Time-Dependent Gauge Transformation for Non-Hermitian Periodically Driven System with a Controllable Non-Hermitian Strength

In the present paper we introduce a general periodically driven non-Hermitian SU(2) system. In this model, the parameter δ is introduced to define the non-Hermitian strength. By constructing a generalized invariant operator using the time-dependent gauge transformation we obtain the exact solution to this model and the dependence of bi-orthogonal basis, metric operator, Berry phase and time-evolution operator on the non-Hermitian parameter.