Quantum time mirrors for general two-band systems

Methods that are devised to achieve reversal of quantum dynamics in time have been named ``quatum time mirrors.'' Such a time mirror can be considered as a generalization of Hahn's spin echo to systems with continuous degrees of freedom. We extend the quantum time mirror protocol originally proposed for Dirac dispersions to arbitrary two-band systems and establish the general requirements for its efficient implementation. We further discuss its sensitivity to various nonhomogeneous perturbations including disorder potentials and the effect of external static magnetic and electric fields. Our general statements are verified for a number of exemplary Hamiltonians, whose phase-coherent dynamics are studied both analytically and numerically. The Hamiltonians considered can be used to describe the low-energy properties of systems as diverse as cold atom-optics setups, direct band gap semiconductors, or (mono- or bilayer) graphene. We discuss the consequences of many-body effects at a qualitative level, and consider the protocol feasibility in state-of-the-art experimental setups.