Probing localization and quantum geometry by spectroscopy

Abstract

The spatial localization of quantum states plays a central role in condensed-matter phenomena, ranging from many-body localization to topological matter. Building on the dissipation-fluctuation theorem, we propose that the localization properties of a quantum-engineered system can be probed by spectroscopy, namely, by measuring its excitation rate upon a periodic drive. We apply this method to various examples that are of direct experimental relevance in ultracold atomic gases, including Anderson localization, topological edge modes, and interacting particles in a harmonic trap. Moreover, inspired by a relation between quantum fluctuations and the quantum metric, we describe how our scheme can be generalized in view of extracting the full quantum-geometric tensor of many-body systems. Our approach opens an avenue for probing localization, as well as quantum fluctuations, geometry and entanglement, in synthetic quantum matter.

7 + 2 pages, 4 figures. Published version

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• Many body localization and thermalization in quantum statistical mechanics
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Spectral signatures of many-body localization with interacting photons
• Imaging the Mott Insulator Shells using Atomic Clock Shifts
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