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Ultracold atoms in optical lattices have emerged as powerful quantumsimulators of translationally invariant systems with many applications in e.g.strongly-correlated and topological systems. However, the ability to locallytune all Hamiltonian parameters remains an outstanding goal that would enablethe simulation of a wider range of quantum phenomena. Motivated by recentadvances in quantum gas microscopes and optical tweezers, we here showtheoretically how local control over individual tunnelling links in an opticallattice can be achieved by incorporating local time-periodic potentials. Wepropose to periodically modulate the on-site energy of individual lattice sitesand employ Floquet theory to demonstrate how this can result in full individualcontrol over the tunnelling amplitudes in one dimension. We provide variousexample configurations realising interesting topological models such asextended Su-Schrieffer-Heeger models that would be challenging to realize byother means. Extending to two dimensions, we present that local periodicdriving in a three-site plaquette allows for full simultaneous control over therelative tunnelling amplitudes and the gauge-invariant flux piercing theplaquette, providing a clear stepping stone in building a fully programmable 2Dtight-binding model. This local modulation scheme is applicable to manydifferent lattice geometries.

Individually tunable tunnelling coefficients in optical lattices using local periodic driving