Geometrical Frustration, Power Law Tunneling and Nonlocal Gauge Fields from Scattered Light

Designing the amplitude and range of couplings in quantum systems is a fundamental tool for exploring a large variety of quantum mechanical effects. Here, we consider off-resonant photon scattering processes on a geometrically shaped molecular cloud. Our analysis shows that such a setup is properly modeled by a Bose-Hubbard Hamiltonian where the range, amplitude, and sign of the tunneling processes of the scattered photonic modes can be accurately tuned. Specifically, by varying the molecular distribution, we demonstrate that different configurations characterized by geometrical frustration, long-range power law hopping processes, and nonlocal gauge fields can be achieved. Our results thus represent a powerful and alternative approach to perform an accurate Hamiltonian engineering of quantum systems with nontrivial coupling structures.