Quantum measurements of spatial conjugate variables: Displacement and   tilt of a Gaussian beam
  We consider the problem of measurement of optical transverse profile parameters and their conjugate variable. Using multi-mode analysis, we introduce the concept of detection noise-modes. For Gaussian beams, displacement and tilt are a pair of transverse profile conjugate variables. We experimentally demonstrate their optimal encoding and detection with a spatial homodyning scheme. Using higher order spatial mode squeezing, we show the sub-shot noise measurements for the displacement and tilt of a Gaussian beam. 
Vincent Delaubert (LKB - Jussieu, ACQAO), Nicolas Treps (LKB -   Jussieu), Charles C. Harb (ACQAO), Ping Koy Lam (ACQAO), Ha...