title: Sympathetic Ground State Cooling and Time-Dilation Shifts in an ^{27}Al^{+} Optical Clock.
abstract: We report on Raman sideband cooling of ^{25}Mg^{+} to sympathetically cool the secular modes of motion in a ^{25}Mg^{+}-^{27}Al^{+} two-ion pair to near the three-dimensional (3D) ground state. The evolution of the Fock-state distribution during the cooling process is studied using a rate-equation simulation, and various heating sources that limit the efficiency of 3D sideband cooling in our system are discussed. We characterize the residual energy and heating rates of all of the secular modes of motion and estimate a secular motion time-dilation shift of -(1.9±0.1)×10^{-18} for an ^{27}Al^{+} clock at a typical clock probe duration of 150 ms. This is a 50-fold reduction in the secular motion time-dilation shift uncertainty in comparison with previous ^{27}Al^{+} clocks.
authors.affiliation: Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA.|Department of Physics, University of Colorado, Boulder, Colorado 80309, USA.
authors.forename: J-S
authors.initials: JS
authors.lastname: Chen
authors.affiliation: Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA.
authors.forename: S M
authors.initials: SM
authors.lastname: Brewer
authors.affiliation: Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA.
authors.forename: C W
authors.initials: CW
authors.lastname: Chou
authors.affiliation: Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA.|Department of Physics, University of Colorado, Boulder, Colorado 80309, USA.
authors.forename: D J
authors.initials: DJ
authors.lastname: Wineland
authors.affiliation: Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA.|Department of Physics, University of Colorado, Boulder, Colorado 80309, USA.
authors.forename: D R
authors.initials: DR
authors.lastname: Leibrandt
authors.affiliation: Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA.
authors.forename: D B
authors.initials: DB
authors.lastname: Hume