CNOT gate on reverse photon modes in a ring cavity

Photon modes of the reverse rotation in a ring QED cavity coupled with a single atom are considered. By applying the Schrieffer–Wolf transformation for the off-resonant light–atom interaction, an effective Hamiltonian of the photon modes evolution is obtained. Heisenberg equations for the input–output photon mode operators are written, and the expression for the wave function of the system is found. The analytical solution shows the condition of the control NOT quantum gate implementation on chiral photon modes. A possible on-chip experimental implementation and recommendations for the construction of an optical quantum computer using this gate are considered.