We propose a method to manipulate, possibly faster than adiabatically, four-level systems with time-dependent couplings and constant energy shifts (detunings in quantum-optical realizations). We inversely engineer the Hamiltonian, in ladder, tripod, or diamond configurations, to prepare arbitrary states using the geometry of four-dimensional rotations to set the state populations, specifically we use Cayley's factorization of a general rotation into right- and left-isoclinic rotations.
@article{arxiv.1710.10207,
title = {Hamiltonian design to prepare arbitrary states of four-level systems},
author = {Y. - C. Li and D. Martínez and S. Martínez-Garaot and X. Chen and J. G. Muga},
journal= {arXiv preprint arXiv:1710.10207},
year = {2018}
}