Heating rates and ion-motion control in a $\mathsf{Y}$-junction surface-electrode trap

We measure ion heating following transport throughout a $\mathsf{Y}$-junction surface-electrode ion trap. By carefully selecting the trap voltage update rate during adiabatic transport along a trap arm, we observe minimal heating relative to the anomalous heating background. Transport through the junction results in an induced heating between 37 and 150 quanta in the axial direction per traverse. To reliably measure heating in this range, we compare the experimental sideband envelope, including up to fourth-order sidebands, to a theoretical model. The sideband envelope method allows us to cover the intermediate heating range inaccessible to the first-order sideband and Doppler recooling methods. We conclude that quantum information processing in this ion trap will likely require sympathetic cooling in order to support high fidelity gates after junction transport.

Figure 1

Left: The Sandia $\mathsf{Y}$-junction surface-electrode trap: 47 of the 61 dc electrodes (black labels) are connected to the DACs, and the remainder (white labels) are grounded. Right: Optical, electrical, and vacuum access. The trap and the chamber are shown in the same orientation. Inset: An ion crystal held above the loading aperture.

Figure 2

Experimental control system: dc voltages are generated by 12 NI PXI 6713 DAC cards. An amplifier circuit ($G$ = 3) increases the voltage prior to filtering by a single pole low-pass filter ($f_c$ = 60 kHz). Six AD9958 DDS boards generate $\le$250-MHz signals for all necessary AOMs. The 45-MHz rf trapping signal is also generated by a DDS, amplified by a 40-dB rf amplifier, and filtered by a $Q\sim 100$ helical resonator. Approximately $1/6$ of the rf amplitude following the resonator is sampled to monitor the applied rf trap voltage. Custom control software manages all hardware subsystems and digital triggers generated by an FPGA are used to coordinate the various subsystems.

Figure 3

Stationary heating rate measurements for the axial mode with a frequency of $1.738$ MHz. (a) A first-order sideband comparison measurement giving a heating rate of $3.00\pm 0.06$ quanta/ms. (b) Measurement of the motional decoherence of Rabi oscillations yielding a heating rate of $4.0\pm 0.2$ quanta/ms.

Figure 4

Dynamic heating in transport. (a) A single measurement cycle: the ion is sideband cooled to $\overline{n}\le 0.5$ and undergoes round-trip transport. A 50-$\mu$s pause, labeled “Relax,” is inserted between the shuttling and measurement to ensure electrode voltages had reached their final, static value. A reference measurement with exactly the same elapsed time is run immediately afterwards to allow isolation of the dynamic heating. (b) The ion shuttled along the loading arm from (E26, E36) for $177.3$ $\mu$m to (E24, E34) and back. (c) Ion heating during transport retrieved from first-order sideband comparison, with different wave-form update frequencies, revealing two resonance peaks. A simple dual-peak Lorentzian fit shows that they are approximately $1/5$ and $1/7$ of the stationary secular frequency (see text). The inset shows that the heating is low at update frequencies between these resonances. The data points are averaged from ten measurements of $\overline{n}$. The sideband comparison method becomes less sensitive to $\overline{n}$ as $\overline{n}$ increases resulting in large error bars near the heating resonances.

Figure 5

Ion heating during junction traverse. (a) The ion shuttled through the junction and back for measurement. The overall path length is 1160 $\mu$m. (b) Doppler recooling measurement of ion heating after shuttling at a wave-form update rate of 330 kHz. This method is not reliable for the intermediate heating regime, which results in an unrealistically large offset value for $\overline{n}$. A fit to multiple junction traverses gives a heating of 266 quanta per round trip. Inset: Recooling data after six junction traverses fit to the numerical model. (c) At an update rate of 350 kHz, the sideband envelope method gives $\overline{n}=9.6\pm 4.9$ for the reference run (blue) and $\overline{n}=235.3\pm 4.6$ for the shuttling run (red). The dots are experimental data and the lines join the points of the envelope fit. This measurement is in agreement with the average heating rate measured by the Doppler recooling method at a similar update rate. (d) A minimal dynamic heating of $73\pm 2$ quanta was measured by the sideband envelope method at a wave-form update rate of 700 kHz. The fit gives $\overline{n}=2.2\pm 0.4$ for the reference run (blue) and $\overline{n}=75.4\pm 1.6$ for the shuttling run (red).