2020
DOI: 10.1103/physrevresearch.2.033368
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Dark solitons revealed in Lieb-Liniger eigenstates

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… Show more

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Cited by 11 publications
(9 citation statements)
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“…In particular, an ansatz on how to assign the Gaussian weights to the yrast states was proposed [15]. The matrix elements of the bosonic field operator of the Lieb-Liniger model are characterized by grey solitons [11], and double elliptic dark solitons are derived in association with the quantum measurement process [16]. Here, we note that solutions of the NS equation in the periodic system are expressed in terms of Jacobi's elliptic functions.…”
Section: Introductionmentioning
confidence: 99%
“…In particular, an ansatz on how to assign the Gaussian weights to the yrast states was proposed [15]. The matrix elements of the bosonic field operator of the Lieb-Liniger model are characterized by grey solitons [11], and double elliptic dark solitons are derived in association with the quantum measurement process [16]. Here, we note that solutions of the NS equation in the periodic system are expressed in terms of Jacobi's elliptic functions.…”
Section: Introductionmentioning
confidence: 99%
“…Here, following the reasoning presented in Ref. [14], we find candidates for solitons in LLGPE numerically for any interaction strength, as the minimal energy states constraint to a π jump of phase at the origin. We tested numerically that these states do not move and do preserve their shape in dynamics, as the solitons should do (cf.…”
Section: Comparison Between Solitons Of Gpe and Llgpementioning
confidence: 75%
“…These two different viewpoints were recently unified in Ref. [14]. The agreement holds, however, for weak interactions only, where the GPE is reliable.…”
Section: Comparison Between Solitons and The Type-ii Excitationsmentioning
confidence: 89%
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