Geometrical frustration, power law tunneling and non-local gauge fields from scattered light

Abstract

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 non-local gauge fields can be achieved. Our results thus represent a powerful and alternative approach to perform an accurate Hamiltonian engineering of quantum systems with non trivial coupling structures.

Current version represents the journal article version. Main changes: Back-of-the-evelope estimations of feasibility and orders of magnitude for the relevant coupling included as End Matter. Changes in the main text: mentioning of the End Matter, paragraph on state preparation and techniques for shaping the geometry of the molecular cloud included. Typos fixed

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