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تسجيل مستخدم جديدEquilibration of the planar modes of ultracold two dimensional ion crystals in a Penning trap
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Planar thermal equilibration is studied using direct numerical simulations of ultracold two-dimensional (2D) 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 $mathbf{E times B}$ 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 thermal temperature and the number of ions. Besides, 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.
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Penning traps, with their ability to control planar crystals of tens to hundreds of ions, are versatile quantum simulators. Thermal occupations of the motional drumhead modes, transverse to the plane of the ion crystal, degrade the quality of quantum
simulations. Laser cooling using electromagnetically induced transparency (EIT cooling) is attractive as an efficient way to quickly initialize the drumhead modes to near ground-state occupations. We numerically investigate the efficiency of EIT cooling of planar ion crystals in a Penning trap, accounting for complications arising from the nature of the trap and from the simultaneous cooling of multiple ions. We show that, in spite of challenges, the large bandwidth of drumhead modes (hundreds of kilohertz) can be rapidly cooled to near ground-state occupations within a few hundred microseconds. Our predictions for the center-of-mass mode include a cooling time constant of tens of microseconds and an enhancement of the cooling rate with increasing number of ions. Successful experimental demonstrations of EIT cooling in the NIST Penning trap [E. Jordan, K. A. Gilmore, A. Shankar, A. Safavi-Naini, M. J. Holland, and J. J. Bollinger, Near ground-state cooling of two-dimensional trapped-ion crystals with more than 100 ions, (2018), submitted.] validate our predictions.
Two-dimensional crystals of ions stored in Penning traps are a leading platform for quantum simulation and sensing experiments. For small amplitudes, the out-of-plane motion of such crystals can be described by a discrete set of normal modes called t
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