  We study the interaction of a weak probe field, having two orthogonally
polarized components, with an optically dense medium of four-level atoms in a
tripod configuration. In the presence of a coherent driving laser,
electromagnetically induced transparency is attained in the medium,
dramatically enhancing its linear as well as nonlinear dispersion while
simultaneously suppressing the probe field absorption. We present the
semiclassical and fully quantum analysis of the system. We propose an
experimentally feasible setup that can induce large Faraday rotation of the
probe field polarization and therefore be used for ultra-sensitive optical
magnetometry. We then study the Kerr nonlinear coupling between the two
components of the probe, demonstrating a novel regime of symmetric, extremely
efficient cross-phase modulation, capable of fully entangling two single-photon
pulses. This scheme may thus pave the way to photon-based quantum information
applications, such as deterministic all-optical quantum computation, dense
coding and teleportation.
