PhonologiQ · Theoretical Investigation of Surface Phonon Polariton-Based Quantum Photonic Circuits

Theoretical Investigation of Surface Phonon Polariton-Based Quantum Photonic Circuits

The key idea of my work is to produce a model of quantum electrodynamics that is robust enough to define the full dynamics of the phonon-polariton states of single or coupled finite polar crystal particles. As this class of particles may provide an avenue toward engineering more energy- and time-efficient computing architectures in both classical and quantum computing paradigms, a complete and economical theory of the quantum dynamics of such particles could have a materially beneficial effect on future research efforts in optical computing and related fields. In particular, I built my work upon the theory of macroscopic quantum electrodynamics (MQED). This theory was invented in the early 2000s to capture the quantum observables of nanometer- to micron-scale crystals or particles made of lossy materials without the need to keep track of individual atomic states. While it has been used successfully since then to model certain quantum fluctuation phenomena, it has not yet been broadly applied to practical problems in cavity optics, i.e. the study of light “trapped” in or near small structures. Much of the theoretical work that has unlocked progress in cavity optics experiments this millennium has been based on classical cavity electrodynamics techniques. The most successful such technique is called a mode decomposition, wherein the independent characteristic patterns of motion of the currents and fields of a particle are identified. Secondary effects, such as influence of some electromagnetic driving source or nearby resonances, can then be treated as perturbations of the underlying mode structure. These mode theories allow intuitive, economical models of such ensembles to be constructed to capture important information—how and where energy is being transferred between particles, how interactions and hybridization affect observed signals, etc.—without the overhead cost of running expensive full-field simulations. MQED does not yet contain the tools to reproduce such a mode decomposition, even though the separation of a system’s dynamics into individual state motion is more important to do in quantum mechanics than in classical mechanics. Adding mode-decomposition functionality to MQED is therefore a key first step in recreating the success of classical cavity optics.

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