Long-time behaviour of self-dressing and indirect spectroscopy

A two-level system interacting with the radiation field is considered. The time-dependent self-dressing of its bare ground state is studied. The time evolution of the system is discussed within the theory of subdynamics. Investigation of the long-time behaviour is the main point of this paper. It is shown that the dressing process is characterized by two well-defined time scales. At short times we recover well known results that show how the cloud of virtual quanta around the system is generated. At long times new phenomena appear. We show that a real quanta, resonant with the transition frequency of the atom, is emitted; also, we show that this emission process is connected to the instability of the excited state of the two-level system. Physical features of this emission, such as its probability, its detectability and its irreversible character, are discussed. Generalizing these results to a multi-level system, the possibility of an “indirect spectroscopy” is introduced. This possibility stems from the fact that, in addition to the usual Weisskopf-Wigner “direct” decay from a state to a lower one, an “indirect” process is also possible: a virtual transition can first bring the system to a higher excited level, from which it subsequently decays by a resonant transition.