  We theoretically and experimentally investigate double electromagnetically
induced transparency (double-EIT) cooling of two-dimensional ion crystals
confined in a Paul trap. The double-EIT ground-state cooling is observed for
\Yb ions with clock state, for which EIT cooling has not been realized like
many other ions with a simple $\Lambda$-scheme. A cooling rate of $\dot{\bar
n}=34~(\pm1.8)~\rm{ms}^{-1}$ and a cooling limit of $\bar n=0.06~(\pm 0.059)$
are observed for a single ion. The measured cooling rate and limit are
consistent with theoretical predictions. We apply double-EIT cooling to the
transverse modes of two-dimensional (2D) crystals with up to 12 ions. In our 2D
crystals, the micromotion and the transverse mode directions are perpendicular,
which makes them decoupled. Therefore, the cooling on transverse modes is not
disturbed by micromotion, which is confirmed in our experiment. For the center
of mass mode of a 12 ions crystal, we observe a cooling rate and a cooling
limit that are consistent with those of a single ion, including heating rates
proportional to the number of ions. This method can be extended to other
hyperfine qubits, and near ground-state cooling of stationary 2D crystals with
large numbers of ions may advance the field of quantum information sciences.

Quantum Physics;Atomic Physics