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

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.