Cody Leary - Project 2
General Area of Research:
Measurement and control of photon wave functions
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 determine the spatial distribution properties, or wave function, of a photon emanating from a laser cavity. Recent advances in the manipulation and control of these transverse degrees of freedom of light have led to the development of a wide variety of devices and applications; these range from the use of tightly-focused optical tweezers in molecular biophysics to directly probe the mechanics of transcription in single RNA molecules  to the construction of all-optical quantum gates for quantum information processing .
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 an asymmetric Mach-Zehnder interferometer, which has been successfully demonstrated by Wooster senior Deepika Sundarraman over the past year. This device, which can accept two input sources of light 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.
This hands-on project will continue efforts in our lab to manipulate and characterize the transverse spatial wave functions of photons using various home-built optical devices such as the aforementioned interferometer. The project will involve working with optical components including lasers, optical fibers, beam splitters, birefringent crystals, charge-coupled device (CCD) cameras, and interferometers, with the possible addition of symbolic matrix techniques in Mathematica for theoretical modeling of the various phenomena under study.
 Abbondanzieri, E.A. et al., 'Direct observation of base-pair steping by RNA polymerase.' Nature 438, 460-465 (2005); Fazal, E. M. and Block, S. M. 'Optical Tweezers Study Life Under Tension.' Nature Photonics 5, 318-321 (2011). Molina-Terriza, G., Torres, J.P. and Torner, L. 'Twisted Photons.' Nature Physics 3, 305-310 (2007).