Stabilizing Non-Hermitian Systems by Periodic Driving

Abstract

The time evolution of a system with a time-dependent non-Hermitian Hamiltonian is in general unstable with exponential growth or decay. A periodic driving field may stabilize the dynamics because the eigenphases of the associated Floquet operator may become all real. This possibility can emerge for a continuous range of system parameters with subtle domain boundaries. It is further shown that the issue of stability of a driven non-Hermitian Rabi model can be mapped onto the band structure problem of a class of lattice Hamiltonians. As an application, we show how to use the stability of driven non-Hermitian two-level systems (0-dimension in space) to simulate a spectrum analogous to Hofstadter's butterfly that has played a paradigmatic role in quantum Hall physics. The simulation of the band structure of non-Hermitian superlattice potentials with parity-time reversal symmetry is also briefly discussed.

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• Floquet engineering of point-gapped topological superconductors
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• Non-Hermitian Floquet Topological Matter -- A Review
• Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals
• Time-dependent $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics in generic non-Hermitian systems
• Non-Hermitian tight-binding network engineering
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• Deterministic chaos and fractal entropy scaling in Floquet CFT
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• Floquet control of global $PT$ symmetry in 2D arrays of quadrimer waveguides
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• Exploring Branched Hamiltonians for a Class of Nonlinear Systems
• $\mathcal{P}\mathcal{T}$ symmetry of a square-wave modulated two-level system
• Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point
• Multiple topological transitions and spectral singularities in non-Hermitian Floquet systems
• Extended unitarity and absence of skin effect in periodically driven systems
• A complete set of eigenstates for position-dependent massive particles in a Morse-like scenario
• Analytical Study of the Non-Hermitian Semiclassical Rabi Model
• Perpetual emulation threshold of PT-symmetric Hamiltonians
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• Relativistic Zitterbewegung in non-Hermitian photonic waveguide systems
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