Effect of loss on single photon parametric amplification

- Linear loss affects parametric amplification of a single photon.
- Equations describing photon loss and amplification are derived.
- Three-photon states are periodically suppressed for particular loss values.

We analyze the transmission of a single photon through a nonlinear waveguide, under the presence of linear losses and a co-propagating classical pump wave facilitating quantum-injected optical parametric amplification. We derive coupled Schrödinger-type equations which describe the processes of photon loss and generation of photon triplets, and obtain their solution to identify the quantum photon state at the output.