Ground-state quantum geometry in superconductor-quantum dot chains

Abstract

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 multiterminal setup of N quantum dots connected to N + 1 superconducting leads to study nontrivial topology in terms of the many-body Chern number of the ground state. 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.

Cooper-pair transistor as a minimal topological quantum circuit

“…One alternative concerns metamaterials which simulate the unit cell of a crystal, such as circuit lattice degrees of freedom [37][38][39][40][41][42][43][44] or the tuning parameters in superconducting qubits [45][46][47]. Most pertinent to our work are recently proposed topological transitions in multiterminal Josephson junctions [29][30][31][48][49][50][51][52][53][54][55][56] which give rise to topological phases even when using only trivial materials [57][58][59][60][61][62][63][64][65][66][67][68]. Here, Weyl points are found in the space of superconducting phase differences acting as quasimomenta, and a Chern number can be directly accessed through a quantized transconductance [57].…”