Bloch theorem on the Bloch sphere

Motivated by the production of strong optical forces on atoms, we have done numerical studies of adiabatic rapid passage in light that is both frequency and amplitude modulated in the form of chirped pulses, and we found unanticipated regularities. We have quantified these regularities in terms of a periodic Hamiltonian, and obtained a result similar to the Bloch theorem, but in the time domain. This led to further numerical studies and a quantitative description of the behavior of an atom under multiply repetitive sweeps.