High Fidelity State Preparation and Measurement of Ion Hyperfine Qubits with $I>\frac{1}{2}$

We present a method for achieving high fidelity state preparation and measurement (SPAM) using trapped ion hyperfine qubits with nuclear spins higher than $I=1/2$. The ground states of these higher nuclear spin isotopes do not afford a simple frequency-selective state preparation scheme. We circumvent this limitation by stroboscopically driving strong and weak transitions, blending fast optical pumping using dipole transitions, and narrow microwave or optical quadrupole transitions. We demonstrate this method with the $I=3/2$ isotope ${}^{137}{\mathrm{Ba}}^{+}$ to achieve a SPAM infidelity of $(9.0\pm 1.3)\times {10}^{-5}$ ($-40.5\pm 0.6\mathrm{dB}$), facilitating the use of a wider range of ion isotopes with favorable wavelengths and masses for quantum computation.

Figure 1

(a) MAOP using coherent microwave pulses (black) and 493 nm flush pulses (aqua). (b) 1762 nm NBOP using coherent 1762 nm pulses (gray), 614 nm quenching (orange), and 493 nm flush (aqua). (c) Cabinet shelving with repeated 1762 nm pulses addressing $|0⟩$. Hyperfine quantum numbers $F$ and $m_F$ are omitted for clarity (see Supplemental Material for level diagram and pulse sequences [19]).

Figure 2

(a) SPAM infidelity vs increasing cycles of MAOP (purple) and NBOP (green). Infidelities are calculated from datasets with $50\times {10}^3$ (for 0 to 9 cycles), $100\times {10}^3$ (10 to 18 cycles), and $200\times {10}^3$ (20 to 30 cycles) trials. Both techniques are initially close to $1/3$ reduction in error per cycle (gray line), but level off at high fidelity. Inset: same data plotted as a function of absolute time, showing 4.3 ms and 4.55 ms for 35 cycles of MAOP and NBOP, respectively. Solid points and fluorescence count histograms represent separate datasets for (b) MAOP (35 cycles) and (c) 1762 nm NBOP (30 cycles with 493 nm flush pulse and 5 cycles without flush), preparing the $|0⟩$ (orange) and $|1⟩$ (blue) qubit state over ${10}^6$ trials per state. The SPAM infidelities were measured to be $(14.4\pm 1.7)\times {10}^{-5}$ (microwaves) and $(6.1\pm 1.1)\times {10}^{-5}$ (1762 nm) [$(22.0\pm 2.1)\times {10}^{-5}$ and $(9.0\pm 1.3)\times {10}^{-5}$ including leakage errors, respectively] using state detection thresholds indicated by vertical lines. All error bars denote one Wilson interval.