We investigate the effects of a time-periodic, non-Hermitian, $\mathcal{PT}\text{−}\mathrm{symmetric}$ perturbation on a system with two (or few) levels, and obtain its phase diagram as a function of the perturbation strength and frequency. We prove that when the perturbation frequency is close to one of the system resonances, even a vanishingly small gain-loss potential leads to $\mathcal{PT}$ symmetry breaking. We also find a restored $\mathcal{PT}\text{−}\mathrm{symmetric}$ phase at high frequencies, and at moderate perturbation strengths, we predict the existence of multiple frequency windows where $\mathcal{PT}$ symmetry is broken and restored. Our results imply that the $\mathcal{PT}\text{−}\mathrm{symmetric}$ Rabi problem shows exceptionally rich phenomena absent in its Hermitian or static counterparts.

• Received 16 July 2014

DOI:https://doi.org/10.1103/PhysRevA.90.040101