Comparison of linear and nonlinear planar mode spectra in an ultracold ion Penning trap plasmas

Penning trap plasmas with a rotating wall potential and Doppler laser cooling provide a platform for quantum simulation and quantum sensing experiments [J. G. Bohnet, et al.,Sci. 352, 1297 (2016), K. Gilmore, et al. Phys. Rev. Lett. 118, 263602 (2017)]. Such ultracold plasmas form a stable circular two-dimensional ion crystal with a temperature of approximately one milli-Kelvin. Axial modes (|| B/out-of-plane motions) of the crystal are well diagnosed and widely utilized for quantum information protocols. Less experimental information is known about the planar modes (⊥ B/in-plane motions) which split into two branches - magnetron (or E x B) modes and cyclotron modes. Direct numerical simulation provides insights into the planar dynamics. For example, simulation has shown thermal displacements from the crystal equilibrium corresponding to 10mk in the planar direction broaden the axial mode spectrum even when these axial modes are cooled below 1mk [Athreya Shankar et al. Phys. Rev. A, 10 102 (2020)]. Here, we linearize the Coulomb force in our existing molecular-dynamics-type Penning trap code [C Tang, et al., Phys. Plasmas, 26 073504, (2019)]. Linearization provides the capability to isolate the planar laser cooling model without the effects of mode coupling both within and between the two planar mode branches.