Absence of long-range coherence in the parametric emission of photonic wires

We analytically investigate the spatial coherence properties of the signal emission from one-dimensional optical parametric oscillators. Because of the reduced dimensionality, quantum fluctuations are able to destroy the long-range phase coherence even far above threshold. The spatial decay of coherence is exponential and, for realistic parameters of semiconductor photonic wires in the strong exciton-photon coupling regime, it is predicted to occur on an experimentally accessible length scale.