Enhanced Photon Routing Beyond the Blockade Limit Via Linear Optics

Directing indistinguishable photons from one input port into separate output ports is a fundamental operation in quantum information processing. The simplest scheme for achieving routing beyond random chance uses the photon blockade effect of a two-level emitter. But this approach is limited by a time-energy uncertainty relation. We show that a linear optical unitary transformation applied after the atom enables splitting efficiencies that exceed this time-energy limit. We show that the linear optical unitary improves the splitting efficiency from 67\% to 82\% for unentangled photon inputs, and from 77\% to 90\% for entangled photon inputs. We then optimize the temporal mode profile of the entangled photon wavefunction to attain the optimal splitting efficiency of 92\%, a significant improvement over previous limits derived using a two-level atom alone. These results provide a path towards optimizing single photon nonlinearities and engineering programmable and robust photon-photon interactions for practical, high-fidelity quantum operations.