Implications of surface noise for the motional coherence of trapped ions

Electric noise from metallic surfaces is a major obstacle towards quantum applications with trapped ions due to motional heating of the ions. Here, we discuss how the same noise source can also lead to pure dephasing of motional quantum states. The mechanism is particularly relevant at small ion-surface distances, thus imposing a new constraint on trap miniaturization. By means of a free induction decay experiment, we measure the dephasing time of the motion of a single ion trapped 50~$\mu$m above a Cu-Al surface. From the dephasing times we extract the integrated noise below the secular frequency of the ion. We find that none of the most commonly discussed surface noise models for ion traps describes both, the observed heating as well as the measured dephasing, satisfactorily. Thus, our measurements provide a benchmark for future models for the electric noise emitted by metallic surfaces.