We put forward an experimentally feasible technique to generate engineered entangled states in d-dimensional Hilbert spaces in parametric down-conversion of photons. The scheme is based on the orbital angular momentum of light and translates the classical, topological information imprinted in the light beam that pumps the two-photon source into quantum information contained in the weights and phases of the quantum entangled two-photon states.Peer ReviewedPostprint (published version

We show experimentally how noncollinear geometries in spontaneous parametric downconversion induce ellipticity of the shape of the spatial mode function. The degree of ellipticity depends on the pump beam width, especially for highly focused beams. We also discuss the ellipticity induced by the spectrum of the pump beam.

A method of intensity-dependent polarization switching is proposed. The effect is based on simultaneous action of two phase-matched second-order processes in a quadratic medium. Using analytical and numerical techniques, we demonstrate that a single linearly polarized fundamental wave, when it is propagating in such a medium, can efficiently generate a new fundamental wave of orthogonal polarization. The polarization switching is explained by an effective four-wave-mixing process that is performed through second-order cascading.

We report an experimental demonstration that shows that the spatial structure carried by engineered coherent superpositions of light beams with orbital angular momentum can be mapped into the nonlinear polarization induced in a cloud of cold cesium atoms. The structure of such polarization was revealed by nearly degenerate four-wave-mixing processes.

We propose a novel type of cascading parametric interaction for generating a nonlinear phase shift in dielectric media with a quadratic nonlinear response based on two-frequency wave mixing of the fundamental and second-harmonic waves. Self-phase modulation of the fundamental wave results from a cascading process consisting of four second-order subprocesses, the direct and reverse subprocesses of Type I second-harmonic generation (SHG) and the direct and reverse subprocesses of Type II SHG. It is found analytically and numerically that the fundamental wave passing through a quadratic medium, tuned for simultaneous near phase matching for these two processes, collects 60% more nonlinear phase shift than does the corresponding twostep cascading. We also obtain the conditions for stationary waves (nonlinear modes) supported by such multistep cascading processes.

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