Spectral signatures of non-trivial topology in a superconducting circuit

Topology, like symmetry, is a fundamental concept in understanding general properties of physical systems. In condensed matter systems, non-trivial topology may manifest itself as singular features in the energy spectrum or the quantization of observable quantities such as electrical conductance and magnetic flux. Using microwave spectroscopy, we show that a superconducting circuit with three Josephson tunnel junctions in parallel can possess energy degeneracies indicative of \emph{intrinsic} non-trivial topology. We identify three topological invariants, one of which is related to a hidden quantum mechanical supersymmetry. Depending on fabrication parameters, devices are gapless or not, and fall on a simple phase diagram which is shown to be robust to perturbations including junction imperfections, asymmetry, and inductance. Josephson tunnel junction circuits, which are readily fabricated with conventional microlithography techniques, allow access to a wide range of topological systems which have no condensed matter analog. Notable spectral features of these circuits, such as degeneracies and flat bands, may be leveraged for quantum information applications, whereas quantized transport properties could be useful for metrology applications.