Ground-state quantum geometry in superconductor-quantum dot chains

Multiterminal Josephson junctions constitute engineered topological systems in arbitrary synthetic dimensions defined by the superconducting phases. Microwave spectroscopy enables the measurement of the quantum geometric tensor, a fundamental quantity describing both the quantum geometry and the topology of the emergent Andreev bound states in a unified manner. In this work we propose an experimentally feasible and scalable multiterminal setup of N quantum dots connected to N+1 superconducting leads which allows us to deterministically study nontrivial topology in terms of the Chern number of the noninteracting ground state. An important result is that the nontrivial topology in a linear chain appears beyond a threshold value of the nonlocal proximity-induced pairing potential which represents the novel theoretical key ingredient of our proposal. Moreover, we generalize the microwave spectroscopy scheme to the multiband case and show that the elements of the quantum geometric tensor of the noninteracting ground state can be experimentally accessed from the measurable oscillator strengths at low temperature.