**Cody Leary**

Information may be encoded into the electromagnetic field of a photon in three fundamentally distinct ways: (i) in the spatial electric field distributions E_{x}(r) and E_{y}(r) associated with the two polarization components of the light; (ii) in the relative phase Φ (r) between these polarization components; and (iii) in the overall phase Θ(r) of the electromagnetic field. It is important to note that each of these objects is generally a function of location across a light beam, through the the spatial coordinate (r). Mathematically, the entire electromagnetic field of the photon may be expressed in terms of these parts as: e^{iΘ(r)} [ E_{x}(r) u_{x} + e^{iΦ(r)} E_{y}(r) u_{y} ]. Means for manipulating the amplitudes E_{x}(r) and E_{y}(r) and relative phase distribution Φ(r) for single photons are currently under development in our lab and many others, for applications in quantum information processing. However, the third way of encoding information into photons — by manipulating the overall phase distribution Φ — has been studied less extensively. One possibility for achieving this is shown in the figure above. Using devices available in the lab, a so-called “hedgehog” mode of light may be produced, which has a spatially varying linear polarization structure with a rotational symmetry, as shown. If the polarization properties of light modes of the above type are continuously manipulated, they may record a “memory” of the manipulation process in the spatial distribution properties of the phase Φ. This means that there is a measurable effect on the light, even if its polarization is first changed and then brought back to its original state — the overall phase structure Θ(r) can vary dramatically depending on the details of the polarization transformation (see figure for details). This project will involve developing theoretical and experimental capabilities for modeling and achieving the controllable impartation of overall phase structures onto single photons. It will involve the construction and improvement of a new experimental apparatus for imparting and measuring these phase structures, in addition to theoretical modeling of the predicted results in *Mathematica*.