  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.
