We investigate the nonequilibrium dynamics of interacting bosons in a two-leg ring ladder pierced by an artificial magnetic flux, where the particles are initially localized in the central sites of both rings, and the ac-driven local energy shifts are applied to the remaining lattice sites. Within the mean-field approximation, we demonstrate the emergence of nonlinear self-trapping for strong interparticle interactions, and characterize the distinct excitation regimes in the absence of the inter-ring tunneling. The artificial magnetic flux typically introduces the Peierls phase factors, which induces complex-valued hopping amplitudes and leads to directed net particle currents along the chains. By further incorporating the finite inter-ring coupling and biased intra-ring hopping, we reveal that the tuning of the drive frequency and Peierls phase allows the precise control over both the intensity and direction of particle currents, which facilitates the transition between chiral and antichiral dynamics. These findings offer insights into the coherent manipulation of matter-wave transports in closed-loop lattice configurations and the exploration of nonequilibrium synthetic quantum systems in related fields.

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• Cold atoms & matter waves
• Cold gases in optical lattices
• Bose gases