The quantum theory of a field in 1+1 dimensions coupled to localized oscillators is developed. The solution to the Heisenberg equation for the field is given in closed form. It is shown that the nonlinearity of the medium is inevitably accompanied by phase noise of the field. This noise explains the preferential growth of the Stokes wave for short propagation distances.

• Received 20 December 1993

DOI:https://doi.org/10.1103/PhysRevLett.73.240