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

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