Non-Hermitian Floquet-Free Analytically Solvable Time Dependant Systems

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.

arXiv comment8 pages, 4 figures

References in corpus (25)

• Photonic Floquet Topological Insulators
• Making Sense of Non-Hermitian Hamiltonians
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Edge states and topological invariants of non-Hermitian systems
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• The physics of exceptional points
• Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
• Anomalous edge state in a non-Hermitian lattice
• Loss-induced suppression and revival of lasing
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Topologically protected midgap states in complex photonic lattices
• Dynamically encircling exceptional points: Exact evolution and polarization state conversion
• General description of quasi-adiabatic dynamical phenomena near exceptional points
• Spectral singularities and Bragg scattering in complex crystals
• Coalescence of spectral singularities and phase diagrams for one-dimensional PT symmetric photonic crystals
• Anti-Parity-Time Symmetric Optical Four-Wave Mixing in Cold Atoms
• Experimental realization of Floquet PT-symmetric systems
• Virtual Parity-Time Symmetry
• Quasi PT-symmetry in passive photonic lattices
• Exotic Multifractal Conductance Fluctuations in Graphene
• $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian Dirac semimetals
• Compatibility of transport effects in non-Hermitian nonreciprocal systems
• Anomalous relocation of topological states