Optimal quasi-adiabatic path in a two-level system

We consider a generic two-level quantum system with control parameters as the coupling between the two states, taking values in a bounded positive interval, and the detuning, restricted in a symmetric interval around zero. Using Stokes theorem, we prove that the optimal path for fast quasi-adiabatic dynamics lies mainly on the border of parameter space, as it was numerically found in a recent study regarding coupled elastic waveguides, modelled as a two-level system. We calculate analytically the adiabaticity parameter as a function of the protocol duration and compare with the finite-time Landau–Zener protocol, where the coupling is kept constant while the detuning varies linearly with time. The optimized-path protocol shows superior performance even for shorter durations, where the Landau–Zener protocol fails. The present study may be useful in different fields with systems modelled as the investigated generic two-level quantum system.