Eigenenergy crossings

Diabatic Versus Adiabatic Dynamics Around Eigenenergy Crossings and... 

An alternative way to explore the zero-held resonance is to chirp a laser pulse that is switched on and off adiabatically, sufficiently far from the resonance. The chirp is such that the frequency is swept through the resonance when the held is on. The resonance appears in a dressed eigenenergy diagram (as a function of time or as a function of the held parameters) as an avoided crossing. 

We assume that the model depends on one slow time-dependent parameter, denoted r(t), and that the shape of the avoided crossing as a function of r is well described around the avoided crossing r = rc (occurring at time t = tc) by its width h and its curvature C (see Fig. 1). We choose the parameterization such that rc = 0. The eigenenergies read... 

Fig. 4 Calculated results of 0-trajectory for the lowest resonance of H2 at bond length of 1.4 bohr. Circles represent calculated complex eigenenergies with complex Cl using cSTO-JVcG with a JV = 4, b JV = 8, c JV = 10, cSTO-MG with d JV = 8 e JV = 10, and f cSTO-lOreG. Solid line is the curve of the rational fraction fitted with these ealeulated results. Cross is the stationary point ealeulated liom these fitted rational fractions...

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