“…It is seen that, the energy invariant subspace related to the HamiltonianĤ R (t) is formed by the following dressed states: |g 1 , 0 , |e, 0 , |e m , 0 and |g 2 , 1 (here we assume that the cavity mode is initially prepared in the vacuum state |0 ). Thus, the desirable single-photon FSP requires the system should be manipulated deterministically from the ground state |g 1 , 0 to the target state |g 2 , 1 [16,17,18]. Although this progress had been achieved by the STIRAP technique with a Λ-level atom-cavity system, the efficiency of the desirable FSP is significantly limited due to the undesired non-adiabatic transitions.…”