From non-Hermitian linear response to dynamical correlations and fluctuation–dissipation relations in quantum many-body systems

(Non-)Hermitian linear response protocol for extracting fluctuation–dissipation relations

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.

Publication
arXiv:2104.03983 [cond-mat.quant-gas]
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Kevin T. Geier
PhD Student

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