ECE PhD Thesis Defense: Christopher Schwarze

ECE PhD Thesis Defense: Christopher Schwarze

Title: Interferometry with Higher-Dimensional Gauge-Invariant Optical Multiports

Presenter: Christopher Schwarze

Advisor: Professor Alexander Sergienko

Chair: Professor Miloš Popović

Committee: Professor Alexander Sergienko, Professor David Simon, Professor Michelle Sander, Professor Roberto Paiella

Google Scholar Link: https://scholar.google.com/citations?hl=en&user=FJA3HkcAAAAJ

Abstract: Optical interferometry is the controlled application of electromagnetic interference. While some interferometric techniques predate the advent of Maxwell's equations by centuries, a variety of contemporary methods find ever-improving use in areas such as optical sensing, signal modulation, imaging, filtering, quantum state generation, and information processing. This versatility is underpinned by the reconfigurable nature of these systems, allowing a single device to embody a continuously-variable family of field scatterers.

This dissertation describes novel generalizations to each of the two core constituents of any interferometric system: the passive scattering centers--such as beam-splitters or other material distributions--which redistribute the energy carried by incident photons, and the phase delays that freely propagating photons experience between pairs of these scattering centers. When an interferometer is modeled as a generic graph, these aspects may be represented by the vertices and edges, respectively, of the graph in question.

To accompany this graphical description, we develop an algebraic formalism for describing the action of each scattering center as well as the graph as a whole. This formalism is built around the identification of symmetries. Both core interferometric mainstays, scatterer and phase shift, can be associated with a class of symmetry transformations. Each class results from a redundancy in the physical description they admit, leading to the notion of a scattering gauge symmetry. In conjunction with this, the concept of a gauge-invariant scattering device is obtained by considering scattering transformations which commute with a prescribed symmetry operator. The formalism therefore can be used to define highly-symmetric scattering devices (and families thereof) to assume novel roles as interferometric building blocks.

The preeminent example is the optical Grover coin, obtained by adopting the diffusion operator from Grover's search algorithm as a generalized optical beam splitter. The associated scattering transformation is maximally symmetric, and in its four-dimensional form, can replace a traditional optical beam-splitter within any interferometric network. This gives rise to higher-dimensional symmetric interferometers for use in both classical and quantum applications.

We present novel Grover-Michelson and Grover-Sagnac interferometers, which produce an enhanced, tunable phase response. A decomposition of the four-port Grover coin is obtained from a novel description of the optical Y-coupler, which in turn enabled experimental demonstrations of Grover coin interferometry.

We also present a general, finite-element based approach for computing the output of any interferometric graph. After this, interferometric phase parametrizations are described; a class of interferometers known as linear-optical phase amplifiers emerge, which act as phase-controlled sources of optical phase. Applications of these devices are discussed with emphasis on a new approach to classical optical computing using tunable phase parametrizations.