Disordered Quantum Matter in Strongly Correlated Optical Lattices

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The purpose of this project is to enhance knowledge of how disorder affects the electronic solids, such as metals, insulators, and superconductors, that form the basis of modern technology. The ability to control how electrons carry heat, energy, and information in solids enables applications such as computers and efficient energy generation and transmission. The disorder and imperfections inherent in solids are often deleterious and can, for example, increase the resistance of metals to electrical current flow. On the other hand, disorder may enhance superconductivity, which is transmitting electrical current without resistance, and thermoelectricity, which is transforming heat into electrical energy. In general, how disorder affects many exotic solids, such as high-temperature superconductors, that may lead to new applications and higher efficiencies is not understood. In part, this lack of understanding arises because the simplest models of how electrons behave in these materials cannot be solved using even the most powerful supercomputers that will be created over the next century. This project will use atoms trapped in a crystal of light and cooled to just a billionth of a degree above absolute zero temperature to simulate these models in an experiment. The ability of disorder to transform solids between metallic, insulating, and superconducting states will be investigated by measuring how the atoms respond to changes in the light and magnetic fields. The possibility to use disorder as a new tool to suppress processes that disrupt applications such as information storage will be explored. These measurements will be employed to test theories that may be used to design novel materials. The influence of disorder on the behavior of strongly correlated electronic solids, such as high-temperature superconductors, is poorly understood, despite the prevalence of imperfections in these materials. Numerical simulations provide limited insight, and theory has been challenged to develop controlled approaches to understanding the interplay of strong interactions and disorder. Furthermore, using measurements on materials to test theory and simulations is complicated by the inability to separately control material parameters, imprecise knowledge of disorder, and complications such as phonon-electron scattering. Ultracold K-40 and Rb-87 atoms trapped in optical lattices will be used to explore the impact of disorder on superfluids in Hubbard models, which are minimal models of strongly correlated electronic solids. In these experiments, controllable and precisely characterized disorder will be introduced using optical speckle. The interactions will be manipulated independently by tuning the optical lattice potential depth and via a Feshbach resonance. The disordered attractive Fermi-Hubbard model will be realized for the first time using atoms by tuning to the attractive side of a Feshbach resonance. Combinations of transport and pair fraction measurements will be employed to answer the long-standing question of how fermionic superfluids localize in strongly correlated systems, i.e., whether pairs or single particles constitute the disorder-induced insulating state. Rethermalization and relaxation in localized superfluids (i.e., Bose-glasses) will be probed by measurements of quasimomentum and density profiles. The atomic momentum distribution will be disturbed from equilibrium using quasi-momentum-selective stimulated Raman transitions, and the density profile will be manipulated using a local, repulsive optical potential created by a focused blue-detuned laser beam. Measurements will be compared with state-of-the-art theory and numerical simulations.