  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.
