Distance scaling of electric-field noise in a surface-electrode ion trap

Abstract

We investigate anomalous ion-motional heating, a limitation to multi-qubit quantum-logic gate fidelity in trapped-ion systems, as a function of ion-electrode separation. Using a multi-zone surfaceelectrode trap in which ions can be held at five discrete distances from the metal electrodes, we measure power-law dependencies of the electric-field noise experienced by the ion on the ion-electrode distance d. We find a scaling of approximately d −4 regardless of whether the electrodes are at room temperature or cryogenic temperature, despite the fact that the heating rates are approximately two orders of magnitude smaller in the latter case. Through auxiliary measurements using application of noise to the electrodes, we rule out technical limitations to the measured heating rates and scalings. We also measure frequency scaling of the inherent electric-field noise close to 1/f at both temperatures. These measurements eliminate from consideration anomalous-heating models which do not have a d −4 distance dependence, including several microscopic models of current interest.

Distance scaling and polarization of electric-field noise in a surface ion trap

“…We find that the Rabi method gives heating rates that are systematically about 17% higher than for the sidebandasymmetry method. This difference is consistent with findings from other experiments [14,18] and may be linked to the non-zero projection of other motional modes on the measurement laser or laser intesnity noise. To simplify comparison of the electric-field noise across the full range of ion-surface distances, we scale the data from the Rabi-oscillation method by a constant factor of 0.85.…”

“…The magnitude of electric-field noise in this experiment was about an order of magnitude higher than the best published results for untreated surface traps. The second study found β = 4.0 for a multizone niobium surface trap [14]. Here, the ion trap contained several trapping zones spaced by on the order of 1 mm, where the electrodes at each zone were scaled to trap ions at different distances from the surface.…”

Simulating the performance of a distance-3 surface code in a linear ion trap

“…A heating rate (ṅ) of about 58 quanta s −1 has been observed for a single 9 Be + ion on a room temperature surface trap with a cleaned surface (40 μs above the trap surface, 3.6 MHz trap frequency) [126] and a silicon based trap in a cryogenic environment used to trap individual 40 Ca + ions exhibited heating rates as low as 0.33 quanta s −1 (0.6(2) quanta s −1 on average) (230 μs from the surface, 1.1 MHz trap frequency) [127]. For 171 Yb + ions located 70 μs above the trap surface with a trap frequency of 3 MHz, these heating rates correspond to expected heating rates of 0.5 quanta s −1 and 0.7 quanta s −1 assuming that the heating rate scales as ω −2.4 for fixed ion and d −4 for fixed ω [126,128]. The heavy mass of Yb + relative to Ca + and Be + results in a lower heating rate for the same spectral noise density and achieving heating rates of 1 quanta s −1 by surface cleaning or cryogenic trapping is feasible.…”

Convenient Real-Time Monitoring of the Contamination of Surface Ion Trap

“…Because the measurement of electric-field noise based on trapped ions is a numerous and complicated process of operation, and the surface adatoms is not the only reason for electric-field noise. Although, the electricfield noise can be measured by trapped ions [6,9,23,24]to indirect describe the surface adatoms, it is unable to monitor in real-time and to reflect the adatoms film. In addition, our contamination measuring method for surface ion trap also can to be a new research means for anomalous heating of ions.…”