Majorana approach for driven quantum systems.

The description of driven two-level quantum systems is important for the development of quantum technologies. Different ways of solving such non-trivial problems provide a versatile understanding of how to work with these systems. We study the evolution of a two-level system with a linear perturbation, known as the Landau-Zener-Stückelberg-Majorana transition. This provides the basis for the so-called adiabatic-impulse model, ubiquitously used for describing diverse quantum systems. The evolution of driven quantum two-level systems usually follows the solution by C. Zener. Less known is the approach by E. Majorana. In our work, we apply Majorana’s approach to obtain not only the final excitation probability but also the time evolution and the phase of the wave function. We analyze the regions where this asymptotic result correctly describes the evolution by comparing the analytical solution with the numerical one. Therefore, we can classify the problems where this approach could be effective.