Efficient Molecular Dynamics Simulations of 3D Ion Crystals in a Penning Trap

We report results from a newly developed molecular dynamics simulation using the fast multipole method (FMM) which models the motion of 3D ion crystals confined in a Penning trap.  Understanding and controlling the motional degrees of freedom of such crystals is essential for experiments in quantum sensing and quantum simulation.^1,2  Previous computational studies of ion crystals in Penning traps have probed the crystal mode spectra and modeled Doppler laser cooling of these modes.^3,4  However, most of this work has been limited to 2D planar crystals, in which case the eigenmodes of the crystal decouple into purely planar and axial modes.⁵  In 3D crystals, mixing of the planar and axial modes occurs via the Coulomb interaction.⁶  We illustrate this mixing by finding 3D crystal equilibria and then calculating the eigenmodes.  Furthermore, our preliminary laser cooling simulations suggest that 3D crystals may be cooled using existing experimental protocols.  Our code utilizes the fast multipole method to compute the Coulomb force which greatly accelerates the simulation for large ion number, N.⁷  Since quantum sensing experiments can detect displacements proportional to N^-½, the ability to simulate large crystals will be important for future studies.

[1] [K.A. Gilmore etal., Science, 373, 6555 (2021)] 

[2] [J.G. Bohnet etal., Science, 352, 6291 (2016)]

[3] [C. Tang etal., Phys. Plasma, 26, 073504 (2019)]

[4] [A. Shankar etal., Phys. Rev. A, 102, 053106 (2020)] 

[5] [C.C.J. Wang etal., Phys. Rev. A, 87, 013422 (2013)] 

[6] [D.H.E. Dubin, Phys Plasmas, 27, 102107 (2020)]

[7] [L. Greengard and V. Rokhlin, Acta Numerica, 6, 229 (1997)]