Compressibility of a bosonic Mott-insulator in a disordered optical lattice

"An open problem at the forefront of physics is gaining a complete understanding of strongly interacting quantum systems. Strong interactions are known to be present, for example, between atoms in superfluid 4He and electrons in certain high-temperature superconductors like the cuprates. Beyond academic interest, a solution to this problem has practical applications. It would enable technological advancements such as the production of materials and devices with novel characteristics by exploiting the physics of strong interactions. Much of the impediment to progress is that the models thought to contain the essential ingredients that give rise to the observed behavior cannot be solved analytically and require prohibitive amounts of computational resources in order to simulate numerically. These limitations are exacerbated with the addition of disorder. The disorder is ubiquitous in nature and thus its contribution to the observed properties of strongly interacting quantum systems must also be understood. The approach taken in this thesis is to simulate a paradigm of disordered, strongly interacting bosons called the ""disordered Bose--Hubbard model"" using ultracold 87Rb atoms moving in a disordered optical lattice. The ground-state phase diagram of the disordered Bose--Hubbard model at unit filling and zero-temperature is largely considered to be settled from a theory viewpoint, though studies at arbitrary densities are missing. Aside from the issue of density, the phase diagram at unit filling is only understood in the thermodynamic limit, which raises questions about the physics of realistic finite systems. Furthermore, understanding finite temperature and dynamics are also open problems. The experiment in this thesis probes the phase boundary in the region of the phase diagram where interactions dominate. At fixed interaction strength, it is argued that disorder destroys the excitation gap and drives a quantum phase transition from an incompressible phase to a compressible phase. We extracted the compressibility by measuring double occupancy and observed its behavior as the disorder strength is varied. We found that the system has a small, thermally induced compressibility that is nearly constant for small disorder strengths. As the disorder strength is further increased, the compressibility increases by a factor of 5-10 over the range of disorder strengths we explored. We quantified the threshold disorder strength beyond which the compressibility begins to increase and found this threshold value increases with increasing interaction strength. Our observations are in agreement with predictions in the atomic limit and support the picture that the interplay between disorder and the excitation gap is the underlying mechanism controlling the behavior of the compressibility. However, the significant temperature of our experiment prevented us from probing the low-temperature behavior and comparing it to the predicted zero-temperature phase boundary. An investigation into the effects of finite temperature by our theory collaborators indicates that experiments must be able to achieve temperatures well beyond current capabilities in order to access the low-temperature Mott-insulator--Bose-glass transition."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2021

Author dc:creator

• Russ, Philip Andrew

Contributors dc:contributor

• DeMarco, Brian
• Gadway, Bryce
• Mason, Nadya
• Vishveshwara, Smitha

• disorder
• optical lattice
• bose hubbard model
• double occupancy
• quantum simulation
• ultracold atoms
• compressibility

Statement dc:rights

• Copyright 2020 Philip Russ

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/109437

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/109437