State Readout of a Trapped Ion Qubit Using a Trap-Integrated Superconducting Photon Detector

We report high-fidelity state readout of a trapped ion qubit using a trap-integrated photon detector. We determine the hyperfine qubit state of a single ${}^9{\mathrm{Be}}^{+}$ ion held in a surface-electrode rf ion trap by counting state-dependent ion fluorescence photons with a superconducting nanowire single-photon detector fabricated into the trap structure. The average readout fidelity is 0.9991(1), with a mean readout duration of $46\mu \mathrm{s}$, and is limited by the polarization impurity of the readout laser beam and by off-resonant optical pumping. Because there are no intervening optical elements between the ion and the detector, we can use the ion fluorescence as a self-calibrated photon source to determine the detector quantum efficiency and its dependence on photon incidence angle and polarization.

Figure 1

Trap configuration. (a) False-color scanning electron micrograph of the ion trap showing the rf electrodes (pink), SNSPD (green), and SNSPD bias leads (yellow). A trapped ion (red sphere, shown in multiple positions along the rf null line) can be transported along the trap axis by applying appropriate time-varying potentials to the outer segmented electrodes (gray). (b) Top view scale diagram showing four labeled trapping zones $A–D$ along the trap axis (double-headed black arrow), as well as the geometry of the laser beams (blue solid arrows, here shown directed at zone $D$) and quantization magnetic field ${\overrightarrow{B}}_0$, which all lie in the plane of the trap at 45° angles to the trap axis. The laser beams can be translated horizontally to follow the ion as it is transported between zones, as indicated by the faint laser beam arrows directed at zone $B$.

Figure 2

Impact of trap rf on SNSPD performance. We plot bright (top) and dark (bottom, log scale) counts in a $200\mu \mathrm{s}$ detection window versus SNSPD bias current, with trap rf either off (green squares) or on (orange circles), using laser scatter to simulate ion fluorescence for the bright counts. The blue line is a fit to a theoretical model accounting for induced rf currents in the SNSPD. The bright counts are background-corrected by subtracting the measured dark counts at each bias current. The 68% confidence intervals on the reported values are smaller than the plot symbols.

Figure 3

Counts and readout error. (a) Count histograms (log scale) for ${10}^5$ trials each of preparing the bright (red) and dark (blue) states, using a $125\mu \mathrm{s}$ detection window. The dashed vertical line indicates the optimal threshold for state discrimination. (b) Mean readout error for $2\times {10}^5$ trials, half prepared dark and half prepared bright, using either standard thresholding or adaptive Bayesian methods for state determination. For the Bayesian method, the horizontal axis is the mean readout duration before reaching a given state determination confidence level. The dashed horizontal line indicates ${10}^{-3}$ mean readout error. Statistical uncertainty in the mean readout error at the 68% confidence level is smaller than the plot symbols.

Figure 4

Count rate spatial dependence. Moving the ion along the trap axis away from the SNSPD reduces the count rate (blue circles) more strongly than is expected based on detector solid angle and ion dipole radiation pattern alone (red line). Including the calculated angular dependence of SNSPD SDE improves agreement (green line). The 68% confidence intervals on the count rates are smaller than the symbols; those on the theoretical calculations are narrower than the plotted lines.