Mode Resolved Protocol for Measuring the In-Plane Mode Temperatures in a 2D Ion Crystal in a Penning Trap

Two dimensional crystals of 100's of ions in a Penning trap have demonstrated numerous promising results in quantum simulation and sensing. One recent result was the demonstration of electric field sensing of 240 ± 10 nV/m in 1 second, with sensitivity to motional displacements 8.8 ± 0.4 dB below the standard quantum limit. A fundamental limitation was 40 Hz fluctuations of the center of mass mode, believed to be in part caused by elevated in-plane mode temperatures of order 10 mK. We present a new experimental protocol to directly measure the in-plane temperature in the rotating frame of the crystal in a mode resolved way. Finally, we summarize ideas for improving the cooling of the in-plane modes.