Probing eigenstate thermalization in quantum simulators via
fluctuation-dissipation relations
- URL: http://arxiv.org/abs/2007.10347v2
- Date: Sat, 12 Dec 2020 08:25:18 GMT
- Title: Probing eigenstate thermalization in quantum simulators via
fluctuation-dissipation relations
- Authors: Alexander Schuckert, Michael Knap
- Abstract summary: The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems.
Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations.
Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
- Score: 77.34726150561087
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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 the relaxation dynamics of
observables as described by the diagonal part of ETH, whose verification
requires substantial numerical input. This leaves many of the general
assumptions of ETH untested. Here, we propose a theory-independent route to
probe the full ETH in quantum simulators by observing the emergence of
fluctuation-dissipation relations, which directly probe the off-diagonal part
of ETH. We discuss and propose protocols to independently measure fluctuations
and dissipations as well as higher-order time ordered correlation functions. We
first show how the emergence of fluctuation dissipation relations from a
nonequilibrium initial state can be observed for the 2D Bose-Hubbard model in
superconducting qubits or quantum gas microscopes. Then we focus on the
long-range transverse field Ising model (LTFI), which can be realized with
trapped ions. The LTFI exhibits rich thermalization phenomena: For strong
transverse fields, we observe prethermalization to an effective
magnetization-conserving Hamiltonian in the fluctuation dissipation relations.
For weak transverse fields, confined excitations lead to non-thermal features
resulting in a violation of the fluctuation-dissipation relations up to long
times. Moreover, in an integrable region of the LTFI, thermalization to a
generalized Gibbs ensemble occurs and the fluctuation-dissipation relations
enable an experimental diagonalization of the Hamiltonian. Our work presents a
theory-independent way to characterize thermalization in quantum simulators and
paves the way to quantum simulate condensed matter pump-probe experiments.
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