Exploring Interacting Topological Fluids in a Synthetic Lattice

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This research will use cold and dilute gases of atoms to investigate new phases of matter shaped by topology and disorder. The ability to harness the diverse behaviors of electrons in different materials, such as metals, insulators, and semiconductors, has led to remarkable technological development and economic growth over the past century. The discovery and engineering of new quantum materials promises to shape future technologies for many decades to come. In particular, materials with nontrivial topology, relating to highly robust properties, promise to play an important role in diverse areas such as spintronics and fault-tolerant quantum computing. While important aspects of these systems are difficult to probe in real materials, the approach of quantum simulation, where a highly tunable quantum system can be used to mimic a more unwieldy quantum system, allows for the exploration of new classes of topological materials. This project will use extremely well-controlled and well-understood systems of neutral atoms, cooled to less than one-millionth of a degree above absolute zero temperature and having ultralow densities a million times less than that of air, to engineer synthetic quantum materials. A key focus of this research will be on the development of new techniques, based on the high degree of spectroscopic control available in simple atomic systems, to engineer designer synthetic materials. These experiments promise to provide laboratory-based studies of hitherto unexplored phenomena, and to shed new light on poorly understood emergent behavior in systems with high ground state degeneracy. The developed techniques will also expand the set of tools used for inertial sensing based on atom interferometry. Additionally, this program will provide scientific and professional training to students in areas of high technological relevance. This research project will develop new techniques for lattice and band structure engineering, to address outstanding problems related to topological and disordered materials. Taking an unconventional approach, where a synthetic lattice is engineered not in real space, but rather in the space spanned by a discrete set of quantum states, this project will enable completely new capabilities related to Hamiltonian engineering, and will open up new classes of material systems to investigation through quantum simulation. The studies focus on a laser-based manipulation of ultracold bosonic quantum gases, where pairs of interfering lasers can drive transitions between distinct atomic momentum states, creating a momentum-space lattice. This project will have three primary goals. The first will be to develop the ability to engineer arbitrary lattice structures in one and two dimensions, and to engineer predicted new classes of topological lattice structures, explore phase transitions driven by the interplay of disorder and topology, and probe the complex quantum critical phenomena occurring as topological order is destroyed by disorder. Second, novel phenomena will be explored that occur in lattice structures with engineered flat energy bands, stemming from geometrical frustration, that can play host to emergent phenomena driven by small perturbations and interactions. Third, alternative methods will be explored for constructing synthetic lattices, not based on atomic momentum states but rather on the atoms' internal spin degree of freedom, which may hold added prospects for studying strongly correlated topological systems.