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

• Main Authors: Shankar, Athreya, Tang, Chen, Affolter, Matthew, Gilmore, Kevin, Dubin, Daniel H. E, Parker, Scott, Holland, Murray J, Bollinger, John J
• Format: Journal Article
• Language: English
• Published: 19-08-2020
• Subjects: Physics - Atomic Physics; Physics - Plasma Physics; Physics - Quantum Physics
• DOI: 10.48550/arxiv.2008.08239

Phys. Rev. A 102, 053106 (2020) 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.