Multiphoton process in cavity QED photons for implementing a three-qubit quantum gate operation

Based on cavity QED of free atoms, we theoretically investigate the implementation of a three-qubit quantum phase gate in which the three qubits are represented by the photons in modes of the cavity. A single four-level atom in double-V type passing through the high-Q cavity is used to implement the gate. We apply the theory of multiphoton resonance and use two-level effective Hamiltonians to predict the proper values for detunings, coupling constants, and interaction times. By the use of both the density matrix approach and wave function method, the influence of the decoherence processes is theoretically and numerically analyzed. Further, we address the effects of deviation in detunings and coupling coefficients and find that the gate operation is substantially insensitive to such variations. Finally, we show that the proposed scheme here can be extended for the implementation of multiqubit quantum phase gates.