Synthetic Topological Matter

Workshop Report

Topological phases of matter have been a focus of much theoretical and experimental attention in recent years. In the usual condensed matter setting, physical realizations of such phases are often constrained by the existence or availability of materials with the desired band structure or desired interactions. While much progress has been made in finding and fabricating new materials and combining them to achieve the desired physics, a new, alternative approach has also recently emerged: namely, to use other systems to mimic the sought-after topological properties. Those include cold-atom systems, where internal degrees of freedom can be manipulated to create synthetic dimensions and synthetic gauge fields, driven Floquet systems, with a multi-frequency space also providing the notion of an extra dimension, multi-terminal Josephson junctions, where superconducting phases can be used to mimic the Brillouin zone of a topological materials, and many others. In addition, topological phenomena have been discovered in classical systems including coupled mechanical oscillators, judiciously constructed electric circuits, and even in water waves.

The one-week workshop “Synthetic Topological Matter” gathered a broad range of researchers seeking to expand the reach of topological physics beyond intrinsic material properties to a variety of such new systems. Participants from many leading institutions across the globe have given presentations on their research during the workshop. In addition, Dr. Sebastian Huber (ETH) presented a colloquium on mechanical topological systems. Underscoring the vibrant nature of the field, a significant fraction of the speakers were junior faculty or postdocs. Furthermore, junior participants, including a number of graduate students, presented posters on their work in two well-attended poster sessions.

The workshop has brought together experimentalists and theorists working on very different systems, which realize emergent topological properties. While similar sets of underlying principles are at play in these widely different systems, one of the important goals of the workshop was to stimulate exchanges between separate fields – in particular, between the condensed matter, cold atom, and quantum optics communities, broadly defined. After all, different systems allow for different probes to be used, and while addressing some questions may be difficult or even impossible in some settings, it might be quite feasible in others. Furthermore, understanding how topological phenomena could be “engineered” and probed in a wide variety of systems such as photonic systems, mechanical systems, as well as systems of excitons and cold atoms significantly enhances the range of interesting phenomena one can attempt to observe in this rich variety of settings. Specifically, several talks addressed the utility of driven, optical, and superconductor-based systems for exploring thermalization and many-body localization. The workshop has allowed many researchers seeking to implement topological control in such a rich variety of systems to exchange ideas across and beyond their respective subfields, further stimulating research in this active field.

The young average age of the participants, the large number of prominent researchers that accepted our invitations, the breadth of the topics presented, as well as an excellent support infrastructure provided by the Max Planck Institute have contributed to a successful workshop.