Reescalonamento temporal e método dos parâmetros ajustáveis como atalhos para adiabaticidade - França, Ângelo Fernandes da Silva (2023)
Shortcuts to adiabaticity (STA) are protocols that accelerate adiabatic quantum dynamics, which by definition are dynamics that require a long evolution time, in order to reproduce the same results, but in a shorter time interval. Such shortening is of fundamental importance because, due to the adiabatic process occurring slowly, it makes the system subject to caused effects such as decoherence, external noise and even transitions between the hamiltonian eigenstates. In this thesis we study some of these STA methods, in particular the time-rescaling method in which we make an illustration in the cases of the parametric harmonic oscillator and in the population inversion in a two-level system, where for the latter case we perform an analysis of the stability of the method. We also developed a new STA proposal called the tunable parameters method, where, through a term added to the reference Hamiltonian, it is possible to accelerate an adiabatic dynamics. Both the tunable parameters and the time-rescaling methods did not require any information about the instantaneous eigenstates of the reference Hamiltonian. To illustrate this new approach, we consider the parametric harmonic oscillator and spin inversion scenarios.