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Probing the Interface of Particles and Waves Using Fourier Transform Spectroscopy

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When a collection of individual units behave synchronously, it is often useful to describe the actions of the group. Broadly speaking in Physics, individuals are described as particles and collective actions are described using waves. However, the dynamic symphony of life ordains that orchestral sections play in harmony for a finite amount of time. To generalize an ancient Chinese proverb: "All objects, long divided, must unite. Long united, must divide." Coherence is the the measure of the spatial and temporal scales that the wave description of reality breaks down. All functions can be Fourier decomposed into a sum of sines and cosine waves, but there exists an intricate relationship between the frequency of a wave and the timescale it can exist on. Heuristically, bigger things move slower. In Quantum Mechanics, this frequency-time relationship has a limit that is quantitatively defined in the Uncertainty Principle. States that have well defined energies (and thus frequencies) must exist for many cycles of oscillation and persist for a long time. Objects that exist for a short amount of time must be composed of many different energies (that oscillate in phase). Collective behavior at a molecular scale can be studied using Fourier transforms. Chapter 1 introduces how light-matter interactions and interferometers are implemented in so called Fourier Transform Spectroscopies to uncover the timescales at which energetic wavepackets disperse. Chapter 2 applies the techniques introduced in Chapter 1 to polymers, repeating chains of individual units that have delocalized electronic states. Chapters 3, 4, and 5 dive deep into coherence observed in photosynthetic proteins, which are evolutionarily optimized formations of chromophores designed to transfer energy. In Chapters 6 and 7, the ability for quantum objects to have coherence with themselves is investigated. Lastly, Chapter 8 generalizes our molecular understanding of coherence to processes occurring at a cellular and whole brain level.

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