Structural Complexity of SU(3) fermions in optical lattices
The development of quantum gas microscopy for two-dimensional optical lattices has provided an unparalleled tool to study condensed matter physics models with ultracold atoms. Spin-resolved projective measurements, or snapshots, have played a significant role in quantifying correlation functions, theory verification, and thus the uncovering of underlying physical phenomena such as magnetic phases of matter. When 173Yb or 87Sr atoms are used in optical lattices, experiments have access to a wider range of models that can be studied in their platform. One of these models (the SU(N) Fermi Hubbard model) has attracted interest due to its predicted exciting magnetic phases when the particle density is varied and the strength of the interaction between two particles increases.
In this project we will apply a recent concept, the multiscale structural complexity to study the snapshots generated using an approximate method to solve the model at a mean-field level called Hartree-Fock. Previous applications of this technique have shown that when the structural complexity is computed for the snapshots it can provide a theory-free property, sensitivity to phase boundaries, immediately accessible to experiments.
The project significance aligns with the current developments in ultracold atoms to perform projective measurements of 173Yb or 87Sr atoms in optical lattices that will yield the kind of pictures or snapshots we will be studying. Some of the tools to be developed in the project will require our understanding of (1) the physics of the Hubbard model, (2) the Hartree Fock (HF) approximation, and (3) the structural complexity measure. The project will involve modifying and running the HF and the SC codes, analyzing the outputs of such codes, and deriving analytical expressions for limiting cases.
Essay prompt: Please write a short essay stating
[1] Why you are interested in the project.
[2] Your programming experience in Python/Julia (or any other language, but those are preferred for this project).
[3] How many credits you want to do.
I am the new Physics faculty at Harvey Mudd and I am looking for motivated students to work on projects in the field of Quantum Many-Body (QMB) Physics. QMB physics aims to understand the collective behavior of a large number of interacting quantum particles. These interactions can create entirely new kinds of matter and display behaviors that you’d never see with just one particle. One of the most exciting frontiers in this field is called quantum simulation. In a quantum simulator, ultra cold atoms (which have been cooled down close to absolute zero via optical techniques) are trapped in an optical lattice (a standing wave made out of light). When atoms are trapped in the lattice they are well described by models used in condensed matter physics to understand the physics of real materials. The degree of control these experiments have over many parameters provides a unique opportunity to explore states of matter with a high degree of precision, which in turn allow us to thoroughly test the theoretical models we use to describe them.