Dynamic and geometric phases in the Stark-Zeeman effect of the hyperfine structure of one-electron atoms

Full text: A theoretical investigation of the Stark-Zeeman effect of the np 2P3/2 fine structure levels of atoms with one radiant electron and a core of closed shells with nuclear spin I = 1 (6Li) or I = 3/2 (7Li, 23Na, 69Ga, 71Ga) predicted crossings and anticrossings. These were confirmed in an experiment. They could be predicted in the adiabatic approximation from the structure of the energy surfaces Εn(B, E) in their dependence on the magnetic field B and the electric field E. Two of these surfaces meet in the crossing points. There are two types of such crossing points resulting from the quadratic dependence of the Stark effect on E. In some crossing points the energy surfaces meet in a bicone, in the other ones they have an osculating contact in the E-direction. When the electric and magnetic fields are varied such that the phase point of the atom surrounds a biconical crossing points then the wave functions of the two levels concerned change sign; on the other hand a path around a crossing point of the second type does not change the sign. We assume that the change in sign corresponds to a geometric phase of absolute value π. As a first step for the feasibility of finding this geometric phase in an experiment, the dynamic phase connected with such time-dependent field variations has been investigated. Values of all these phases will be presented. (author)