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. Dubin, Scott E. Parker, Murray Holland, John Bollinger
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, which is exploited for quantum information protocols, can be described by a discrete set of normal modes called the drumhead modes. 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 in the range of 10 mK. Our study therefore motivates the need for designing improved techniques to cool the in-plane degrees of freedom.
, Tang, C.
, Affolter, M.
, Gilmore, K.
, Dubin, D.
, Parker, S.
, Holland, M.
and Bollinger, J.
Broadening of the drumhead mode spectrum due to in-plane thermal fluctuations of two-dimensional trapped-ion crystals in a Penning trap, Physical Review A, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=930873
(Accessed October 1, 2023)