contribution. This is shown in Fig. \[fig:combinedpotentials\]a. In addition, for $\phi=0$ the off-resonant potentials shift the coupling out of resonance, changing the adiabatic dressed states. As a result, the admixture of the excited internal state in the lower dressed level is relatively small. As the lattices are shifted, and the resonant contribution dominates, the admixture of the excited state increases. In Fig. \[fig:combinedpotentials\]b, we plot the admixture of the $^3$P$_0$ level, averaged over one period of the lower dressed potential for different values of the detuning $\delta$. We note that for the detuning values we choose here, this value is always small. This will lead to a significant reduction in collisional loss rates due to $^3$P$_0$-$^3$P$_0$ collisions when two atoms are on the same lattice site.

Loading a quantum register
--------------------------

In order to produce a quantum register with one atom in every lattice site, we begin from a spin-polarised gas of fermionic alkaline earth-like atoms, produced by optical pumping. This should be a degenerate Fermi gas so that the densities are sufficiently high to load a single atom per lattice site. Note that we choose Fermions here because for Yb and Sr, it is the fermionic isotopes that have 