= Solution
Use state-dependent <fluorescence>. With 397 nm light on $S_{1/2}\leftrightarrow P_{1/2}$ and an 866 nm repumper on $D_{3/2}\leftrightarrow P_{1/2}$, an ion initially in $D_{3/2}$ is brought into a bright cycling manifold. The repumper prevents population trapping in $D_{3/2}$. An ion in $D_{5/2}$ remains dark while the 854 nm light is off, since it has no allowed link to this cycle. A detected bright or dark record therefore measures the <qubit> in its logical basis by <electron shelving>.
To reset, apply 854 nm light to empty the shelved state, and use 397 nm plus repumping for <Doppler cooling> and internal-state preparation. <Doppler cooling> alone generally does not reach the <ground state>. In the resolved-sideband and <Lamb-Dicke regime>, drive the <Motional sideband>[red motional Raman sideband]
$$
|D_{3/2},n\rangle\longrightarrow|D_{5/2},n-1\rangle
$$
and then optically repump to $D_{3/2}$ with little change in motional occupation. Each cycle removes approximately one vibrational quantum. The $n=0$ state is dark to this red sideband because its <matrix> element contains $\sqrt n$. Repeat with appropriate <wavevector> projections and <frequency> differences for all modes to be cooled, then optically pump into the selected $D_{3/2}$ sublevel. Small recoil during repumping is necessary for a high ground-state <probability>. <Nobel Lecture: Superposition, entanglement, and raising Schrödinger’s cat by David J. Wineland>[Sections III–IV, fluorescence readout and resolved-sideband control of ion motion]{ref}
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