Programmable quantum walk in synthetic dimension using an optical tweezer

We use the motional states of a single atom trapped in an optical tweezer as a synthetic lattice for a tight-binding model. Each motional Fock state acts as a lattice site, and driven couplings between these states implement hopping. By exploiting the trap anharmonicity with spatial shaking and intensity modulation, we can independently program on-site disorder and complex nearest- and next-nearest-neighbor tunneling. This gives us a highly controllable platform for Hamiltonian engineering and for generating non-Gaussian motional states through quantum walk dynamics.