CAREER: New Synthetic Approaches to Engineering Topology: from Quantum Many-Body Rydberg Atom Arrays to Classical Mechanical Networks

Transport (moving something from one position to another) is central to describing many important phenomena in the physical sciences. In physics, there remain open challenges to understanding how physical quantities like charge, heat, and even information evolve and undergo transport in systems of many interacting particles, especially when quantum effects are taken into account. Recently, new approaches to the study of transport in quantum systems have emerged based on the concepts of 'synthetic dimensions' and 'synthetic lattices,' in which our normal picture of transport in real space is abstracted to the transport of population in a space spanned by the internal states of small quantum systems such as individual atoms or molecules. For example, population can 'move' between the electronic states of an atom (like hydrogen) through the absorption of light from an incident laser field. In this way, a collection of atoms, which is well-understood and highly controllable with lasers or other electromagnetic fields, can be used to 'simulate' a more complex condensed matter system, and lead to advances in our understanding of the complex system. The experimental effort in the current project will extend this type of approach to the study of transport to a new regime of strong inter-particle interactions. The team will conduct experiments based on samples of atoms that can be individually controlled and detected at the microscopic level. Microwave electromagnetic fields will be used to precisely control the transport of population between states of the atoms, allowing for new kinds of explorations into transport phenomena. Additionally, the team will lead an effort to broaden the scope and impact of undergraduate research opportunities, with a primary emphasis on increasing the participation of members from underrepresented groups. This effort will focus on building a new, undergraduate student-led research project on networks of mechanical oscillators that are coupled by 'synthetic,' or engineered and indirect, forces. This effort will incorporate undergraduates from diverse backgrounds in cutting-edge research related to new kinds of transport phenomena, and will use these human-scale experiments to generate visualization video content that will be utilized for outreach and instruction.

This project builds on previous work designing synthetic lattices in neutral atoms and photons, extending these ideas to a new platform for the exploration of many-body transport phenomena based on the internal degrees of freedom of ultracold Rydberg atoms. By considering the problem of quantum transport taking place in an internal state space (driven by coherent microwave transitions and strong dipole-dipole interactions) rather than real space, this approach leverages the ability to manipulate internal degrees of freedom with spectroscopic control. This spectroscopic control allows for the precise engineering of synthetic lattices with nontrivial band topology, kinetic frustration, and tunable disorder. Resonant dipole-dipole interactions between Rydberg atoms will lead to new phenomena with relevance to the interplay of topology and strong interactions, to the study of relaxation and thermalization in isolated interacting disordered systems, and perhaps to the emergence of entirely new forms of many-body phenomena. The research team will explore the ability to engineer novel synthetic lattice models in the internal state space of Rydberg atoms, and will explore how resonant dipole-dipole interactions lead to new many-body phenomena in these synthetic lattices. An additional effort related to broadening the scope and impact of undergraduate research will lead a project to create topological lattice models based on synthetically-coupled oscillator networks. This research effort will enable new functionality of engineered mechanical networks, including new capabilities for designing non-reciprocity, artificial gauge fields, disorder, and strong nonlinearities. The undergraduate led research team will use these newly developed methods to study transport phenomena in new classes of mechanical oscillator networks.

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.