Measurement of ion motional heating rates over a range of trap frequencies and temperatures

We present measurements of the motional heating rate of a trapped ion at different trap frequencies and temperatures between $\sim 0.6$ and 1.5 MHz and $\sim 4$ and 295 K. Additionally, we examine the possible effect of adsorbed surface contaminants with boiling points below $\sim 105{}^{\circ }\mathrm{C}$ by measuring the ion heating rate before and after locally baking our ion trap chip under ultrahigh vacuum conditions. We compare the heating rates presented here to those calculated from available electric-field noise models. We can tightly constrain a subset of these models based on their expected frequency and temperature scaling interdependence. Discrepancies between the measured results and predicted values point to the need for refinement of theoretical noise models in order to more fully understand the mechanisms behind motional trapped-ion heating.

Figure 1

Measured axial motional heating rate as a function of trap frequency for different trap temperatures. Error bars reflect statistical error propagated through the sideband ratio fitting procedure. Solid lines are fits to power law frequency scalings $\dot{\overline{n}}\left(f\right)\propto f^{-\alpha -1}$, which correspond to electric-field noise spectral densities $S_E\left(f\right)\propto f^{-\alpha }$. Inset shows the extracted fit exponents $\alpha$ with error bars from uncertainties of fits. The weighted average value from this data $\alpha =0.6\left(1\right)$ is shown as a horizontal line.

Figure 2

Measured axial motional heating rate as a function of trap temperature for different trap frequencies. Solid lines are fits for power law temperature scaling with zero-temperature offset, $\dot{\overline{n}}\left(T\right)={\dot{\overline{n}}}_0[1+{\left(\frac{T}{T_0}\right)}^{\beta }]$. The inset shows the extracted fit exponents $\beta$ with weighted average value of 1.59(3) shown as a horizontal line.

Figure 3

Measured axial motional heating rates at different trap frequencies and temperatures before and after local baking of the ion trap chip at $107{}^{\circ }\mathrm{C}$ for $\sim 72$ hours under UHV conditions. The frequency dependence of the heating rate and associated electric-field noise is largely unchanged following this procedure, suggesting that adsorbed water and laboratory solvents are not major causes of motional ion heating.