From Non-Hermitian Linear Response to Dynamical Correlations and Fluctuation-Dissipation Relations in Quantum Many-Body Systems

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 anti-commutators poses a formidable experimental challenge. Here, we propose a general technique for measuring unequal-time anti-commutators 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.

15+18 pages, 5+6 figures. Version as published in PRX Quantum. Main changes: emphasize benefits of non-Hermitian linear response protocols and their proposed realizations through additional numerical benchmarks, expand discussion of cross connections to related concepts, include numerical analysis of finite-size effects and distance dependence of off-site FDRs

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