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We explore the possibility of achieving a significant nonlinear phase shiftamong photons propagating in nanoscale waveguides exploiting interactions amongphotons that are mediated by vibrational modes and induced through StimulatedBrillouin Scattering (SBS). We introduce a configuration that allows slowingdown the photons by several orders of magnitude via SBS involving sound wavesand two pump fields. We extract the conditions for maintaining vanishingamplitude gain or loss for slowly propagating photons while keeping theinfluence of thermal phonons to the minimum. The nonlinear phase among twocounter-propagating photons can be used to realize a deterministic phase gate.

Nonlinear Quantum Optics in Optomechanical Nanoscale Waveguides