Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference.

The quantum two-level system (TLS) is one of the basic models in quantum physics and ubiquitous in nature. On the one hand, this is the “simplest nonsimple quantum problem” [1]; and, on the other hand, this provides the basis for quantum technologies, in which a TLS refers to a qubit. We investigate many different approaches to simplify calculating interesting behavior of such “simple” quantum system. We investigate periodically driven TLSs in different approaches [2] such as adiabatic-impulse model (AIM), rotating-wave approximation (RWA), Floquet method, numerical solving of Schrodinger and Lindblad equations, to describe interferometry and different aspects of each method. Then we compare them to find advantages and disadvantages of each method [2].

[1] M. Berry (1995), “Two-state quantum asymptotics,” Ann. N.Y. Acad. Sci. 755 (1), 303.

[2] O. V. Ivakhnenko, S. N. Shevchenko, F. Nori, " Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference", review article arXiv:2203.16348, (accepted Physics Reports) (2022).