Dark solitons revealed in Lieb-Liniger eigenstates
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 b...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2020-09-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.033368 |
| _version_ | 1797211265886584832 |
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| author | Weronika Golletz Wojciech Górecki Rafał Ołdziejewski Krzysztof Pawłowski |
| author_facet | Weronika Golletz Wojciech Górecki Rafał Ołdziejewski Krzysztof Pawłowski |
| author_sort | Weronika Golletz |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T10:23:45Z |
| format | Article |
| id | doaj.art-610f1463098d426eb73867fbc1d35288 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:23:45Z |
| publishDate | 2020-09-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-610f1463098d426eb73867fbc1d352882024-04-12T17:00:07ZengAmerican Physical SocietyPhysical Review Research2643-15642020-09-012303336810.1103/PhysRevResearch.2.033368Dark solitons revealed in Lieb-Liniger eigenstatesWeronika GolletzWojciech GóreckiRafał OłdziejewskiKrzysztof PawłowskiWe 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.http://doi.org/10.1103/PhysRevResearch.2.033368 |
| spellingShingle | Weronika Golletz Wojciech Górecki Rafał Ołdziejewski Krzysztof Pawłowski Dark solitons revealed in Lieb-Liniger eigenstates Physical Review Research |
| title | Dark solitons revealed in Lieb-Liniger eigenstates |
| title_full | Dark solitons revealed in Lieb-Liniger eigenstates |
| title_fullStr | Dark solitons revealed in Lieb-Liniger eigenstates |
| title_full_unstemmed | Dark solitons revealed in Lieb-Liniger eigenstates |
| title_short | Dark solitons revealed in Lieb-Liniger eigenstates |
| title_sort | dark solitons revealed in lieb liniger eigenstates |
| url | http://doi.org/10.1103/PhysRevResearch.2.033368 |
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