Non-Hermitian Floquet-Free Analytically Solvable Time Dependant Systems

The non-Hermitian models, which are symmetric under parity (P) and time-reversal (T) operators, are the cornerstone for the fabrication of new ultra-sensitive optoelectronic devices. However, providing the gain in such systems usually demands nonlinear processes, limiting their application mainly in the quantum realm. In this paper, to achieve this obstacle, we introduce a class of time-dependent non-Hermitian Hamiltonians (not necessarily Floquet) that can describe a two-level system with temporal modulated on-site potential and couplings. We show that implementing an appropriate non-Unitary gauge transformation converts the original system to an effective one with a balanced gain/loss. This will allow us to analytically derive the evolution of states. Our proposed class of Hamiltonians can be employed in different platforms, such as electronic circuits, acoustics, and photonics, to design PT-symmetric structures without amplification and absorption mechanisms.