Spectroscopy and Thermometry of Drumhead Modes in a Mesoscopic Trapped-Ion Crystal Using Entanglement

We demonstrate spectroscopy and thermometry of individual motional modes in a mesoscopic 2D ion array using entanglement-induced decoherence as a method of transduction. Our system is a \ensuremath{\sim}400\text{ }\text{ }\ensuremath{\mu}\mathrm{m}diameter planar crystal of several hundred ^{9}\mathrm{Be}^{+}ions exhibiting complex drumhead modes in the confining potential of a Penning trap. Exploiting precise control over the...