Efficient Simulation Framework for Laser Cooling Ion Crystals in a Penning Trap

Penning trap ion crystals offer a remarkable platform for quantum sensing and simulation experiments with hundreds of qubits; however, complex many-body dynamics challenge these efforts. We present a first principles simulation framework for studying laser cooling dynamics in 2D ion crystals and efficiently simulating larger 3D ion crystals of thousands of ions using the fast multipole method. Current experiments with 2D ion crystals are challenged by the slow laser cooling of their ExB modes, but our simulations suggest a hundred-fold cooling rate speed up over experiment can be achieved by coupling the ExB motion to the rapidly laser cooled axial motion. Additionally, using the fast multipole method, we investigate mixing of planar and axial modes in 3D ion crystals and suggest the feasibility of cooling 3D crystals. Our scalable approach enables studying large crystals that would allow for higher sensitivity in future quantum sensing experiments.