Crossing of energy levels

Andon A. Rangelov

S Arushanyan, A. Melikyan, S. G. Saakyan

It was shown previously that in taking into account only dipole transitions, the crossing of quasi-energy levels is possible in the system if any of the transitions forms a closed loop [1]. It followed herefrom that for the analysis of the crossing conditions, it is necessary to consider a system which has at least four levels. In this paper we show that we can uniquely specify which quasi-energy levels cross at the given values of the parameters of the atomic system and radiation field, without solving an algebraic quartic equation. It was found that the most suitable system for the implementation of the crossing is the group of energy levels 5 S 1/2 , 5 P 1/2 , 5 P 3/2 and 5 D 3/2 of a rubidium atom. The performed calculations of the laser field intensity and frequency values at which crossing takes place in this system show that they are easily attainable. It turned out that in this system there occur crossing of quasi-energy levels corresponding to the excited atomic levels.

Dale M. Grimes

Willi-Hans Steeb

Abstract We consider a Hamilton operator in a finite dimensional Hilbert space with energy level crossing. We discuss the question how energy level crossing and entanglement of states in this Hilbert space are intertwined. Since energy level crossing is related to symmetries of the Hamilton operator we also derive these symmetries and give the reduction to the invariant Hilbert subspaces.

Luigi E. Picasso