Non-Hermitian Floquet-Free Analytically Solvable Time Dependant Systems

TL;DR

This paper introduces a class of time-dependent non-Hermitian Hamiltonians that can be analytically solved and used to design systems with hidden PT-symmetry, avoiding the need for gain and loss mechanisms.

Contribution

The authors develop a method to transform complex non-Hermitian systems into analytically solvable models with balanced gain and loss through non-unitary gauge transformations.

Findings

Analytical solutions for a new class of non-Hermitian Hamiltonians.

Potential applications in photonics, acoustics, and electronics.

Design of structures with hidden PT-symmetry without imaginary gain or loss.

Abstract

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 precise contorol of nonlinear processes, limiting their application. In this paper, to bypass this obstacle, we introduce a class of time-dependent non-Hermitian Hamiltonians (not necessarily Floquet) that can describe a two-level system with temporally 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 and loss. This will allow us to derive the evolution of states analytically. Our proposed class of Hamiltonians can be employed in different platforms such as electronic circuits, acoustics, and photonics to design structures with hidden PT-symmetry potentially without imaginary onsite amplification and absorption mechanism to obtain an exceptional point.