  Nonreciprocity originating from classical interactions among nonlinear
scatterers has been attracting increasing attention in the quantum community,
offering a promising tool to control excitation transfer for quantum
information processing and quantum computing. In this work, we explore the
possibility of realizing largely nonreciprocal total cross sections for a pair
of quantum metasurfaces formed by two parallel periodic arrays of two-level
atoms. We show that large nonreciprocal responses can be obtained in such
nonlinear systems by controlling the position of the atoms and their transition
frequencies, without requiring that the environment in which the atoms are
placed is nonreciprocal. We demonstrate the connection of this effect with the
population of a slowly-decaying dark state, which is critical to obtain large
nonreciprocal responses.
