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.
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