(a) The energy separation between the doublet dressed state for n = 1 as a function of dipolar coupling strength J and the atom–cavity detuning Δ_ac. The separation reaches the minimum for Δ_ac + J = 0, as indicated by the dashed line. The dressed energy level for n = 1,2 versus the dipolar coupling strength J for (b) Δ_ac = 0, and versus the atom–cavity detuning Δ_ac for (c) J = 1 and (d) J = 5. Here, the dressed energy for n = 2 has been divided by a factor of 2. Further parameters are (κ,Γ,γ,η) = (0.2,0.1,0.1,0.1) and we have fixed units of g = 1.