Field theoretical treatment of approximations to radiative transitions in atoms

P. Cavaliere, G. Ferrante, C Leone

Electron-atom ionisation in the presence of a resonant EM field is considered theoretically, taking the hydrogen atom as an example. The radiation field is taken to have a frequency matching the 1s-2p transition frequency. The theoretical treatment is based on the Coulomb-Born wave approximation and on the two-level atom model. The physical picture arising from the resulting field-assisted triple differential cross section (TDC) is that of ionisation events taking place simultaneously from the ground and the excited 2p states, the role of the radiation field being mainly that of pumping target atoms.

Zoltan Fried, Lloyd C. Kannenberg

E. Ficocelli Varracchio

L. Mandeļ, E. Wolf

Light is both radiated and absorbed by atoms, and the interaction between the quantized electromagnetic field and an atom represents one of the most fundamental problems in quantum optics. However, real atoms are complicated systems, and even the simplest real atom, the hydrogen atom, has a non-trivial energy level structure. It is therefore often necessary or desirable to approximate the behavior of a real atom by that of a much simpler quantum system. For many purposes only two atomic energy levels play a significant role in the interaction with the electromagnetic field, so that it has become customary in many theoretical treatments to represent the atom by a quantum system with only two energy eigenstates. This is the most basic of all quantum systems, and it generally simplifies the treatment substantially. In a real atom the selection rules limit the allowed transitions between states, so that, in some cases, a certain state may couple to only one other. Moreover, optical pumping techniques have been developed that allow such preferred states to be prepared in the laboratory, and they have been successfully used in experiments (Abate, 1974). The two-level atom approximation is therefore close to the truth and not merely a mathematical convenience in some experimental situations. In the following we begin by developing the algebra for such a two-level atom. Dynamical variables for a two-level atom We consider an atomic quantum system with the two energy levels shown in Fig. 15.1.

Geoffrey V. Marr

Weihan Tan, Weiping Lu, Robert G. Harrison

In describing the nonlinear interaction of radiation with matter it is well known that the perturbation expansion technique is used to calculate the atomic wave functions and the transitions between the states of a system. However the technique, though involving all states of the system, is valid only in the limit of weak interaction fields and non-resonant interactions. For strong fields and resonant interactions, density matrix or dressed atom formulisms are commonly used though these exact treatments are restricted to simple two level schemes or approximations of these; their application to general resonant-near resonant multilevel interactions being prohibitively complex.