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

We investigate anomalous ion-motional heating, a limitation to multiqubit quantum-logic gate fidelity in trapped-ion systems, as a function of ion-electrode separation. Using a multizone surface-electrode 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 the application of noise to the electrodes, we rule out technical limitations to the measured heating rates and scalings. We also measure the 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.

Figure 1

Variable-height surface-electrode trap. The upper figure shows the layout of the electrodes in the central region of the chip where the ions are trapped. Purple dots represent the centers of the various zones axially separated along the common radio-frequency electrode (highlighted in green). The ions are trapped above these locations at the distance labeled in each of the respective zones. Sets of electrodes to which noise was added to determine the technical-noise scaling are denoted by color; electrodes in each set were connected together on-chip. The lateral extent of this figure is approximately 7.6 mm. The lower figure is a photograph of the 1 ${\mathrm{cm}}^2$ chip, after demounting from the chamber and the removal of wire bonds, with a U.S. one-cent piece for scale. The different zones can be seen in the center of the chip, largest to smallest from the bottom to the top in this image.

Figure 2

Scaling of ion heating rate with ion-electrode distance at two different temperatures. Heating rates were measured on a single-ion axial mode at 850 kHz in all cases; the red, solid [blue, open] points are for a chip temperature of 295(1)K [5(1) K]. The lines are fits to the data in each set, and the exponents and uncertainties denoted in the legend are determined from these fits. Error bars are standard uncertainties in the heating rates as propagated through the sideband-ratio measurements.

Figure 3

Frequency scaling of the heating rate of the ion's axial mode as a function of trap frequency at two different temperatures with $d=64\mu \mathrm{m}$. Red, solid [blue, open] points are taken at 295(1)K [5(1) K]. The lines are power-law fits to the data points taken at each temperature, and the determined exponents and uncertainties are denoted in the legend.

Figure 4

Heating-rate contributions due to the injection of technical noise. Noise is injected onto adjacent electrodes as described in the text. The solid points shown in red are experimental data, all taken at $5\left(1\right)$ K. A background heating rate (i.e., with no added noise) is measured at each distance and is subtracted from the the total heating rate. The blue, open circles are the expectation of the increased heating rate due to calculation of the characteristic distances of the various electrode sets (see text). The diagonal bars on the latter data represent the (correlated) uncertainty range of heating rates expected due to the uncertainty in ion position. The legend depicts the fitted exponent scalings and uncertainties.