Analytic solutions for generalized $PT$-symmetric Rabi models

We theoretically investigate the exact solutions for generalized parity–time($PT$)-reversal-symmetric Rabi models driven by external fields with monochromatic periodic, linear, and parabolic forms, respectively. The corresponding exact solutions are presented in terms of the confluent Heun equations without any approximation. In principle, the analytic solutions derived here are valid in the whole parameter space. Such a kind of study may offer potential coherent control schemes of the $PT$-symmetric two-level systems. (paper)