Photons, or light particles, have four independent internal degrees of freedom. Two of these-- the light's color (wavelength) and its polarization-- are better known. The remaining two so-called "transverse spatial" degrees of freedom, which are less often studied, determine the spatial distribution properties, or wave function, of a photon emanating from a laser cavity. This concept of a photon wave function stands in direct analogy with the probability distribution of an electron in a hydrogen orbital.
In this project we will study the transverse spatial wave functions of photons, while learning to measure and control their properties. A crucial tool for transverse wave function measurement and manipulation is known as the one-dimensional photon parity interferometer, a prototype of which was built and calibrated this year by a Wooster senior, This device, which can accept two input photons and also has two outputs, is capable of "mixing" the wave functions of two input beams such that the output beams undergo nontrivial changes in their wave functions of a topological nature.
Due to this and other properties of the interferometer, there are many possible avenues for research using this tool, including but not limited to: the imparting of "orbital angular momentum" to photons such that a photon's wave function is "twisted" around the direction of its propagation; the nontrivial interaction of two different photonic degrees of freedom--a photon's polarization and its spatial wave function--as both are manipulated inside the interferometer; and the measurement and classification of photon wave functions with respect to their one-dimensional parity properties.
The project will involve building and working with optical components, laser cavities, interferometers, and symbolic matrix techniques in Mathematica for theoretical modeling of the various phenomena involved.