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

TL;DR

This paper investigates an imaginary stark ladder model in a dissipative lattice, revealing unique symmetry-induced phase transitions and localized damping phenomena through spectral analysis and dynamical evolution studies.

Contribution

It introduces a dissipative chain realization with linearly increasing dissipation, uncovering novel symmetry-breaking transitions and localization effects in a non-Hermitian setting.

Findings

Passive $ ext{PT}$-symmetry breaking transition with eigenvalues changing from real to complex

Emergence of pure imaginary spectrum with equal spacing indicating $K$-symmetry restoration

Localized damping observed in the strong dissipation limit

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 $\mathcal{PT}$ symmetry, the model exhibits quite different feature from its Hermitian counterpart. With the increase of dissipation strength, the system first undergoes a passive $\mathcal{PT}$-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 $\mathcal{PT}$-unbroken extended states to the $\mathcal{PT}$-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.