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Mechanisms for the emergence of Gaussian correlations

by Marek Gluza, Thomas Schweigler, Mohammadamin Tajik, João Sabino, Federica Cataldini, Frederik S. Møller, Si-Cong Ji, Bernhard Rauer, Jörg Schmiedmayer, Jens Eisert, Spyros Sotiriadis

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Submission summary

Authors (as registered SciPost users): Marek Gluza · Frederik Skovbo Møller · Jörg Schmiedmayer · Thomas Schweigler · Spyros Sotiriadis · Mohammadamin Tajik
Submission information
Preprint Link:  (pdf)
Date accepted: 2022-03-16
Date submitted: 2022-03-09 08:55
Submitted by: Gluza, Marek
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Experiment
  • Quantum Physics
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Experimental


We comprehensively investigate two distinct mechanisms leading to memory loss of non-Gaussian correlations after switching off the interactions in an isolated quantum system undergoing out-of-equilibrium dynamics. The first mechanism is based on spatial scrambling and results in the emergence of locally Gaussian steady states in large systems evolving over long times. The second mechanism, characterized as `canonical transmutation', is based on the mixing of a pair of canonically conjugate fields, one of which initially exhibits non-Gaussian fluctuations while the other is Gaussian and dominates the dynamics, resulting in the emergence of relative Gaussianity even at finite system sizes and times. We evaluate signatures of the occurrence of the two candidate mechanisms in a recent experiment that has observed Gaussification in an atom-chip controlled ultracold gas and elucidate evidence that it is canonical transmutation rather than spatial scrambling that is responsible for Gaussification in the experiment. Both mechanisms are shown to share the common feature that the Gaussian correlations revealed dynamically by the quench are already present though practically inaccessible at the initial time. On the way, we present novel observations based on the experimental data, demonstrating clustering of equilibrium correlations, analyzing the dynamics of full counting statistics, and utilizing tomographic reconstructions of quantum field states. Our work aims at providing an accessible presentation of the potential of atom-chip experiments to explore fundamental aspects of quantum field theories in quantum simulations.

Published as SciPost Phys. 12, 113 (2022)

Author comments upon resubmission

Dear Editors,

We would like to thank the referee for their feedback, corrections and suggestions for improvement, which we have thoroughly taken into account in the new version. We note that both referees are satisfied with the quality of our work and the significance of our findings. Consequently, they both ultimately recommend publication in SciPost Physics. In the following, we address their questions and comments in detail and explain what we have done to accommodate the concerns raised.

The comments of the first Referee have pushed us to expand on the mechanism of Gaussification by canonical transmutation, specifically to discuss how the discussed effect may come into play in systems other than the phononic excitations of cold atomic gases which we have focused on. We believe that this resulted in significantly more merit in the outlook and conclusions of our work.

In turn, the second Referee provided several very relevant comments. We took them very seriously and were happy to do so because it allowed us to iron out some of the statements that were important to the crux of our work. We feel glad about having had the opportunity to clarify the passages pointed out by the Referee because these should be much clearer now.

With best regards,
The Authors

List of changes

List of changes:
- added a paragraph in conclusions about Gaussification by canonical transmutation in systems other than 1d cold atomic gases
- added a paragraph in conclusions discussing topological excitations in context of Gaussification by canonical transmutation
- clarified sentence about conditions for emergence of statistical mechanics
- rewrote a paragraph clarifying aspects of Gaussification by spatial scrambling in effective field theory
- clarified the passage on the role of correlation functions in experiments on quantum many body systems
- added more information about the role of homogeneity in the experiment
- clarified formula (7) excluding overlapping positions
- clarified description related to the role of initial Gaussian correlations
- described the propagators in eqs (11-12)
- corrected the formatting of the caption on p. 8
- improved description of the temporal ongoing of Gaussification by canonical transmutation
- clarified the description of the meaning of fig 5
- corrected the referral to fig 5 and not 6 below eq (25)
- added reference to the formula (28)

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