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Sympathetic Ground State Cooling and Time-Dilation Shifts in an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>Al</mml:mi></mml:mrow><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>27</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math> Optical Clock
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 …