Pulse-driven near-resonant quantum adiabatic dynamics: lifting of quasi-degeneracy

We study the quantum dynamics of a two-level system driven by a pulse that starts near-resonant for small amplitudes, yielding nonadiabatic evolution, and induces an adiabatic evolution for larger amplitudes. This problem is analyzed in terms of lifting of degeneracy for rising amplitudes. It is solved exactly for the case of linear and exponential rising. Approximate solutions are given in the case of power law rising. This allows us to determine approximative formulas for the lineshape of resonant excitation by various forms of pulses such as truncated trig-pulses. We also analyze and explain the various superpositions of states that can be obtained by the Half Stark Chirped Rapid Adiabatic Passage (Half-SCRAP) process.