  Chiral light-matter interaction between photonic nanostructures with quantum
emitters shows great potential to implement spin-photon interfaces for quantum
information processing. Position-dependent spin momentum locking of the quantum
emitter is important for these chiral coupled nanostructures. Here, we report
the position-dependent chiral coupling between quantum dots (QDs) and cross
waveguides both numerically and experimentally. Four quantum dots distributed
at different positions in the cross section are selected to characterize the
chiral properties of the device. Directional emission is achieved in a single
waveguide as well as in both two waveguides simultaneously. In addition, the QD
position can be determined with the chiral contrasts from four outputs.
Therefore, the cross waveguide can function as a one-way unidirectional
waveguide and a circularly polarized beam splitter by placing the QD in a
rational position, which has potential applications in spin-to-path encoding
for complex quantum optical networks at the single-photon level.
