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Quantization effects due to topological invariants such as Chern numbers havebecome very relevant in many systems, yet key quantities such as the quantumgeometric tensor providing local information about quantum states remainexperimentally difficult to access. Recently, it has been shown thatmultiterminal Josephson junctions constitute an ideal platform to synthesizetopological systems in a controlled manner. We theoretically study propertiesof Andreev states in topological Josephson matter and demonstrate that thequantum geometric tensor of Andreev states can be extracted by syntheticallypolarized microwaves. The oscillator strength of the absorption rates providesdirect evidence of topological quantum properties of the Andreev states.

Microwave Spectroscopy Reveals the Quantum Geometric Tensor of Topological Josephson Matter