Abstract: This paper reviews our work on dynamical localization of the two-level system (TLS). By mapping the quantum dynamics of a driven TLS to the classical one of a particle experiencing a two-dimensional harmonic force as well as a periodic magnetic field, deep insights into the mechanism of localization have been gained. Using this scheme we are able to obtain the condition for localization of a TLS subject to the linearly polarized field. The localization induced by δ-function pulses and circularly polarized fields has been analytically investigated. It is found that the circularly-polarized-field induced localization can be fully described by the geometry of an ellipse within a unit circle on a complex plane.

Key words: Two-level system, Tunneling, Localization, Linearly polarized field, 　Circularly polarized field