  Previous realizations of synthetic gauge fields for ultracold atoms do not
allow the spatial profile of the field to evolve freely. We propose a scheme
which overcomes this restriction by using the light in a multimode cavity, in
conjunction with Raman coupling, to realize an artificial magnetic field which
acts on a Bose-Einstein condensate of neutral atoms. We describe the evolution
of such a system, and present the results of numerical simulations which show
dynamical coupling between the effective field and the matter on which it acts.
Crucially, the freedom of the spatial profile of the field is sufficient to
realize a close analogue of the Meissner effect, where the magnetic field is
expelled from the superfluid. This back-action of the atoms on the synthetic
field distinguishes the Meissner-like effect described here from the
Hess-Fairbank suppression of rotation in a neutral superfluid observed
elsewhere.
