Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations
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 r...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2020-12-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.043315 |
| _version_ | 1797211109687558144 |
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| author | Alexander Schuckert Michael Knap |
| author_facet | Alexander Schuckert Michael Knap |
| author_sort | Alexander Schuckert |
| collection | DOAJ |
| description | 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 two-dimensional (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 nonthermal 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. |
| first_indexed | 2024-04-24T10:21:16Z |
| format | Article |
| id | doaj.art-209350c3ca444a92a77b4ce8e297cb30 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:21:16Z |
| publishDate | 2020-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-209350c3ca444a92a77b4ce8e297cb302024-04-12T17:04:42ZengAmerican Physical SocietyPhysical Review Research2643-15642020-12-012404331510.1103/PhysRevResearch.2.043315Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relationsAlexander SchuckertMichael KnapThe 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 two-dimensional (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 nonthermal 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.http://doi.org/10.1103/PhysRevResearch.2.043315 |
| spellingShingle | Alexander Schuckert Michael Knap Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations Physical Review Research |
| title | Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations |
| title_full | Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations |
| title_fullStr | Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations |
| title_full_unstemmed | Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations |
| title_short | Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations |
| title_sort | probing eigenstate thermalization in quantum simulators via fluctuation dissipation relations |
| url | http://doi.org/10.1103/PhysRevResearch.2.043315 |
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