Measuring Anomalous Heating in a Planar Ion Trap with Variable Ion-Surface Separation

Cold ions trapped in the vicinity of conductive surfaces experience heating of their oscillatory motion. Typically, the rate of this heating is orders of magnitude larger than expected from electric field fluctuations due to thermal motion of electrons in the conductors. This effect, known as anomalous heating, is not fully understood. One of the open questions is the heating rate’s dependence on the ion-electrode separation. We present a direct measurement of this dependence in an ion trap of simple planar geometry. The heating rates are determined by taking images of a single ${}^{172}{\mathrm{Yb}}^{+}$ ion’s resonance fluorescence after a variable heating time and deducing the trapped ion’s temperature from measuring its average oscillation amplitude. Assuming a power law for the heating rate versus ion-surface separation dependence, an exponent of $-3.79\pm 0.12$ is measured.

Figure 1

Trapping height variation principle. (a) Schematic representation of the surface trap in maximum trapping height mode. A rf voltage of amplitude $U$ is applied to the electrodes shown in dark grey, the central electrode is grounded. Equipotential lines of the effective potential in the plane perpendicular to the trap axis ($y$ direction) are shown. (b) The trap and effective potential when an additional rf voltage of amplitude $1/2U$ is applied to the central electrode to reduce the trapping height.

Figure 2

Ion images summed over the radial direction (blue crosses) and Gaussian fits (red solid lines) at (a) $t=0\mathrm{ms}$, (b) $t=1.4\mathrm{ms}$, and (c) $t=2.8\mathrm{ms}$ after opening the cooling laser. The heating time $T_H$ is 15 s, exposure time is 0.2 ms, 209 experimental runs are summed.

Figure 3

Spread of the resonance fluorescence of an ion in the axial direction expressed as rms width $\sigma$ of the fitted Gaussians (some of which are shown in Fig. 2, the corresponding points are marked with filled circles) depending on time. An exponential fit is shown in red.

Figure 4

Heating rate (in Kelvin per second) dependence on the axial secular frequency. The trapping height is $134\pm 1.5\mu \mathrm{m}$ for all data points.

Figure 5

Heating rate (in Kelvin per second) dependence on the trapping height. The axial frequency is $196\pm 2\mathrm{kHz}$ for all data points.