Amplitude control of a quantum state in a non-Hermitian Rice-Mele model driven by an external field

In the Hermitian regime, the Berry phase is always a real number. It may be imaginary for a non-Hermitian system, which leads to amplitude amplification or attenuation of an evolved quantum state. We study the dynamics of the non-Hermitian Rice-Mele model driven by a time-dependent external field. The exact results show that it can have a full real spectrum for any value of the field. Several rigorous results are presented for the Berry phase with respect to the varying field. We demonstrate that the Berry phase is the same complex constant for any initial state in a single sub-band. Numerical simulation indicates that the amplitude control of a state can be accomplished by a quasiadiabatic process within a short time.