CAREER: Analog Quantum Simulation of Quasicrystalline Topological Quantum Materials with Ultracold Atoms in Optical Quasicrystal Lattice Potentials

Yale University, New Haven CT

Investigators

Abstract

This CAREER project aims to explore how mathematical ideas from geometry and topology combine with quantum mechanics to affect properties of quasicrystalline materials. All materials require quantum mechanics to explain their basic properties. However, “quantum materials” are a subset of materials that exhibit macroscopically observable quantum effects. Topology in materials refers to a mathematical property that remains unchanged when a material is distorted. The discovery of topological phases of matter has been an eye-opening breakthrough in condensed matter physics and has led to surprises in possible phases of matter and in the behavior of electrons flowing through materials. Geometry is important for describing crystal symmetries and it places constraints on the behavior of materials, depending on the specific symmetries at play. Altogether, topological quantum materials (TQMs) are materials for which quantum mechanics, geometry and topology are important for describing emergent material properties. The research this CAREER award enables has high synergy with ongoing experimental and theoretical efforts across atomic physics, condensed matter physics, chemistry and beyond. This CAREER project will use atomic physics techniques to build and probe an experimental analogue of a quasicrystalline material with unusual symmetries. This research team will build an experiment that traps atoms in dynamically reconfigurable and aperiodic grids of light; here, the atoms are analogous to electrons in a material, and the light grid is analogous to the underlying patterns of atoms in a material. They will observe the behavior of atoms moving around the light grid and take measurements that provide detailed information on how geometry and topology play a role in the analogue quasicrystal. The PI will continue to generate impactful community-based programming that supports physicists and continue to develop high-visibility role models and new educational opportunities for students to learn about the scientific and technical aspects of cutting-edge research in physics. This research group is also developing educational opportunities for a group of over 1,000 young local students and will engage the students with quantum science from their laboratory. This CAREER project will experimentally explore the physics of quasicrystalline quantum materials by mimicking these materials with quantum degenerate matter in optical lattices. A quasicrystal is an aperiodic crystal with rotational symmetries that are mathematically forbidden in periodic crystals. The standard mathematical analysis techniques used to understand the behavior of periodic crystals does not work for quasicrystals due to a lack of translation symmetry. Quasicrystals exhibit anomalous and, potentially, topological transport properties that are thus difficult to understand analytically. This project aims to experimentally probe the effects of geometry and topology in the quantum behavior of a quasicrystal and how these effects lead to unusual transport properties in quasicrystals. New experimental techniques developed during this project are poised to open a new class of experimental probes of quasicrystalline material properties and of atomic physics systems. These experiments may lead to a jump in the understanding of the fundamental properties of TQMs, and the quantum many-body problem more broadly, especially for addressing scientific questions that are hard to answer with quantum many-body theory alone. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.