Double controlled quantum phase gate based on three atoms trapped in separate optical cavities

We propose a Controlled–Controlled-phase gate (CCZ) using three atoms trapped in separate optical cavities and connected by two optical fibers considered in the short fiber limit. The gate is realized within the null, single and double-excitation subspaces. The Hamiltonian of the atom-cavity-fiber system is presented, and we give Hamiltonian matrix expressions for different initial states. We study the fidelity of the proposed CCZ gate which depends upon the physical parameters of the entire system and show that it can reach 99.28%. We numerically simulate the impact of the spontaneous emission and photon leakage from the fibers and the cavities on the fidelity.