Fidelity of a Single-Photon Router Based on Cavity Reflection from a Coupled Emitter

A photon reflected from a cavity that contains a coupled emitter acquires a phase that depends on the emitter state. That conditional phase is the working principle of a photon router and of several photon-photon gate proposals, and its usefulness is set by the cooperativity. This study computes the quantities that follow from stated assumptions for a one-sided cavity coupled to a two-level emitter, probed on resonance by a narrowband single photon, using the relations set out in the Methods. The headline results are fidelity at C 5 = 0.9091, fidelity at C 20 = 0.9756, fidelity at C 100 = 0.995, reflection at C 5 = 0.8182, loss at C 20 = 0.09518. The central question is stated as follows: For cooperativities from one half to one hundred, what reflection amplitudes, conditional phase error and routing fidelity follow in the standard input-output model? The answer obtained here is conditional on the assumptions listed in the paper and in the deposited calculation; changing an assumption changes the numbers in the way the sensitivity discussion describes. Conditional phase shifts approaching pi and gate fidelities limited mainly by cooperativity are the standard theoretical expectations for this geometry, with experiments reporting smaller shifts where cooperativity is modest. The work is a computation, not a laboratory measurement, and it is labelled accordingly. Where the computed result is unfavourable to the device or effect under study, that outcome is reported in the same terms as a favourable one, because a bound that only appears when it is welcome is not a bound at all. All numerical statements in this abstract are reproduced by the deposited script from the stated inputs.