Polarization-selective optical nonlinearities in cold Rydberg atoms

We study the interaction between a probe and a trigger weak fields in a sample of cold rubidium atoms in the presence of a coupling and a dressing strong fields. Dipole Rydberg blockade may occur and can be set to depend on the probe and trigger polarizations giving rise to diverse regimes of electromagnetically induced transparency (EIT) with a concomitant small probe and trigger absorption and dispersion. This is shown to be relevant to the implementation of polarization conditional probe and trigger cross nonlinearities in cold Rydberg atoms.