From Non-Hermitian Linear Response to Dynamical Correlations and Fluctuation-Dissipation Relations in Quantum Many-Body Systems
Year: 2022
Authors: Geier K.T.; Hauke P.
Autors Affiliation: INO-CNR BEC Center, Dipartimento di Fisica, Universita di Trento, Povo, 38123, INO-CNR BEC Center and Dipartimento di Fisica, Universita di Trento, Povo 38123, Italy, , , Italy; INO-CNR BEC Center, Dipartimento di Fisica, Universita di Trento, Povo, 38123, INO-CNR BEC Center and Dipartimento di Fisica, Universita di Trento, Povo 38123, Italy, , , Italy; Institute for Theoretical Physics, Ruprecht-Karls-Universitdt Heidelberg, Philosophenweg 16, Heidelberg, 69120, Institute for Theoretical Physics, Ruprecht-Karls-Universitdt Heidelberg, Philosophenweg 16, Heidelberg 69120, Germany, , , Germany; Institute for Theoretical Physics, Ruprecht-Karls-Universitdt Heidelberg, Philosophenweg 16, Heidelberg, 69120, Institute for Theoretical Physics, Ruprecht-Karls-Universitdt Heidelberg, Philosophenweg 16, Heidelberg 69120, Germany, , , Germany; Kirchhoff Institute for Physics, Ruprecht-Karls-Universitdt Heidelberg, Im Neuenheimer Feld 227, Heidelberg, 69120, Kirchhoff Institute for Physics, Ruprecht-Karls-Universitdt Heidelberg, Im Neuenheimer Feld 227, Heidelberg 69120, Germany, , Germany
Abstract: Quantum many-body systems are characterized by their correlations. While equal-time correlators and unequal-time commutators between operators are standard observables, the direct access to unequal-time anticommutators poses a formidable experimental challenge. Here, we propose a general technique for measuring unequal-time anticommutators using the linear response of a system to a non-Hermitian perturbation. We illustrate the protocol at the example of a Bose-Hubbard model, where the approach to thermal equilibrium in a closed quantum system can be tracked by measuring both sides of the fluctuation-dissipation relation. We relate the scheme to the quantum Zeno effect and weak measurements, and illustrate possible implementations at the example of a cold-atom system. Our proposal provides a way of characterizing dynamical correlations in quantum many-body systems with potential applications in understanding strongly correlated matter as well as for novel quantum technologies.
Journal/Review: PRX QUANTUM
Volume: 3 (3) Pages from: 030308-1 to: 030308-34
More Information: We thank J. Berges, M. Garttner, S. Lannig, M. K. Oberthaler, A. Pineiro Orioli, J. Reichstetter, and A. Salzinger for discussions. This project has received funding from the European Research Council (ERC) under the European Union´s Horizon 2020 research and innovation programme (ERC StG StrEnQTh, Grant Agreement No. 804305). We further acknowledge support by Provincia Autonoma di Trento. This work is part of the Collaborative Research Centre ISOQUANT (project ID 273811115) and has been supported by Q@TN, the joint lab between the University of Trento, FBK-Fondazione Bruno Kessler, INFN-National Institute for Nuclear Physics, and CNR-National Research Council. The authors acknowledge support by the state of Baden-Wurttemberg through bwHPC.KeyWords: statistical-mechanics; thermalization; entanglement; chaos; atomsDOI: 10.1103/PRXQuantum.3.030308