Use of quantum quenches to probe the equilibrium current patterns of ultracold atoms in an optical lattice

Atomic bosons and fermions in an optical lattice can realize various condensed-matter states that support equilibrium current patterns in the presence of synthetic magnetic fields or non-Abelian gauge fields. As a route to probing such mass currents, we propose a nonequilibrium quantum quench of the Hamiltonian that dynamically converts the current patterns into experimentally measurable real-space density patterns. We illustrate how a specific such ``unidirectional'' quench of the optical lattice can be used to uncover bulk checkerboard and stripe current orders in lattice Bose superfluids and Fermi gases, as well as chiral edge currents in a quantum Hall state.