Interactions in Shaken Lattice Interferometry

Press, Alana

Undergraduate Honors Thesis

Interactions in Shaken Lattice Interferometry Public Deposited

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Citeable URL: https://scholar.colorado.edu/concern/undergraduate_honors_theses/3j3333508

Abstract

Precision sensing and measurement is of fundamental importance to any scientific endeavor. As technologies have advanced, measurements have reached the precipice of quantum limited sensing. As a result of this rapid advancement, the field of quantum metrology has become a distinct and important field of physics research. Recently, major advancements in quantum technology have created the opportunity that, in the near future, simple quantum mechanical devices may be used to probe extreme physics via tabletop experiment. Specifically, matter-wave interferometry is an area of interest due to its potential for accurate measurements of a myriad of fields, forces, and interactions. In direct analogue to optical interferometry, matter-wave interferometry uses the principle of coherently splitting and recombining a wave to measure the difference in the lengths of the paths taken. The key difference is that matter-wave interferometry uses massive particles instead of light. The smaller de Broglie wavelengths of particles allow for more precise measurements compared to those of light, at the cost of added complexities through interaction. Additionally, massive particles are subject to gravity and can sense inertial changes that photons can't. Although matter may have a theoretical edge over light, there has not yet been an experimental matter-wave interferometer that surpasses the best optical interferometer in accuracy. The use of a precisely controlled shaken lattice provides a completely new pathway for realizing matter-wave interferometry and may generating higher fidelities and precision than otherwise achievable through conventional means.

Although shaken lattice interferometry has been shown to be an accurate and effective method for small atomic systems, there is a downside in its ability to scale to larger atomic ensembles. When the lattice is loaded with a bosonic gas on the order of 50,000 atoms, atomic interactions become important. In this thesis, I will discuss the mean field effects of this gas in the lattice, and how to control these effects to improve upon existing matter-wave inteferometry. I do this by using the Gross-Pitaevskii equation to describe the interacting wave-function evolution. Then, I use existing shaking functions derived for a noninteracting system in a fully interacting simulation to model these effects in the current configuration of experiments. I improve upon these methods in the presence of interaction by using the interacting model to learn new shaking functions, whereupon I compare and contrast how they behave in interacting and non-interacting models. Finally, I show how these models can be used to precisely measure a simulated constant acceleration similar to gravity.

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