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We study an atom-cavity hybrid system where fermionic atoms in aone-dimensional lattice are subject to a cavity-induced dynamic gaugepotential. The gauge coupling leads to highly-degenerate steady states in whichthe fermions accumulate to one edge of the lattice under an open boundarycondition. Such a phenomenon originates from the many-body Liouvilliansuperoperator of the system, which, being intrinsically non-Hermitian, isunstable against boundary perturbations and manifests the non-Hermitian skineffect. Contrary to the single-body case, the steady state of a multi-atomsystem is approached much slower under the open boundary condition, as thelong-time damping of the cavity mode exhibits distinct rates at differenttimes. This stage-wise slowdown is attributed to the competition betweenlight-assisted hopping and the dynamic gauge coupling, which significantlyreduces the steady-state degeneracy under the open boundary condition, asdistinct hosts of quasi-steady states dominate the dynamics at different timescales.

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