with complex or frustrated tunnelling elements. In one dimension, we can generate arbitrary sequences of tunnelling elements including topologically non-trivial systems such as the Su-Schrieffer-Heeger (SSH) model. Realising single-site resolved tunnelling greatly broadens the Hamiltonians available to quantum gas experiments for quantum simulation.