• Open Access

Dark solitons revealed in Lieb-Liniger eigenstates

Weronika Golletz, Wojciech Górecki, Rafał Ołdziejewski, and Krzysztof Pawłowski
Phys. Rev. Research 2, 033368 – Published 8 September 2020

Abstract

We study how dark solitons, i.e., solutions of one-dimensional, single-particle, nonlinear, time-dependent Schrödinger equation, emerge from eigenstates of a linear many-body model of contact-interacting bosons moving on a ring, the Lieb-Liniger model. This long-standing problem has been addressed by various groups, which presented different, seemingly unrelated, procedures to reveal the solitonic waves directly from the many-body model. Here, we propose a unification of these results using a simple ansatz for the many-body eigenstate of the Lieb-Liniger model, which gives us access to systems of hundreds of atoms. In this approach, mean-field solitons emerge in a single-particle density through repeated measurements of particle positions in the ansatz state. The postmeasurement state turns out to be a wave packet of yrast states of the reduced system.

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  • Received 28 May 2019
  • Revised 17 June 2020
  • Accepted 6 August 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.033368

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)

Nonlinear DynamicsAtomic, Molecular & Optical

Authors & Affiliations

Weronika Golletz1,2,3, Wojciech Górecki1,4, Rafał Ołdziejewski1,5,6, and Krzysztof Pawłowski1

  • 1Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
  • 2Instytut Fizyki Teoretycznej, Uniwersytet Jagielloński, ulica Profesora Stanisława Łojasiewicza 11, PL-30-348 Kraków, Poland
  • 3Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
  • 4Faculty of Physics, University of Warsaw, ulica Pasteura 5, 02-093 Warsaw, Poland
  • 5Max Planck Institute of Quantum Optics, 85748 Garching, Germany
  • 6Munich Center for Quantum Science and Technology, Schellingstrasse 4, 80799 Munich, Germany

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Issue

Vol. 2, Iss. 3 — September - November 2020

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