  Dense arrays of trapped ions provide one way of scaling up ion trap quantum
information processing. However, miniaturization of ion traps is currently
limited by sharply increasing motional state decoherence at sub-100 um
ion-electrode distances. We characterize heating rates in cryogenically cooled
surface-electrode traps, with characteristic sizes in 75 um to 150 um range.
Upon cooling to 6 K, the measured rates are suppressed by 7 orders of
magnitude, two orders of magnitude below previously published data of similarly
sized traps operated at room temperature. The observed noise depends strongly
on fabrication process, which suggests further improvements are possible.
