Quantum dark solitons in the one-dimensional Bose gas

Shamailov, Sophie S.; Brand, Joachim

doi:10.1103/physreva.99.043632

Cited by 29 publications

(72 citation statements)

References 51 publications

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“…The temperature should be chosen low enough to suppress strong thermal fluctuations in the 1D condensates [48]. Quantum fluctuations, which become relevant at low particle number densities, are not expected to destroy the soliton character but may lead to other effects like center-of-mass diffusion [49].…”

Section: Discussionmentioning

confidence: 99%

Nonlinear standing waves in an array of coherently coupled Bose-Einstein condensates

et al. 2018

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Stationary solitary waves are studied in an array of M linearly-coupled one-dimensional Bose-Einstein condensates (BECs) by means of the Gross-Pitaevskii equation. Solitary wave solutions with the character of overlapping dark solitons, Josephson vortex -antivortex arrays, and arrays of half-dark solitons are constructed for M > 2 from known solutions for two coupled BECs. Additional solutions resembling vortex dipoles and rarefaction pulses are found numerically. Stability analysis of the solitary waves reveals that overlapping dark solitons can become unstable and susceptible to decay into arrays of Josephson vortices. The Josephson vortex arrays have mixed stability but for all parameters we find at least one stationary solitary wave configuration that is dynamically stable. The different families of nonlinear standing waves bifurcate from one another. In particular we demonstrate that Josephson-vortex arrays bifurcate from dark soliton solutions at instability thresholds. The stability thresholds for dark soliton and Josephson-vortex type solutions are provided, suggesting the feasibility of realization with optical lattice experiments. arXiv:1806.09974v1 [cond-mat.quant-gas]

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Section: Discussionmentioning

confidence: 99%

Nonlinear standing waves in an array of coherently coupled Bose-Einstein condensates

et al. 2018

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“…The MF regime defined in such a way is very difficult to handle in the frame of many-body analysis, which is usually limited to systems with small number of atoms N. Apart from the few existing semianalytical results [22,24,25], the majority of approaches are devoted to small systems of ≈10-20 atoms [20,21,[33][34][35][36] solved with brute force methods or around ≈100 atoms solved with sophisticated and time-consuming numerics [28,29,37,38]. Our way around these numerical difficulties is to use a natural and simple ansatz for the yrast states in the MF regime.…”

Section: The Lieb-liniger Model and Yrast Statesmentioning

confidence: 99%

“…An opposite direction was taken in Refs. [22][23][24][25] where the dark solitons are constructed as a specific superposition of 033368-5 yrast states. Namely, the MF product state is expressed as…”

Section: Dark Solitons As Superpositions Of Yrast Statesmentioning

confidence: 99%

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Dark solitons revealed in Lieb-Liniger eigenstates

Golletz

Górecki

Ołdziejewski

et al. 2020

Phys. Rev. Research

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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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“…Equation(14) can be derived from defining m P = −md E s /dµ[51,52]. The general relation between m P and N d will be discussed elsewhere[53].…”

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confidence: 99%

Quasiparticles of widely tuneable inertial mass: The dispersion relation of atomic Josephson vortices and related solitary waves

Brand

Shamailov

2018

SciPost Phys.

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Superconducting Josephson vortices have direct analogues in ultracold-atom physics as solitary-wave excitations of two-component superfluid Bose gases with linear coupling. Here we numerically extend the zero-velocity Josephson vortex solutions of the coupled Gross-Pitaevskii equations to non-zero velocities, thus obtaining the full dispersion relation. The inertial mass of the Josephson vortex obtained from the dispersion relation depends on the strength of linear coupling and has a simple pole divergence at a critical value where it changes sign while assuming large absolute values. Additional low-velocity quasiparticles with negative inertial mass emerge at finite momentum that are reminiscent of a dark soliton in one component with counter-flow in the other. In the limit of small linear coupling we compare the Josephson vortex solutions to sine-Gordon solitons and show that the correspondence between them is asymptotic, but significant differences appear at finite values of the coupling constant. Finally, for unequal and non-zero self- and cross-component nonlinearities, we find a new solitary-wave excitation branch. In its presence, both dark solitons and Josephson vortices are dynamically stable while the new excitations are unstable.

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Quantum dark solitons in the one-dimensional Bose gas

Cited by 29 publications

References 51 publications

Nonlinear standing waves in an array of coherently coupled Bose-Einstein condensates

Nonlinear standing waves in an array of coherently coupled Bose-Einstein condensates

Dark solitons revealed in Lieb-Liniger eigenstates

Quasiparticles of widely tuneable inertial mass: The dispersion relation of atomic Josephson vortices and related solitary waves

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