Tight-binding lattices with an oscillating imaginary gauge field

Abstract

We consider non-Hermitian dynamics of a quantum particle hopping on a one-dimensional tight-binding lattice made of $N$ sites with asymmetric hopping rates induced by a time-periodic oscillating imaginary gauge field. A deeply different behavior is found depending on the lattice topology. While in a linear chain (open boundary conditions) an oscillating field can lead to a complex quasi energy spectrum via a multiple parametric resonance, in a ring topology (Born-von Karman periodic boundary conditions) an entirely real quasi energy spectrum can be found and the dynamics is pseudo-Hermitian. In the large $N$ limit, parametric instability and pseudo-Hermitian dynamics in the two different lattice topologies are physically explained on the basis of a simple picture of wave packet propagation.

10 pages, 6 figures

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• Ultrafast and Anharmonic Rabi Oscillations between Non-Bloch-Bands
• Designing non-Hermitian real spectra through electrostatics
• Fate of zero modes in a finite Su-Schrieffer-Heeger Model with $\mathcal{P}\mathcal{T}$ Symmetry
• Landau-Zener-Stückelberg Interferometry in $\mathcal{P}\mathcal{T}$-symmetric Non-Hermitian models
• Nonadiabatic robust excitation transfer assisted by an imaginary gauge field
• Loschmidt echo and fidelity decay near an exceptional point
• Non-Hermitian Floquet invisibility
• Defect-driven incoherent skin localization
• Relativistic Zitterbewegung in non-Hermitian photonic waveguide systems