Double dressing by both the number of atoms and the number of photons inside cavity

We study a system of N two-level atoms interacting with a coherent field a resonant cavity in a self-consistent manner. No direct correlation between the atoms, such as induced by dipole–dipole interaction, is included. Initially all atoms are not exited, and there are n₀ photons in the cavity. We show that the system reveals collective-like behavior, which stems from mutual influence of the atoms and coherent field in the cavity. In distinction from conventional dressing of atomic states by strong electromagnetic field, the system of N two-level atoms in a resonant cavity is actually dressed by both the number of photons and the number of atoms N. This double dressing results in both N and n₀-dependent oscillation frequency, ω(n₀,N). At N>>n₀ the spectral density contains, apart from the main peak at the collective atomic frequency gN, additional features at odd sub-harmonics. There is interference signature at the double dressing spectrum which has half-peaks and half-dips that is a synchronization among the frequencies of photon and the atomic dressings. It is a beautiful manifestation of quantum interference in the present novel double dressing by the number n of photons and by the number N of atoms.