  We investigate the possibility of achieving a slow signal field at the level
of single photons inside nanofibers by exploiting stimulated Brillouin
scattering, which involves a strong pump field and the vibrational modes of the
waveguide. The slow signal is significantly amplified for a pump field with a
frequency higher than that of the signal, and attenuated for a lower pump
frequency. We introduce a configuration for obtaining a propagating slow signal
without gain or loss and with a relatively wide bandwidth. This process
involves two strong pump fields with frequencies both higher and lower than
that of the signal, where the effects of signal amplification and attenuation
compensate each other. We account for thermal fluctuations due to the
scattering off thermal phonons and identify conditions under which thermal
contributions to the signal field are negligible. The slowing of light through
Brillouin optomechanics may serve as a vital tool for optical quantum
information processing and quantum communications within nanophotonic
structures.
