  We theoretically propose and experimentally demonstrate a
parallel-electromagnetically-induced transparency (parallel-EIT) cooling
technique for ion crystals in the Paul trap. It has less stringent requirements
on the cooling resonance condition than the standard
electromagnetically-induced transparency (EIT) cooling, thus allowing, in
principle, to simultaneously cool the motional mode spectrum with an arbitrary
range. A proof-of-principle validation for this cooling scheme is
experimentally demonstrated with up to 4 trapped 40Ca+ ions. We observe
simultaneous near-ground-state cooling for all motional modes with best average
phonon number about 0.2. By tuning the trap frequency in a large range to
imitate a broadband motional mode spectrum, we can still reach almost the same
cooling limit for all the modes while standard EIT cooling shows limited
cooling range. Our method has a simple experimental configuration, requiring
only appropriate modulation of the probe beam of standard EIT cooling, and can
be applied to various types of ions (e.g., 171Yb+, 40Ca+). This cooling scheme
provides a powerful tool for the initialization of the trapped-ion quantum
computers and simulators.
