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Equilibration of the planar modes of ultracold two-dimensional ion crystals in a Penning trap



Chen Tang, Athreya Shankar, Daniel Dubin, Dominic Meiser, Scott Parker, John J. Bollinger


Planar thermal equilibration is studied using direct numerical simulations of ultracold two-dimensional ion crystals in a Penning trap with a rotating wall. The large magnetic field of the trap splits the modes that describe in-plane motion of the ions into two branches: high-frequency cyclotron modes dominated by kinetic energy and low-frequency E × B modes dominated by potential energy associated with thermal position displacements. Using an eigenmode analysis we extract the equilibration rate between these two branches as a function of the ratio of the frequencies that characterize the two branches and observe this equilibration rate to be exponentially suppressed as the ratio increases. Under experimental conditions relevant for current work at NIST, the predicted equilibration time is orders of magnitude longer than any relevant experimental timescales. We also study the coupling rate dependence on the initial energy of the planar modes and the number of ions. In addition, we show how increasing the rotating wall strength improves crystal stability. These details of in-plane mode dynamics help set the stage for developing strategies to efficiently cool the in-plane modes and improve the performance of single plane ion crystals for quantum information processing.
Physical Review A


Coulomb crystals, cyclotron modes, ExB modes, Penning trap, strongly magnetized, thermal equilibration, trapped ions


Tang, C. , Shankar, A. , Dubin, D. , Meiser, D. , Parker, S. and Bollinger, J. (2020), Equilibration of the planar modes of ultracold two-dimensional ion crystals in a Penning trap, Physical Review A, [online],, (Accessed April 19, 2024)
Created May 11, 2020, Updated March 8, 2024