  Non-Hermitian, one-dimensional potentials which are also non-local, allow for
scattering asymmetries, namely, asymmetric transmission or reflection responses
to the incidence of a particle from left or right. The symmetries of the
potential imply selection rules for transmission and reflection. In particular,
parity-time (PT) symmetry or the symmetry of any local potential do not allow
for asymmetric transmission. We put forward a feasible quantum-optical
implementation of non-Hermitian, non-local, non-PT potentials to implement
different scattering asymmetries, including transmission asymmetries.
