  We theoretically investigate the flow of the atomic excitations in a driven
chiral-coupled atomic chain with nonreciprocal decay channels. This
one-dimensional system allows infinite-range dipole-dipole interaction, and
enables directional guided modes of scattered light. Under a weakly driven
condition, we are able to simulate the transport properties of atomic
excitations between the left and right parts of the chain. In the steady
states, the transport is highly dependent on the equidistant positions of the
ordered array, the excitation field detunings, and the directionality of such
chiral-coupled system. We discuss the parameter regimes which are resilient or
sensitive to position fluctuations, and provide insights to precise and genuine
state preparations. Furthermore, we study the effect of position fluctuations
on the transport of excitations. Our results can shed light on deterministic
state preparations and pave the way for many-body state manipulations in the
driven and dissipative chiral-coupled systems.
