An overview of simply pulsed qubits
  The behavior of simply pulsed qubits (quantum systems with two linearly independent states) may be characterized by the energy difference $\Delta E$ between the two states of the qubit and by an external stimulating potential $V(t)$ that causes transitions between them. Thus, the operation of such quantum mechanical systems may be categorized in various regions that explicitly depend on $\Delta E$ and $V(t)$. Limiting cases of degenerate, perturbative, and adiabatic regions are discussed. A comprehensive and illustrative map for simply pulsed qubits is presented that can be used as a visual tool for students. Furthermore, analytic solutions may be obtained when the interaction $V(t)$ is proportional to $\delta(t-t_k)$, namely when a fast interaction, called a kick, is used. 
A. Chalastaras, L. Kaplan, Kh. Kh. Shakov, M. Smith, and J. H. McGuire