  Cooling the trapped atoms toward their motional ground states is key to
applications of quantum simulation and quantum computation. By utilizing
nonreciprocal couplings between constituent atoms, we present an intriguing
dark-state cooling scheme in $\Lambda$-type three-level structure, which is
shown superior than the conventional electromagnetically-induced-transparency
cooling in a single atom. The effective nonreciprocal couplings can be
facilitated either by an atom-waveguide interface or a free-space photonic
quantum link. By tailoring system parameters allowed in dark-state cooling, we
identify the parameter regions of better cooling performance with an enhanced
cooling rate. We further demonstrate a mapping to the dark-state sideband
cooling under asymmetric laser driving fields, which shows a distinct heat
transfer and promises an outperforming dark-state sideband cooling assisted by
collective spin-exchange interactions.
