A quantum rectifier in a one-dimensional photonic channel

By using a fully quantum approach based on an input-output formulation of the stochastic Schr\"{o}dinger equation, we show rectification of radiation fields in a one-dimensional waveguide doped with a pair of ideal two-level systems for three topical cases: classical driving, under the action of noise, and single photon pulsed excitation. We show that even under the constant action of unwanted noise the device still operates effectively as an optical isolator, which is of critical importance for noise resistance. Finally, harnessing stimulated emission allows for non-reciprocal behavior for single photon inputs, thus showing purely quantum rectification at the single-photon level. The latter is a considerable step towards the ultimate goal of devising an unconditional quantum rectifier for arbitrary quantum states.