Hamiltonian engineering with synthetic dimensions

Hamiltonian engineering can provide insights into the control and manipulation of quantum systems, which may pave the way for progress in quantum sensing and quantum many-body physics. Here, I will focus on a specific type of Hamiltonian engineering technique based on the spectroscopic coupling of atomic states. I will describe how we use two-photon Bragg resonances to couple discrete momentum states of our BEC, forming a synthetic lattice of momentum states in one dimension. Taking advantage of the site-resolved control afforded by our synthetic lattice technique, I will show some experimental results regarding transport in a one-dimensional quasiperiodic mosaic lattice. I will then discuss two-dimensional momentum state lattices. Finally, I will offer prospective directions in leveraging atomic interactions to probe many-body topological physics and squeezed states in our experimental platform.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Agrawal, Shraddha

Contributors dc:contributor

• Gadway, Bryce R.
• DeMarco, Brian L.
• Cooper, Stephen L
• Lorenz, Virginia

• Hamiltonian Engineering
• Momentum State Lattices

Statement dc:rights

• Copyright 2025 Shraddha Agrawal

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/130003

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F130003