  We analyze several variations of a single-photon optical switch operating in
the continuous wave regime, as presented in the accompanying paper [Tsiamis et
al., Continuous wave single photon switch based on a Rydberg atom ensemble].
The devices are based on ensembles of Rydberg atoms that interact through van
der Waals interaction. Continuously probing the atomic cloud with a weak
coherent probe field, under the conditions of electromagnetically induced
transparency (EIT) leads to total reflection/transmission of the probe in the
absence of control photons. Exciting a Rydberg state with a single control
photon breaks the EIT conditions, drastically altering the probe's
reflectance/transmittance. We examine how the collective Rydberg interaction in
an atomic ensemble enclosed in an optical cavity or in free space induces two
probe-induced dephasing processes. These processes localize the control photons
and modify the probe's reflectance/transmittance, enhancing the lifetime of
control excitations and increasing the devices' efficiency. The devices are
characterized by the probability to absorb a control photon and the associated
gain as described by the change in the probe's reflectance/transmittance. The
results are confirmed through numerical calculations of realistic one- and
three-dimensional atomic ensembles in a cavity and an one-dimensional atomic
ensemble in free space. The proposed continuous wave devices complement
previously realized single photon transistors and expand the possible quantum
light manipulation circuitry.
