Spontaneous emission spectrum of a two-level atom in a very high Q cavity

In this paper we consider an initially excited two-level system coupled to a monomode cavity, and compute exact expressions for the spectra spontaneously emitted by each system in the general case where they have arbitrary linewidths and frequencies. Our method is based on the fact that this problem has an easily solvable classical counterpart, which provides a clear interpretation of the evidenced phenomena. We show that if the cavity linewidth is much lower than the atomic linewidth, photons are emitted at the cavity frequency, even if the atom and the cavity are strongly detuned. We also study the links between the spontaneous emission spectra and the fluorescence spectra emitted when the atom is driven by a classical field of tunable frequency.