  We study theoretically the population transfer in two-level atoms driven by
chirped lasers. It is known that in the Hermitian case, the rapid adiabatic
passage (RAP) is stable for an above-critical chirp below which the final
populations of states Rabi oscillate with varying laser power. We show that if
the excited state is represented by a resonance, the separatrix marking this
critical phenomenon in the space of the laser pulse parameters emanates from an
exceptional point (EP) -- a non-Hermitian singularity formed in the atomic
system by the fast laser field oscillations and encircled due to slow
variations of the laser pulse envelope and instantaneous frequency. This
critical phenomenon is neatly understood via extending the "slow" time variable
into the complex plane, uncovering a set of branch points which encode
non-adiabatic dynamics, where the switch between RAP and Rabi oscillations is
triggered by a coalescence of two such branch points. We assert that the
intriguing interrelation between the two different singularities -- the EP and
the branch point coalescence in complex time plane -- can motivate feasible
experiments involving laser driven atoms.
