Spatial pump-meter quantum correlations in a vectorial Kerr-medium model

We consider a vectorial Kerr-medium model including transverse spatial effects. We analyze cases in which, immediately above the threshold of the spatial instability, the homogeneous pump wave gives rise to two tilted waves corresponding to a stripe pattern in the near field. We analyze both the self-focusing and the self-defocusing case and we point out the existence of anti-correlations between the quantum fluctuations of the intensity of the pump and the sum of the intensities of the two tilted waves creating the transverse pattern in the near field. We also evaluate the efficiency of this scheme as a quantum nondemolition (QND) scheme which uses the tilted waves as a “meter” to measure the intensity fluctuations of the pump. Our results show the posibility of a QND measurement in the self-defocusing case. In this case, and for a linearly polarized pump, the output pump beam (uniform in the transverse plane) and the pattern have orthogonal polarization and could be easily separated experimentally.