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

• URL: http://arxiv.org/abs/2008.08239v1
• Date: Wed, 19 Aug 2020 03:30:21 GMT
• Title: Broadening of the drumhead mode spectrum due to in-plane thermal fluctuations of two-dimensional trapped ion crystals in a Penning trap
• Authors: Athreya Shankar, Chen Tang, Matthew Affolter, Kevin Gilmore, Daniel H. E. Dubin, Scott Parker, Murray J. Holland and John J. Bollinger
• Abstract summary: 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. We establish in-plane thermal fluctuations in ion positions as a major contributor to the broadening of the drumhead mode spectrum.
• Score: 5.267246878862164
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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