Scalable hyperfine qubit state detection via electron shelving in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mn>5</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mn>7</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> manifolds in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mrow/><mml:mn>171</mml:mn></mml:msup><mml:msup><mml:mrow><mml:mi>Yb</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math>
Claire Edmunds, Ting Rei Tan, Alistair R. Milne, A. Singh, Michael J. Biercuk, Cornelius Hempel
Abstract
Qubits encoded in hyperfine states of trapped ions are ideal for quantum computation given their long lifetimes and low sensitivity to magnetic fields, yet they suffer from off-resonant scattering during detection, often limiting their measurement fidelity. In ${}^{171}{\text{Yb}}^{+}$ this is exacerbated by a low fluorescence yield, which leads to a need for complex and expensive hardware, a problematic bottleneck especially when scaling up the number of qubits. We demonstrate a detection routine based on electron shelving to address this issue in ${}^{171}{\text{Yb}}^{+}$ and achieve a $5.6\ifmmode\times\else\texttimes\fi{}$ reduction in single-ion detection error on an avalanche photodiode to $1.8(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ in a 100 $\ensuremath{\mu}\mathrm{s}$ detection period and a $4.3\ifmmode\times\else\texttimes\fi{}$ error reduction on an electron multiplying CCD camera with $7.7(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ error in 400 $\ensuremath{\mu}\mathrm{s}$. We further improve the characterization of a repump transition at 760 nm to enable a more rapid reset of the auxiliary ${}^{2}{F}_{7/2}$ states populated after shelving. Finally, we examine the detection fidelity limit using the long-lived ${}^{2}{F}_{7/2}$ state, achieving further $300\ifmmode\times\else\texttimes\fi{}$ and $12\ifmmode\times\else\texttimes\fi{}$ reductions in error to $6(7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and $6.3(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ in 1 ms on the respective detectors. While shelving-rate limited in our setup, we suggest various techniques to realize this detection method at speeds compatible with quantum information processing, providing a pathway to ultrahigh-fidelity detection in ${}^{171}{\text{Yb}}^{+}$.