Cavity-QED-based quantum phase gate

We describe a quantum phase gate in which the two qubits are represented by the photons in the two modes of the cavity field. The gate is implemented by passing a three-level atom in a cascade configuration through the cavity. The upper levels of the atom are resonant with one of the cavity modes whereas the lower levels are appropriately detuned from the other mode of the cavity. A $\pi$ phase shift is introduced when there is one photon each in the two modes and the atom is initially in the ground state. We also discuss the one-bit unitary gate in such a system and discuss potential applications.