Year: 2021
Type: dissertation
Abstract: It takes some convincing to realize that light has a polarization degree of freedom, as our eyes are usually ignorant of light's polarization. Since overcoming this hurdle of intuition, polarization has become a fantastic resource that can be easily manipulated both physically and mathematically, opening the door to a wide variety of applications. We have only recently begun to appreciate how many more doors are opened by the quantum mechanical degrees of freedom inherent to optical polarization. One use of optical polarization is for polarimetry: measuring the changes in light's polarization after it interacts with a material is an excellent procedure for nondestructively probing the characteristics and composition of the intervening material. More sensitive measurements require brighter probe light; however, sufficiently intense light will begin to destroy the sample being probed. In this thesis, we seek to provide more sensitive polarimetry without resorting to bright beams of light. Tailoring the quantum properties of various states of light has been shown to increase their usefulness for other estimation protocols and we show how to extend this paradigm to quantum enhancements in polarimetry. We begin by finding the quantum states underlying classical polarization. Each particular set of classical polarization properties corresponds to a large variety of quantum states. Next, we establish quantum descriptions of classical polarization transformations corresponding to arbitrary Jones and Mueller matrices, including quantum mechanical insights into the distinction between processes that can and cannot be described by Jones matrices. We propose candidates for the most likely quantum states underlying classical decompositions into polarized and unpolarized fractions, carefully inspecting how these quantum states behave under polarization transformations. This language allows us to inspect quantum-enhanced sensing in the multiparameter context of polarimetry. We show the dramatic possibilities for quantum enhancements in any metrological scenario that is mathematically equivalent to a rotation, of which polarization rotations are a primary example; in contrast, we also show most attenuating and depolarizing polarization transformations to forbid such dramatic enhancements. Finally, we discuss polarization and its generalizations in the context of generating quantum entanglement via linear optics. These applications serve as mere examples of the usefulness promised by light’s quantum polarization degrees of freedom.
Source: TSpace (University of Toronto)
Author: Goldberg, Aaron Zev
Institution: University of Toronto
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: University of Toronto
OpenAlex ID: W7132882003