Optics Rotation Project

My project entails the construction of a single-qubit universal quantum logic gate for bipartite order N=1 orbital angular momentum (OAM) modes of single photons. The gate is universal in the sense that it is able to perform any one-qubit state transformation. The exact realization of the universal gate follows the familiar polarization gate consisting of two rotatable Quarter-Wave Plates sandwiching a rotatable Half-Wave Plate. This setup is probably most well known from its use as a Pancharatnam-Berry Phase-Shifter, although it's also generally used in Tomographic schemes. In the OAM equivalent, pi and pi/2 Astigmatic Mode-Converters play the role of Half and Quarter-Wave Plates, respectively, where the vertical and horizontal polarization states are mirrored by the HG10 and HG01 Hermite-Gauss eigenmodes of the Cartesian solution to the paraxial wave equation. This exact realization, in terms of a parallel to polarization Wave-Plates, was chosen for convenience as it called for the least amount of optical elements. Similar schemes based on SU(2) Euler rotations and Spatial Basis interferometric gates were also investigated, and may be more suitable for other schemes, depending on whether one desires flexibility or ease of construction. (Of note, OAM gates based upon Euler rotations, realized by the introduction of anisotropy to the transverse profile of a few-mode optical fiber by an applied field, may be able to achieve fast switching times. Similarly, if the introduced anisotropy differed for different polarization eigenstates, a single-photon polarization-OAM two-qubit gate with the ability to switch between Identity and C-NOT operations could be realized.) Our setup for the universal logic gate has just been finished, with lots of help from Dr. Marty Cohen and Dr. John Noe of the LTC. We've done imaging of the output modes at various settings of the gate, and perhaps more quantitative Process Tomography on the Gate will follow if time allows.

Bryce Gadway
May 2008
Laser Teaching Center