We study, both experimentally and theoretically, electromagnetically induced transparency cooling of the drumhead modes of planar 2-dimensional arrays with up to $Napprox 190$ Be${}^+$ ions stored in a Penning trap. Substantial sub-Doppler cooling is observed for all $N$ drumhead modes. Quantitative measurements for the center-of-mass mode show near ground state cooling with motional quantum numbers of $bar{n} = 0.3pm0.2$ obtained within $200~mu s$. The measured cooling rate is faster than that predicted by single particle theory, consistent with a quantum many-body calculation. For the lower frequency drumhead modes, quantitative temperature measurements are limited by apparent damping and frequency instabilities, but near ground state cooling of the full bandwidth is strongly suggested. This advancement will greatly improve the performance of large trapped ion crystals in quantum information and quantum metrology applications.
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