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.
Highlights
Probing localization and quantum geometry by spectroscopyTomoki Ozawa 1 and Nathan Goldman2 1Interdisciplinary Theoretical and Mathematical Sciences Program, RIKEN, Wako, Saitama 351-0198, Japan 2Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, CP 231, 1050 Brussels, Belgium (Received 11 May 2019; revised manuscript received 11 June 2019; published 15 November 2019)
Localization plays a central role in various branches of quantum physics
The discovery of topological states of matter revealed an interesting interplay between topology and localization: The bulk-boundary correspondence guarantees the existence of robust boundary modes, which are localized at the edge of the material [7,8]
Summary
Tomoki Ozawa 1 and Nathan Goldman2 1Interdisciplinary Theoretical and Mathematical Sciences Program, RIKEN, Wako, Saitama 351-0198, Japan 2Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, CP 231, 1050 Brussels, Belgium (Received 11 May 2019; revised manuscript received 11 June 2019; published 15 November 2019). 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. 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
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