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 engi
neering. 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.
Applying a magnetic field gradient to a trapped ion allows long-wavelength microwave radiation to produce a mechanical force on the ions motion when internal transitions are driven. We demonstrate such a coupling using a single trapped Yb{171}~ion, a
nd use it to produce entanglement between the spin and motional state, an essential step towards using such a field gradient to implement multi-qubit operations.
