Many-body non-Hermitian skin effect under dynamic gauge coupling

TL;DR

This paper investigates the many-body non-Hermitian skin effect in a fermionic atom-cavity system with a dynamic gauge potential, revealing edge accumulation, slow convergence to steady states, and the impact of boundary conditions on degeneracy.

Contribution

It introduces a novel many-body non-Hermitian skin effect driven by cavity-induced dynamic gauge coupling, highlighting differences from single-particle behavior and the role of boundary conditions.

Findings

Fermions accumulate at the lattice edge due to the non-Hermitian skin effect.

Steady state convergence is slower in multi-atom systems with boundary effects.

Dynamic gauge coupling reduces steady-state degeneracy and causes stage-wise damping rates.

Abstract

We study an atom-cavity hybrid system where fermionic atoms in a one-dimensional lattice are subject to a cavity-induced dynamic gauge potential. The gauge coupling leads to highly-degenerate steady states in which the fermions accumulate to one edge of the lattice under an open boundary condition. Such a phenomenon originates from the many-body Liouvillian superoperator of the system, which, being intrinsically non-Hermitian, is unstable against boundary perturbations and manifests the non-Hermitian skin effect. Contrary to the single-body case, the steady state of a multi-atom system is approached much slower under the open boundary condition, as the long-time damping of the cavity mode exhibits distinct rates at different times. This stage-wise slowdown is attributed to the competition between light-assisted hopping and the dynamic gauge coupling, which significantly reduces the steady-state degeneracy under the open boundary condition, as distinct hosts of quasi-steady states dominate the dynamics at different time scales.