stored in dressed states ${|0 \rangle}$ and ${|1 \rangle}$, which are dressed superpositions of states in the $^1$S$_0$ and $^3$P$_0$ manifolds with a definite values of $m_I$. These can be coupled via off-resonant Raman processes to long-lived auxilliary states ${|0x \rangle}$ and ${|1x \rangle}$ in the $^3$P$_2$ manifold for the purpose of readout. In order to read out a particular qubit state, this state should be coupled to the $^3$P$_2$ manifold. It can then be detected by fluorescence on the cycling transition $^3$P$_2$-$^3$D$_3$.[]{data-label="fig:readoutlevels"}](readoutlevels){width="8.5cm"}

Because of their non-zero electron spin, states in the long-lived $^3$P$_2$ manifold are much more sensitive to magnetic fields than the $^3$P$_0$ and $^1$S$_0$ level, and we can use these shifts to make possible a spatially-dependent readout of spin states by applying a magnetic gradient field, in a manner first mentioned in Ref. [@dereviankoaddressing]. In applying such a field, the $^3$P$_2$ level can be significantly shifted, whilst the $^1$S$_0$ and $^3$P$_0$ states are not substantially shifted, and thus the form of the dressed lattice potential is not substantially changed. In particular, a gradient field of 1 G/cm will provide an energy gradient of 4.1 MHz/cm for the ${|^3{\rm P}_2,F=13/2,m_f=-13/2 \rangle}$ state, or an energy difference of about 