Hamiltonian engineering via invariants and dynamical algebra

Abstract

We use the dynamical algebra of a quantum system and its dynamical invariants to inverse engineer feasible Hamiltonians for implementing shortcuts to adiabaticity. These are speeded up processes that end up with the same populations as slow, adiabatic ones. As application examples, we design families of shortcut Hamiltonians that drive two- and three-level systems between initial and final configurations, imposing physically motivated constraints on the terms (generators) allowed in the Hamiltonian.