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Decay and recurrence of non-Gaussian correlations in a quantum many-body system


Gaussian models provide an excellent effective description of many quantum many-body systems ranging from condensed-matter systems1,2 all the way to neutron stars3. Gaussian states are common at equilibrium when the interactions are weak. Recently it was proposed that they can also emerge dynamically from a non-Gaussian initial state evolving under non-interacting dynamics4,5,6,7,8,9,10,11. Here we present the experimental observation of such a dynamical emergence of Gaussian correlations in a quantum many-body system. This non-equilibrium evolution is triggered by abruptly switching off the effective interaction between the observed collective degrees of freedom, while leaving the interactions between the microscopic constituents unchanged. Starting from highly non-Gaussian correlations, consistent with the sine–Gordon model12, we observe a Gaussian state emerging over time as revealed by the decay of the fourth- and sixth-order connected correlations in the quantum field. A description of this dynamics requires a novel mechanism for the emergence of Gaussian correlations, which is relevant for a wide class of quantum many-body systems. In our closed system with non-interacting effective degrees of freedom, we do not expect full thermalization13,14,15,16,17,18,19. This memory of the initial state is confirmed by observing recurrences20 of non-Gaussian correlations.

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Fig. 1: Schematic of the experimental procedure.
Fig. 2: Time evolution of the relative size of the fourth-order connected correlation functions.
Fig. 3: Recurrence of the non-Gaussian phase fluctuations.

Data availability

Source data are provided with this paper. The experimental raw data (absorption images) for Figs. 2 and 3 can be found in ref. 42. All other data are available from the corresponding author upon reasonable request.


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We thank I. Mazets, S. Erne, T. Gasenzer, J. Berges and T. Langen for helpful discussions. This work is supported by the DFG/FWF Collaborative Research Centre ‘SFB 1225 (ISOQUANT)’, and the ESQ Discovery Grant ‘Emergence of physical laws: from mathematical foundations to applications in many body physics’ of the Austrian Academy of Sciences (ÖAW). F.C., F.S.M., B.R., J. Sabino and T.S. acknowledge support by the Austrian Science Fund (FWF) in the framework of the Doctoral School on Complex Quantum Systems (CoQuS). S.S. acknowledges support by the Slovenian Research Agency (ARRS) under grant QTE (N1-0109) and by the ERC Advanced Grant OMNES (694544). S.-C.J. acknowledges support by an Erwin Schrödinger Quantum Science & Technology (ESQ) Fellowship funded through the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant 801110. J. Sabino acknowledges support by the Fundação para a Ciência e a Tecnologia (PD/BD/128641/2017). J.E. acknowledges funding from the DFG (FOR 2724, EI 519/9-1, EI 519/7-1, CRC 183), the FQXi and the European Union’s Horizon 2020 research and innovation programme under grant 817482 (PASQuanS). J.E., M.G., J. Schmiedmayer and S.S. thank the Erwin Schrödinger Institute for its hospitality and support under the programme ‘Quantum Simulation—from Theory to Application’ (LCW 2019).

Author information

Authors and Affiliations



T.S. performed the experiment and data analysis with contributions by M.T., B.R., F.C., S.-C.J., F.S.M. and J. Sabino. T.S. did the theory calculations with contributions by M.G. and S.S. J. Schmiedmayer and J.E. provided scientific guidance in experimental and theoretical questions. J. Schmiedmayer conceived the experiment. All authors contributed to the interpretation of the data and to the writing of the manuscript.

Corresponding authors

Correspondence to Thomas Schweigler or Jörg Schmiedmayer.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Additional results for the time evolution of the relative size of the fourth-order connected correlation functions.

As for Fig. 2 (see there for the meaning of the plotted quantities and error bars), but for several different initial phase-locking strengths (quantified by \({\langle \cos (\varphi )\rangle }_{{\rm{init}}}\)) and different trapping geometries. The results for a \({\langle \cos (\varphi )\rangle }_{{\rm{init}}}\) of 0.81 and 0.88 have been obtained with a harmonic confinement. For all other results, a 75 μm long box trap has been superimposed onto the harmonic confinement (Methods). We find that Gaussian correlations emerge dynamically for all measurements, independent of the initial phase-locking strength or the trapping geometry. The speed for the decay of M(4) increases with the initial phase-locking in agreement with our theoretical model. One can understand the trend by realizing that the phase-fluctuations of the initial state get smaller with increasing phase-locking and are therefore more quickly overshadowed by the mixed-in initial density fluctuations.

Source data

Supplementary information

Supplementary Information

Supplementary Figs. 1–5, discussion of the experimental results and theoretical model.

Source data

Source Data Fig. 2

Numerical values of the plotted quantities.

Source Data Fig. 3

Numerical values of the plotted quantities.

Source Data Extended Data Fig. 1

Numerical values of the plotted quantities.

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Schweigler, T., Gluza, M., Tajik, M. et al. Decay and recurrence of non-Gaussian correlations in a quantum many-body system. Nat. Phys. 17, 559–563 (2021).

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