103 research outputs found
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
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