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 similar to 400 mu m-diameter planar crystal of several hundred Be-9(+) ions exhibiting complex drumhead modes in the confining potential of a Penning trap. Exploiting precise control over the Be-9(+) valence electron spins, we apply a homogeneous spin-dependent optical dipole force to excite arbitrary transverse modes with an effective wavelength approaching the interparticle spacing (similar to 20 mu m). Center-of-mass displacements below 1 nm are detected via the entanglement of spin and motional degrees of freedom.