General Runge-Gross-type theorem for dipole laser-matter interaction

We prove a bijective mapping between the set of v-representable one-particle densities and the set of v-representable density matrix operators for certain sets of external potentials v. The physically most important case is the set of all external potentials describing systems interacting with a laser in dipole approximation. No further restriction with respect to the initial configuration or time dependence of the electric field is required.