Violation of conservation of topological charge in optical down conversion

Summary form only given. Spontaneous degenerate parametric scattering [down-conversion] is a 3-photon process with one pump photon of frequency 2/spl omega/ and two output photons of frequency /spl omega/. We report the experimental observation of the down conversion with the optical vortex serving as a pump beam. An optical vortex is defined as a beam containing a phase singularity, i.e. The change of phase around the center of the beam equals 2 /spl pi/m; where the integer m is the topological charge. Each photon in the vortex beam possess orbital angular momentum L=m/spl planck/. The law of conservation of angular momentum is expected to be valid in a homogenous linear or nonlinear medium. Topological charge conservation was confirmed in second-harmonic generation experiments, and may be expected to hold under degenerate parametric scattering. However, in the quantum domain, the uncertainly relations, /spl Delta//spl phi//spl Delta/N>2/spl pi/, (where /spl phi/ is the phase and N is the number of photons) provides an opportunity to violate this conservation principle, since the phase of the two down-converted photons is undetermined to within /spl Delta//spl phi/=2/spl pi//2 for every converted fundamental photon. That is, the down converted signal may contain no information about the topological phase of the pump beam. Based on our experiments and numerical calculations of the down-converted signal we suggest that the phase information is indeed lost under down conversion, therefore violating the conservation of topological charge.