  It is well known that non-Hermitian, non-reciprocal systems may harbor
exponentially localized skin modes. However, in this work, we find that,
generically, non-Hermiticity gives rise to abrupt and prominent kinks in the
semi-classical wave packet trajectories of quantum gases, despite the absence
of sudden physical impulses. This physically stems from a hitherto
underappreciated intrinsic non-locality from non-Hermitian pumping, even if all
physical couplings are local, thereby resulting in enigmatic singularities in
the band structure that lead to discontinuous band geometry and Berry
curvature. Specifically, we focus on the realization of the kinked response in
an ultracold atomic setup. For a concrete experimental demonstration, we
propose an ultracold atomic setup in a two-dimensional optical lattice with
laser-induced loss such that response kinks can be observed without fine-tuning
in the physical atomic cloud dynamics. Our results showcase unique
non-monotonic behavior from non-Hermitian pumping beyond the non-Hermitian skin
effect and suggest new avenues for investigating non-Hermitian dynamics on
ultracold atomic platforms.
