Using Spin Dephasing for Mode Thermometry in a 2D Trapped-Ion Crystal

Crystals of hundreds of ions confined in Penning traps allow for studies of large quantum systems in a two-dimensional geometry. The transverse ``drumhead" modes of our 2D crystal along with the valence electron spin of the trapped $^9$Be$^+$ serve as a resource for generating spin-motion and spin-spin entanglement. Applying a spin-dependent optical dipole force to a macroscopic spin superposition, we determine the absolute temperature of a single drumhead mode by directly measuring spin dephasing induced by thermal fluctuations of the motion. This technique does not rely on resolved-sideband transitions and is applicable over a large range of mode temperatures. Furthermore, by measuring the spin distribution directly, we distinguish between coherent and thermal mode occupation. Trapped ions are extremely sensitive to small external forces ($\sim$1 yN), and we will discuss extensions of this technique for use in spectroscopy and ion trap characterization.