  The implementation of the fractional quantum Hall effect in ultracold atomic
quantum gases remains, despite substantial advances in the field, a major
challenge. Since atoms are electrically neutral, a key ingredient is the
generation of sufficiently strong artificial gauge fields. Here we
theoretically investigate the synthetization of such fields for bosonic erbium
atoms by phase imprinting with two counterpropagating optical Raman beams.
Given the nonvanishing orbital angular momentum of the rare-earth atomic
species erbium in the electronic ground state and the availability of
narrow-line transitions, heating from photon scattering is expected to be lower
than in atomic alkali-metal species. We give a parameter regime for which
strong synthetic magnetic fields with good spatial homogeneity are predicted.
We also estimate the size of the Laughlin gap expected from the s-wave
contribution of the interactions for typical experimental parameters of a
two-dimensional atomic erbium microcloud. Our analysis shows that cold
rare-earth atomic ensembles are highly attractive candidate systems for
experimental explorations of the fractional quantum Hall regime.
