Insensitivity of the rate of ion motional heating to trap-electrode material over a large temperature range

We present measurements of trapped-ion motional-state heating rates in niobium and gold surface-electrode ion traps over a range of trap-electrode temperatures from approximately 4 K to room temperature (295 K) in a single apparatus.Using the sideband-ratio technique after resolved-sideband cooling of single ions to the motional ground state, we find low-temperature heating rates more than two orders of magnitude below the room-temperature values and approximately equal to the lowest measured heating rates in similarly sized cryogenic traps. We find similar behavior in the two very different electrode materials, suggesting that the anomalous heating process is dominated by non-material-specific surface contaminants. Through precise control of the temperature of cryopumping surfaces, we also identify conditions under which elastic collisions with the background gas can lead to an apparent steady heating rate, despite rare collisions.

Figure 1

Ion levels and motional decoherence measurement. (a) Electronic level diagram of ${}^{88}$Sr${}^{+}$ including relevant transitions and Zeeman sublevels. Transitions (i) and (ii) are used for Doppler cooling and repumping to keep the ion in the cooling cycle, respectively. These transitions are also used for ion state detection. The others are used for (iii) optical pumping (OP), (iv) sideband cooling (SC) and probing, and (v) quenching during OP and SC and before each experiment. (b) Example of data from a heating rate measurement in a niobium trap at $3.8$ K using the sideband spectroscopy method. The red and blue sidebands of the $S_{1/2}$–$D_{5/2}$ transition (insets at particular probe delays) are fit to a Rabi line shape to extract their amplitudes, which are used to calculate $\langle n\rangle$ as a function of probe delay (main figure) after cooling to the ground state. A linear fit to these points provides the heating rate. Insets show $S$-state probability as a function of probe frequency near the sidebands. Errors depicted in the insets are statistical including projection noise and are propagated through the sideband fits to produce errors in the main figure points.

Figure 2

Motional heating rate of the $1.32$ MHz axial mode versus trap temperature for two niobium traps and a gold trap. The right axis is translated into electric-field noise spectral density via $S_E\left(\omega \right)=\frac{4m\hslash \omega }{q^2}\frac{d\langle n\rangle }{dt}$. Here $\omega =2\pi \times f$ is the angular trap frequency, $q$ is the ion charge, and $m$ is the ion mass. All error bars are statistical based on errors propagated through fits of the sideband spectra (cf. Fig. 1). The dotted lines are fits to power laws in temperature to all data; see text for details. For 70 K and above, the scaling exponent is 2.13(5), and below this temperature, the exponent is 0.54(4).

Figure 3

Electric-field noise spectral density, normalized by angular trap frequency, as a function of ion-electrode distance $d$. Measurements in surface traps from several groups are included. Closed (open) symbols are room-temperature (cryogenic) measurements. The measurements associated with this work are the blue (gold) four-pointed stars for the niobium (gold); in the case of this work, the open symbols represent data taken at $3.8$–$5.1$ K. Other groups' cryogenic measurements are taken over a range of 4–10 K (see individual references for details). Bow-tie symbols represent room-temperature data from groups incorporating in situ surface milling: vertical (horizontal) bow ties are for pre-(post-)milling measurements. References [7, 8, 9, 10, 18, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35] for all plotted data are given in the legend.