We demonstrate photodissociation of BeH$^+$ ions within a Coulomb crystal of thousands of $^9$Be$^+$ ions confined in a Penning trap. Because BeH$^+$ ions are created via exothermic reactions between trapped, laser-cooled Be$^+$($^2text{P}_{3/2}$) an
d background H$_2$ within the vacuum chamber, they represent a major contaminant species responsible for infidelities in large-scale trapped-ion quantum information experiments. The rotational-state-insensitive dissociation scheme described here makes use of 157 nm photons to produce Be$^+$ and H as products, thereby restoring Be$^+$ ions without the need for reloading. This technique facilitates longer experiment runtimes at a given background H$_2$ pressure, and may be adapted for removal of MgH$^+$ and AlH$^+$ impurities.
We employ spin-dependent optical dipole forces to characterize the transverse center-of-mass (COM) motional mode of a two-dimensional Wigner crystal of hundreds of $^9$Be$^+$. By comparing the measured spin dephasing produced by the spin-dependent fo
rce with the predictions of a semiclassical dephasing model, we obtain absolute mode temperatures in excellent agreement with both the Doppler laser cooling limit and measurements obtained from a previously published technique (B. C. Sawyer et al. Phys. Rev. Lett. textbf{108}, 213003 (2012)). Furthermore, the structure of the dephasing histograms allows for discrimination between initial thermal and coherent states of motion. We also apply the techniques discussed here to measure, for the first time, the ambient heating rate of the COM mode of a 2D Coulomb crystal in a Penning trap. This measurement places an upper limit on the anomalous single-ion heating rate due to electric field noise from the trap electrode surfaces of $frac{dbar{n}}{dt}sim 5$ s$^{-1}$ for our trap at a frequency of 795 kHz, where $bar{n}$ is the mean occupation of quantized COM motion in the axial harmonic well.
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 $sim$400 $mu$m-diameter planar crystal of several hundred $^9$Be
$^+$ ions exhibiting complex drumhead modes in the confining potential of a Penning trap. Exploiting precise control over the $^9$Be$^+$ 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 ($sim$20 olinebreak$mu$m). Center-of-mass displacements below 1 nm are detected via entanglement of spin and motional degrees of freedom.
