  We consider theoretically ultra-cold interacting bosonic atoms confined to a
wire geometry and coupled to the field of an optical cavity. A spin-orbit
coupling is induced via Raman transitions employing a cavity mode and a
transverse running wave pump beam, the transition imprints a spatial dependent
phase onto the atomic wavefunction. Adiabatic elimination of the cavity field
leads to an effective Hamiltonian for the atomic degrees of freedom, with a
self-consistency condition. We map the spin-orbit coupled bosonic wire to a
bosonic ladder in a magnetic field, by discretizing the spatial dimension.
Using the numerical density matrix renormalization group method, we show that
in the continuum limit the dynamical stabilization of a Meissner superfluid is
possible, for parameters achievable by nowadays experiments.
