Dynamics of a two-state system through a real level crossing

The dynamics of a two-state system whose energies undergo a real crossing at some instant of time is studied. At this instant, both the coupling and the detuning vanish simultaneously, which leads to an exact degeneracy of the eigenenergies of the system. It is found that the dynamics of the system is primarily determined by the manner in which the degeneracy occurs. This interesting behavior is reminiscent of a symmetry breaking process, since the totally symmetric situation occurring at the crossing is significantly altered by infinitesimal quantities, which remove the degeneracy, with very important dynamical implications from there on. A very simple analytical formula is derived, which is found to describe the population changes very accurately

Generalized interaction-free evolutions

A thorough analysis of the evolutions of bipartite systems characterized by the “effective absence” of interaction between the two subsystems is reported. First, the connection between the concepts underlying interaction-free evolutions (IFE) and decoherence-free subspaces (DFS) is explored, showing intricate relations between these concepts. Second, starting from this analysis and inspired by a generalization of DFS already known in the literature, we introduce the notion of generalized IFE (GIFE), also providing a useful characterization that allows one to develop a general scheme for finding GIFE states