Engineering imaginary stark ladder in a dissipative lattice: passive $\mathcal{P}\mathcal{T}$ symmetry, K symmetry and localized damping

Abstract

We study an imaginary stark ladder model and propose a realization of the model in a dissipative chain with linearly increasing site-dependent dissipation strength. Due to the existence of a $K$-symmetry and passive $\mathcal{P}\mathcal{T}$ symmetry, the model exhibits quite different feature from its Hermitian counterpart. With the increase of dissipation strength, the system first undergoes a passive $\mathcal{P}\mathcal{T}$-symmetry breaking transition, with the shifted eigenvalues changing from real to complex, and then a $K$-symmetry restoring transition, characterized by the emergence of pure imaginary spectrum with equal spacing. Accordingly, the eigenstates change from $\mathcal{P}\mathcal{T}$-unbroken extended states to the $\mathcal{P}\mathcal{T}$-broken states, and finally to stark localized states. In the framework of the quantum open system governed by Lindblad equation with linearly increasing site-dependent dissipation, we unveil that the dynamical evolution of single particle correlation function is governed by the Hamiltonian of the imaginary stark ladder model. By studying the dynamical evolution of the density distribution under various initial states, we demonstrate that the damping dynamics displays distinct behaviors in different regions. A localized damping is observed in the strong dissipation limit.

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• Wannier-Stark localization in one-dimensional amplitude-chirped lattices
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• Exceptional rings in nonlinear non-Hermitian planar optical microcavities: implementation, signal enhancement, and topology
• Dynamic manifestation of exception points in a non-Hermitian continuous model with an imaginary periodic potential
• Dissipation induced ergodic-nonergodic transitions in finite-height mosaic Wannier-Stark lattices