Individually tunable tunnelling coefficients in optical lattices using local periodic driving

TL;DR

This paper presents a theoretical method to locally control tunnelling amplitudes in optical lattices using periodic driving, enabling the simulation of complex quantum models with tunable parameters.

Contribution

It introduces a novel Floquet-based approach for individual tunnelling control in optical lattices, facilitating the realization of topological and gauge field models.

Findings

Full control over tunnelling amplitudes in 1D models.

Implementation of topological models like extended Su-Schrieffer-Heeger.

Generation of magnetic field gradients in 2D lattices.

Abstract

Ultracold atoms in optical lattices have emerged as powerful quantum simulators of translationally invariant systems with many applications in e.g.\ strongly-correlated and topological systems. However, the ability to locally tune all Hamiltonian parameters remains an outstanding goal that would enable the simulation of a wider range of quantum phenomena. Motivated by recent advances in quantum gas microscopes and optical tweezers, we here show theoretically how local control over individual tunnelling links in an optical lattice can be achieved by incorporating local time-periodic potentials. We propose to periodically modulate the on-site energy of individual lattice sites and employ Floquet theory to demonstrate how this provides full individual control over the tunnelling amplitudes in one dimension. We provide 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, we demonstrate that local periodic driving in a Lieb lattice engineers a 2D network with fully controllable tunnelling magnitudes. In a three-site plaquette, we show full simultaneous control over the relative tunnelling amplitudes and the gauge-invariant flux piercing the plaquette, providing a clear stepping stone to building a fully programmable 2D tight-binding model. We also explicitly demonstrate how utilise our technique to generate a magnetic field gradient in 2D. This local modulation scheme is applicable to many different lattice geometries.