  It has recently been shown that light can be stored in Bose-Einstein
condensates for over a second. Here we propose a method for realizing a
controlled phase gate between two stored photons. The photons are both stored
in the ground state of the effective trapping potential inside the condensate.
The collision-induced interaction is enhanced by adiabatically increasing the
trapping frequency and by using a Feshbach resonance. A controlled phase shift
of $\pi$ can be achieved in one second.
