Temperature Dependence of Electric Field Noise above Gold Surfaces

Electric field noise from fluctuating patch potentials is a significant problem for a broad range of precision experiments, including trapped ion quantum computation and single spin detection. Recent results demonstrated strong suppression of this noise by cryogenic cooling, suggesting an underlying thermal process. We present measurements characterizing the temperature and frequency dependence of the noise from 7 to 100 K, using a single ${\mathrm{Sr}}^{+}$ ion trapped $75\mu \mathrm{m}$ above the surface of a gold plated surface electrode ion trap. The noise amplitude is observed to have an approximate $1/f$ spectrum around 1 MHz, and grows rapidly with temperature as $T^{\beta }$ for $\beta$ from 2 to 4. The data are consistent with microfabricated cantilever measurements of noncontact friction but do not extrapolate to the dc measurements with neutral atoms or contact potential probes.

Figure 1

Temperature dependence of the measured field noise in trap II (dots) and the fit to $S_E(T)=42\mathbf{(}1+(T/46\mathrm{K}{)}^{4.1}\mathbf{)}\times {10}^{-15}{\mathrm{V}}^2/{\mathrm{m}}^2/\mathrm{Hz}$ (dashed line).

Figure 2

Noise spectrum at 6 different temperatures measured in trap IIIa. Plotted are the values of $S_E(f)f$ and fit lines to $S_E(f)f=f^{1-\alpha }$. The fit exponent $\alpha$ and the measurement temperature are indicated above fit lines.

Figure 3

Anomalous behavior observed in trap II, after cleaning in an ultrasonic bath. Datapoints taken at 0.86 MHz (red circle) and 1.23 MHz (blue $\times$) were scaled to 1 MHz assuming $1/f$ scaling and fitted to an Arrhenius curve (dashed line).