Polarization phase gate with a tripod atomic system.

We analyze the nonlinear optical response of a four-level atomic system driven into a tripod configuration.
The large cross-Kerr nonlinearities that occur in such a system are shown to produce nonlinear phase shifts of
order p. Such a substantial shift may be observed in a cold atomic gas in a magneto-optical trap where it could
be feasibly exploited towards the realization of a polarization quantum phase gate. The experimental feasibility
of such a gate is here examined in detail.