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, <inline-graphic></inline-graphic> kHz. For a single <inline-graphic></inline-graphic>Yb<inline-graphic></inline-graphic> ion, the sideband cooling cycle reduces the average phonon number, <inline-graphic></inline-graphic> from the Doppler limit to <inline-graphic></inline-graphic> 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 <inline-graphic></inline-graphic>Yb<inline-graphic></inline-graphic> ions, resulting in a phonon number of <inline-graphic></inline-graphic> 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. [ABSTRACT FROM AUTHOR]