Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations

摘要: The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. So far, however, experimental studies have focused on relaxation dynamics observables as described by diagonal part ETH, whose verification requires substantial numerical input. This leaves many general assumptions ETH untested. Here, we propose theory-independent route probe full in simulators observing emergence fluctuation-dissipation relations, which directly off-diagonal ETH. We discuss and protocols independently measure fluctuations dissipations well higher-order time ordered correlation functions. first show how fluctuation dissipation relations from nonequilibrium initial state can be observed 2D Bose-Hubbard model superconducting qubits or gas microscopes. Then focus long-range transverse field Ising (LTFI), realized with trapped ions. LTFI exhibits rich phenomena: For strong fields, observe prethermalization an effective magnetization-conserving Hamiltonian relations. weak confined excitations lead non-thermal features resulting violation up long times. Moreover, integrable region LTFI, generalized Gibbs ensemble occurs enable diagonalization Hamiltonian. Our work presents way characterize paves simulate condensed matter pump-probe experiments.