  Coherent control of traveling acoustic excitations in a waveguide system is
an interesting way to manipulate and transduce classical and quantum
information. So far, these interactions, often based on optomechanical
resonators or Brillouin scattering, have been studied in the steady-state
regime using continuous waves. However, waveguide experiments are often based
on optical pump pulses which require treatment in a dynamic framework. In this
paper, we present an effective Hamiltonian formalism in the dynamic regime
using optical pulses that links waveguide optomechanics and cavity
optomechanics, which can be used in the classical and quantum regime including
quantum noise. Based on our formalism, a closed solution for coupled-mode
equation under the undepleted assumption is provided and we found that the
strong coupling regime is already accessible in current Brillouin waveguides by
using pulses. We further investigate several possible experiments within
waveguide optomechanics, including Brillouin-based coherent transfer, Brillouin
cooling, and optoacoustic entanglement.
