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arXiv · 2008.08239

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

Athreya Shankar·Chen Tang·Matthew Affolter·Kevin Gilmore·Daniel H. E. Dubin·Scott Parker·Murray J. Holland·John J. Bollinger
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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.

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Athreya Shankar, Chen Tang, Matthew Affolter, Kevin Gilmore, Daniel H. E. Dubin, Scott Parker, Murray J. Holland, John J. Bollinger. 2020-08-19. Broadening of the drumhead mode spectrum due to in-plane thermal fluctuations of two-dimensional trapped ion crystals in a Penning trap. https://doi.org/10.1103/physreva.102.053106

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