Large-Scale $2+1$D $\mathrm{U}(1)$ Gauge Theory with Dynamical Matter in a Cold-Atom Quantum Simulator

Understand

A major driver of quantum-simulator technology is the prospect of probing high-energy phenomena in synthetic quantum matter setups at a high level of control and tunability.

• Here, we propose an experimentally feasible realization of a large-scale $2+1$D $\mathrm{U}(1)$ gauge theory with dynamical matter and gauge fields in a cold-atom quantum simulator with spinless bosons.
• We present the full mapping of the corresponding Gauss's law onto the bosonic computational basis.
• We then show that the target gauge theory can be faithfully realized and stabilized by an emergent gauge protection term in a two-dimensional single-species Bose--Hubbard optical Lieb superlattice with two spatial periods along either direction, thereby requiring only moderate experimental resources already available in current cold-atom setups.