Shortcuts to adiabaticity: theoretical framework, relations between different methods, and versatile approximations

Shortcuts to adiabaticity guide given systems to final destinations of adiabatic control via fast tracks. Various methods were proposed as varieties of shortcuts to adiabaticity. Basic theory of shortcuts to adiabaticity was established in the 2010s, but it has still been developing and many fundamental findings have been reported. In this Topical Review, we give a pedagogical introduction to theory of shortcuts to adiabaticity and revisit relations between different methods. Some versatile approximations in counterdiabatic driving, which is one of the methods of shortcuts to adiabaticity, will be explained in detail. We also summarize recent progress in studies of shortcuts to adiabaticity.