Nonlinear atom optics

We study an ensemble of N bosonic atoms coupled by dipole-dipole interaction and also interacting with an electromagnetic field. Effective single-atom nonlinear Schrödinger equations are derived. The implications of these equations are discussed in the context of some standard atom optics geometries, illustrating in particular how many-body effects modify the Pendellösung of Bragg scattering. In another regime, the problem is reduced to a classical massive Thirring model, with the possibility of generating atomic Thirring solitons.