Radio frequency sideband cooling and sympathetic cooling of trapped ions in a static magnetic field gradient

We report a detailed investigation on near-ground state cooling of one and two trapped atomic ions. We introduce a simple sideband cooling method for confined atoms and ions, using RF radiation applied to bare ionic states in a static magnetic field gradient, and demonstrate its application to ions confined at secular trap frequencies, ωz≈2π×117 kHz. For a single 171Yb+ ion, the sideband cooling cycle reduces the average phonon number, n from the Doppler limit to n= 0.30(12). This is in agreement with the theoretically estimated lowest achievable phonon number in this experiment. We extend this method of RF sideband cooling to a system of two 171Yb+ ions, resulting in a phonon number of n= 1.1(7) in the centre-of-mass mode. Furthermore, we demonstrate the first realization of sympathetic RF sideband cooling of an ion crystal consisting of two individually addressable identical isotopes of the same species.