Exact analytical results for a two-level quantum system under a Lorentzian-shaped pulse field

We investigate a two-level quantum system driven by a Lorentzian-shaped pulse field. An analytical solution is presented in terms of the confluent Heun functions. It is shown that for specially chosen parameter conditions, there are a number of the exact analytical solutions in an explicit form. The dependence of the final transition probabilities in the two levels on the system parameters is derived analytically and confirmed numerically.