Broadening of the drumhead mode spectrum due to in-plane thermal fluctuations of two-dimensional trapped ion crystals in a Penning trap

Abstract

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 the drumhead modes, which can be used to implement a range of quantum information protocols. However, experimental observations of crystals with Doppler-cooled and even near-ground-state-cooled drumhead modes reveal an unresolved drumhead mode spectrum. In this work, we establish in-plane thermal fluctuations in ion positions as a major contributor to the broadening of the drumhead mode spectrum. In the process, we demonstrate how the confining magnetic field leads to unconventional in-plane normal modes, whose average potential and kinetic energies are not equal. This property, in turn, has implications for the sampling procedure required to choose the in-plane initial conditions for molecular dynamics simulations. For current operating conditions of the NIST Penning trap, our study suggests that the two dimensional crystals produced in this trap undergo in-plane potential energy fluctuations of the order of $10$ mK. Our study therefore motivates the need for designing improved techniques to cool the in-plane degrees of freedom.

17 pages, 10 figures

References in corpus (2)

• Bang-bang shortcut to adiabaticity in the Dicke model as realized in a Penning trap experiment
• Normal Modes, Rotational Inertia, and Thermal Fluctuations of Trapped Ion Crystals

Cited by in corpus (13)

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• Bilayer crystals of trapped ions for quantum information processing
• Individual-Ion Addressing and Readout in a Penning Trap
• Equilibration of the planar modes of ultracold two dimensional ion crystals in a Penning trap
• Rapid cooling of the in-plane motion of two-dimensional ion crystals in a Penning trap to millikelvin temperatures
• In-situ-tunable spin-spin interactions in a Penning trap with in-bore optomechanics
• Numerical Simulations of 3D Ion Crystal Dynamics in a Penning Trap using the Fast Multipole Method
• Adiabatic Cooling of Planar Motion in a Penning Trap Ion Crystal to Sub-Millikelvin Temperatures
• Parametric Amplification of Spin-Motion Coupling in Three-Dimensional Trapped-Ion Crystals
• Efficient Three-Dimensional Sub-Doppler Cooling of ${}^{40}$Ca${}^{+}$ in a Penning Trap