The quenched dynamics of an ultracold homogeneous atomic two-dimensional Bose gas subjected to periodic quenches across the Berezinskii-Kosterlitz-Thouless (BKT) phase transition are discussed. Specifically, we address the effect of periodic cycling of the effective atomic interaction strength between a thermal disordered state above, and a highly ordered state below the critical BKT interaction strength, by means of numerical simulations of the stochastic projected Gross-Pitaevskii equation. Probing the emerging dynamics as a function of the frequency of sinusoidal driving from low to high frequencies reveals diverse dynamical features, including phase-lagged quasi adiabatic reversible condensate formation, resonant excitation consistent with an intrinsic system relaxation timescale, and gradual establishment of dynamically-recurring or time-averaged non-equilibrium states with enhanced coherence which are neither condensed, nor thermal. Our study paves the way for experimental observation of such driven non-equilibrium ultracold superfluid states.
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