Symmetric photon-photon coupling by atoms with Zeeman-split sublevels

We propose a simple scheme for highly efficient nonlinear interaction between two weak optical fields. The scheme is based on the attainment of electromagnetically induced transparency simultaneously for both fields via transitions between magnetically split $F=1$ atomic sublevels, in the presence of two driving fields. Thereby, equal slow group velocities and symmetric cross coupling of the weak fields over long distances are achieved. By simply tuning the fields, this scheme can either yield giant cross-phase modulation or ultrasensitive two-photon switching.