  We demonstrate confinement of individual atomic ions in a radio-frequency
Paul trap with a novel geometry where the electrodes are located in a single
plane and the ions confined above this plane. This device is realized with a
relatively simple fabrication procedure and has important implications for
quantum state manipulation and quantum information processing using large
numbers of ions. We confine laser-cooled Mg-24 ions approximately 40 micrometer
above planar gold electrodes. We measure the ions' motional frequencies and
compare them to simulations. From measurements of the escape time of ions from
the trap, we also determine a heating rate of approximately five motional
quanta per millisecond for a trap frequency of 5.3 MHz.
