Steady state of atoms in a resonant field with elliptical polarization

We present a complete set of analytical and invariant expressions for the steady-state density matrix of atoms in a resonant radiation field with arbitrary intensity and polarization. The field drives the closed dipole transition with arbitrary values of the angular momenta J(g) and J(e) of the ground and excited state. The steady-state density matrix is expressed in terms of spherical harmonics of a complex direction given by the field polarization vector. The generalization to the case of broadband radiation is given. We indicate various applications of these results.