  We demonstrate ground-state cooling of a trapped ion using radio-frequency
(RF) radiation. This is a powerful tool for the implementation of quantum
operations, where RF or microwave radiation instead of lasers is used for
motional quantum state engineering. We measure a mean phonon number of
$\overline{n} = 0.13(4)$ after sideband cooling, corresponding to a
ground-state occupation probability of 88(7)\%. After preparing in the
vibrational ground state, we demonstrate motional state engineering by driving
Rabi oscillations between the n=0 and n=1 Fock states. We also use the ability
to ground-state cool to accurately measure the motional heating rate and report
a reduction by almost two orders of magnitude compared to our previously
measured result, which we attribute to carefully eliminating sources of
electrical noise in the system.
