Optical lattices - spin I know different potentials can be realised with spin dependent optical lattices.
My question is, how do the optical lattices become spin dependent?
I cannot find a good explanation on the literature, unfortunately.
 A: This can be done by using an optical lattice with a wavelength close to the transition on an atom (detuning on the order of the hyperfine splitting). In that configuration, the dipole force felt by a given spin state is generally dependent on the light polarization. By controlling the polarization of the optical lattice (for instance, using two counter propagating waves with orthogonal polarization and well-controlled phase), one can control the potential for each of the spin states.
See for instance Mandel et al. 2003: https://arxiv.org/abs/cond-mat/0301169
On the other hand, when the optical lattice is very detuned compared to the hyperfine splitting, the dipole potential becomes state and polarization independent (at least for two spin states of the same hyperfine manifold). In that situation, it is not possible to create a spin-dependent optical lattice anymore, but you might still be able to resolve the spin of your atoms, using for instance a magnetic field gradient to separate the spins using the Zeeman effect.
See for instance Boll et al. 2016: https://arxiv.org/abs/1605.05661
Or more recently, Koepsell et al. 2020 (prepublication): https://arxiv.org/abs/2002.07577
