Exact Floquet solutions in a Parity-Time-Symmetric Rabi Model

It is shown that a semiclassical Rabi model with parity-time (PT) symmetry has a hidden $sl(2)$ symmetry and hence possesses quasi-exact solutions. These are located precisely at the exceptional points of the spectrum, the boundaries of the PT-symmetric phase. The corresponding constraints on the model parameters can be interpreted as a resonance relationship between the constant and periodic driving terms.