Lattice models display bound states for repulsive interactions that smoothly connect to high-energy two-particle states of doubly occupied sites, namely doublons, for strong on-site interactions. In this work, we show that a distinct type of repulsively bound states, namely vortex bound states of two bosons, appear in dimerized square lattices pierced by a uniform $\pi$ flux for moderate interactions. By focusing on a ladder geometry as an illustrative example, we characterize their properties, including chirality-changing decay channels induced by flux detuning, and we develop protocols to perform state preparation in optical lattices via adiabatic sequences or recently developed current imprinting methods. Finally, we show how to measure currents and thus chirality by quenching the system onto isolated pairs of nearest-neighbor sites and then sampling the corresponding dynamics. These results can also provide an experimentally realistic strategy for state preparation and probing of chiral gapped many-body phases in optical lattices.

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• Cold gases in optical lattices
• Quantum engineering
• Quantum simulation
• Hubbard model