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Extracting the Field Theory Description of a Quantum Many-Body System from Experimental Data

Torsten V. Zache, Thomas Schweigler, Sebastian Erne, Jörg Schmiedmayer, and Jürgen Berges
Phys. Rev. X 10, 011020 – Published 29 January 2020
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Abstract

Quantum field theory is a powerful tool to describe the relevant physics governing complex quantum many-body systems. Here, we develop a general pathway to extract the irreducible building blocks of quantum field theoretical descriptions and its parameters purely from experimental data. This determination is accomplished by extracting the one-particle irreducible (1PI) correlation functions from which one can construct all physical observables. To match the capabilities of experimental techniques, our approach employs a formulation of quantum field theory based on equal-time correlation functions only. We illustrate the theoretical foundations of our procedure by applying it to the sine-Gordon model in thermal equilibrium and then demonstrate explicitly how to extract these quantities from an experiment where we quantum simulate the sine-Gordon model by two tunnel-coupled superfluids. We extract all 1PI correlation functions up to the 1PI four-point function (interaction vertex) and their variation with momentum, encoding the “running” of the couplings. The measured 1PI correlation functions are compared to the theoretical estimates, verifying our procedure. Our work opens new ways of addressing complex many-body questions emerging in a large variety of settings from fundamental science to practical quantum technology.

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  • Received 5 November 2019

DOI:https://doi.org/10.1103/PhysRevX.10.011020

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & OpticalGeneral PhysicsQuantum Information, Science & TechnologyCondensed Matter, Materials & Applied PhysicsParticles & FieldsStatistical Physics & Thermodynamics

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Constructing Field Theories Using Quantum Simulators

Published 29 January 2020

Quantum simulators can help researchers extract the key parameters of a quantum field theory from experiments.

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Authors & Affiliations

Torsten V. Zache1, Thomas Schweigler2, Sebastian Erne2,3, Jörg Schmiedmayer2, and Jürgen Berges1

  • 1Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
  • 2Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna, Austria
  • 3School of Mathematical Sciences, Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom

Popular Summary

The collective behavior emerging from many interacting particles is relevant for a large variety of phenomena observed in nature. An efficient description of such complex many-body systems is quantum field theory (QFT). The fundamental structures of QFT are based on the irreducible correlations among its constituents. In our work, we demonstrate how to extract these correlations from experimental data, which reveal how macroscopic phenomena emerge from the underlying microscopic details.

Specifically, we employ a formulation of QFT based on observables that are measured at given instants of time. This approach is perfectly suited for quantum simulation experiments, where synthetic quantum systems are typically probed at given measurement times. We show that the extraction of the irreducible correlations gives direct access to the effective interactions of the many-body system. This reveals the dependence of the interactions on the momentum or length scale, a phenomenon known as “running couplings” in the context of high-energy physics. Using both numerical simulations and a proof-of-principle experiment, we verify our procedure for the example of the sine-Gordon model—a model with a wide range of applications from condensed-matter physics to high-energy physics—which is quantum simulated by two tunnel-coupled superfluids.

These results establish a general framework for the analysis of large-scale analog quantum simulators. Extracting the relevant physical information can provide new insights into fundamental questions from high-energy and condensed-matter physics, and in taking quantum phenomena from a fundamental science to a practical technology.

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Vol. 10, Iss. 1 — January - March 2020

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