2026-09-22T11:46:00Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/130003 2026-02-10 col_2142_5131 col_2142_8859 com_2142_5130 com_2142_8858 com_2142_234

application/pdf en text Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-08-01 The student, Shraddha Agrawal, accepted the attached license on 2025-05-23 at 02:14. The student, Shraddha Agrawal, submitted this Dissertation for approval on 2025-05-23 at 11:54. This Dissertation was approved for publication on 2025-05-28 at 13:38. DSpace SAF Submission Ingestion Package generated from Vireo submission #22307 on 2025-10-21 at 10:05:19 Hamiltonian engineering with synthetic dimensions Agrawal, Shraddha 2025-05-28 Gadway, Bryce R. DeMarco, Brian L. Cooper, Stephen L Lorenz, Virginia Hamiltonian Engineering Momentum State Lattices eng 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. 2025-08 Text https://hdl.handle.net/2142/130003 Copyright 2025 Shraddha Agrawal Physics Physics University of Illinois Urbana-Champaign Ph.D. Dissertation