  The concept of parity-time (PT) symmetry has been used to identify a novel
route to nonreciprocal dynamics in optical momentum space, imposing the
directionality on the flow of light. Whereas PT-symmetric potentials have been
implemented under the requirement of V(x) = V*(-x), this precondition has only
been interpreted within the mathematical frame for the symmetry of Hamiltonians
and has not been directly linked to nonreciprocity. Here, within the context of
light-matter interactions, we develop an alternative route to nonreciprocity in
momentum space by employing the concept of causality. We demonstrate that
potentials with real and causal momentum spectra produce unidirectional
transitions of optical states inside the k-continuum, which corresponds to an
exceptional point on the degree of PT-symmetry. Our analysis reveals a critical
link between non-Hermitian problems and spectral theory and enables the
multi-dimensional manipulation of optical states, in contrast to
one-dimensional control from the use of a Schrodinger-like equation in previous
PT-symmetric optics.
