  In condensed matter, Chiral Spin Liquids (CSL) are quantum spin analogs of
electronic Fractional Quantum Hall states (in the continuum) or Fractional
Chern Insulators (on the lattice). As the latter, CSL are remarquable states of
matter, exhibiting topological order and chiral edge modes. Preparing CSL on
quantum simulators like cold atom platforms is still an open challenge. Here we
propose a simple setup on a finite cluster of spin-1/2 located at the sites of
a square lattice. Using a Resonating Valence Bond (RVB) non-chiral spin liquid
as initial state on which fast time-modulations of strong nearest-neighbor
Heisenberg couplings are applied, following different protocols
(out-of-equilibrium quench or semi-adiabatic ramping of the drive), we show the
slow emergence of such a CSL phase. An effective Floquet dynamics, obtained
from a high-frequency Magnus expansion of the drive Hamiltonian, provides a
very accurate and simple framework fully capturing the out-of-equilibrium
dynamics. An analysis of the resulting prepared states in term of Projected
Entangled Pair states gives further insights on the topological nature of the
chiral phase. Finally, we discuss possible applications to quantum computing.
