PT spectroscopy of the Rabi problem

We investigate the effects of a time-periodic, non-hermitian, PT-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 demonstrate that when the perturbation frequency is close to one of the system resonances, even a vanishingly small perturbation leads to PT symmetry breaking. We also find a restored PT-symmetric phase at high frequencies, and at moderate perturbation strengths, we find multiple frequency windows where PT-symmetry is broken and restored. Our results imply that the PT-symmetric Rabi problem shows surprisingly rich phenomena absent in its hermitian or static counterparts.