Spectral Signatures of Non-Trivial Topology in a Superconducting Circuit

Abstract: Topology, like symmetry, is a fundamental concept in understanding general properties of physical systems. In condensed matter, nontrivial topology may manifest itself as singular features in the energy spectrum or the quantization of electrical properties such as conductance and magnetic flux. Using microwave spectroscopy, we determine that a superconducting circuit with three Josephson tunnel junctions in parallel can possess degeneracies indicative of \emph{intrinsic} nontrivial topology. We identify three topological invariants, one of which is related to a hidden quantum mechanical supersymmetry. Measurements show that devices fabricated in different topological regimes fall on a simple phase diagram which should be robust to junction imperfections and geometric inductance. Josephson tunnel junction circuits, which are readily fabricated with conventional microlithography techniques, allow access to a wide range of topological systems that may have no condensed matter analog. Notable spectral features of these circuits, such as degeneracies and flat bands, may find use in quantum information, sensing, and metrology.