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

TL;DR

This paper investigates how in-plane thermal fluctuations in two-dimensional ion crystals in Penning traps cause broadening of the drumhead mode spectrum, affecting quantum simulation fidelity and suggesting improved cooling methods.

Contribution

It identifies in-plane thermal fluctuations as a key factor in spectrum broadening and explores the effects of magnetic fields on in-plane normal modes in Penning traps.

Findings

In-plane thermal fluctuations significantly broaden the drumhead mode spectrum.

Magnetic fields induce unconventional in-plane normal modes with unequal potential and kinetic energies.

Current conditions cause in-plane potential energy fluctuations of about 10 mK.

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.