Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0506020 · Physical Review Letters

Propagation of a Dark Soliton in a Disordered Bose-Einstein Condensate

Nicolas Bilas, Nicolas Pavloff

Published Sep 23, 2005• 30 citations
arXivHTMLPDF

Abstract

We consider the propagation of a dark soliton in a quasi-1D Bose-Einstein condensate in presence of a random potential. This configuration involves nonlinear effects and disorder, and we argue that, contrarily to the study of stationary transmission coefficients through a nonlinear disordered slab, it is a well-defined problem. It is found that a dark soliton decays algebraically, over a characteristic length which is independent of its initial velocity, and much larger than both the healing length and the 1D scattering length of the system. We also determine the characteristic decay time.

DOI
10.1103/physrevlett.95.130403

Related papers

Propagation of matter-wave solitons in periodic and random nonlinear potentials

F. Kh. Abdullaev, Josselin C. Garnier

We study the motion of bright matter-wave solitons in nonlinear potentials, produced by periodic or random spatial variations of the atomic scattering length. We obtain analytical results for the soliton motion, the radiation of matter wave, and the radiative soliton decay in such configurations of the Bose-Einstein condensate. The stable regimes of propagation are analyzed. The results are in remarkable agreement with the numerical simulations of the Gross-Pitaevskii equation with periodic or random spatial variations of the mean field interactions.

arXiv:cond-mat/0511264•Physical Review A•Dec 30, 2005•105 citations

Dark soliton in a disorder potential

Małgorzata Mochol-Grzelak, Marcin Płodzień, Krzysztof Sacha

We consider a dark soliton in a Bose-Einstein condensate in the presence of a weak disorder potential. Deformation of the soliton shape is analyzed within the Bogoliubov approach and by employing an expansion in eigenstates of the P\"oschl-Teller Hamiltonian. Comparison of the results with the numerical simulations indicates that the linear response analysis reveals a good agreement even if the strength of disorder is of the order of the chemical potential of the system. In the second part of the paper we concentrate on the quantum nature of the dark soliton and demonstrate that the soliton may reveal Anderson localization in the presence of disorder. The Anderson-localized soliton may decay due to quasiparticle excitations induced by the disorder. However, we show that the corresponding lifetime is much longer than the condensate lifetime in a typical experiment.

arXiv:1111.5248•Physical Review A•Feb 21, 2012•13 citations

Soliton Solutions in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential

张解放, 杨琴

We present both the bright and dark solitons of Bose-Einstein condensates with a time-dependent atomic scattering length in an expulsive parabolic potential. As a discussed example, we select the experimental parameter, i.e. the Feshbach-managed nonlinear coefficient reading a(t) = go exp(λt), and obtain the results which can be recovered in the literature [Phys. Rev. Lett. 94 (2005) 050402].

Chinese Physics Letters•Jan 1, 2005•0 citations

Stochastic longevity of a dark soliton in a finite-temperature Bose-Einstein condensate

Karen Wright, Ashton S. Bradley

We study the decay of a dark soliton in a homogeneous Bose-Einstein condensate. We give an analytical treatment of a decaying soliton, deriving an expression for the soliton velocity and decay time in the absence of thermal noise. We test the result against numerical simulations of a spatially confined system and find good agreement in the regime of low temperature ($k_BT\ll μ$). Thermal fluctuations are found to slow the escape of the soliton, extending its lifetime beyond the predictions of the noise-free theory; the effect becomes significant at a characteristic temperature $k_BT\sim μ$. This stabilization by noise allows us to infer an analytical lower bound for the dark soliton decay time.

arXiv:1104.2691•Apr 14, 2011•1 citation

Soliton Solutions in Bose–Einstein Condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential

Zhang Jie-Fang, Yang Qin

We present both the bright and dark solitons of Bose–Einstein condensates with a time-dependent atomic scattering length in an expulsive parabolic potential. As a discussed example, we select the experimental parameter, i.e. the Feshbach-managed nonlinear coefficient reading a ( t ) = g 0 exp(λ t ), and obtain the results which can be recovered in the literature [Phys. Rev. Lett. 94 (2005) 050402].

Chinese Physics Letters•Jul 29, 2005•16 citations

Dynamics of dark solitons in quasi-one-dimensional Bose-Einstein condensates

Guoxiang Huang, Jacob Szeftel, Shanhua Zhu

We develop a systematic analytical approach to consider the dynamics of linear and nonlinear excitations in trapped quasi-one-dimensional Bose-Einstein condensates with repulsive atom-atom interactions. We show that, for a condensate strongly confined in two transverse directions, the ground state of the system involves the high-order eigenmodes of the transverse confining potential in the transverse directions and effective high-order Thomas-Fermi wave functions in the axial direction. The linear excitations of the system have a Bogoliubov-type spectrum with the excitation frequency varying slowly along the axial direction. We find that, in a weak nonlinear approximation, the amplitude of a nonlinear excitation is governed by a variable coefficient Korteweg--de Vries equation with additional terms contributed from the transverse structure and the inhomogeneity in the axial direction of the condensate, which results in varying amplitude, width, and velocity for dark solitons. Because of the inhomogeneity the dark solitons undergo deformation and emit radiations when traveling along the axial direction. We finally demonstrate that a dark soliton will disintegrate into several ones plus a residual wave train when passing over a steplike potential.

Physical Review A•Apr 23, 2002•130 citations
We consider the propagation of a dark soliton in a quasi-1D Bose-Einstein condensate in presence of a random potential. This configuration involves nonlinear effects and disorder, and we argue that, contrarily to the study of stationary transmission coefficients through a nonlinear disordered slab, it is a well-defined problem. It is found that a dark soliton decays algebraically, over a characteristic length which is independent of its initial velocity, and much larger than both the healing length and the 1D scattering length of the system. We also determine the characteristic decay time.
We study the motion of bright matter-wave solitons in nonlinear potentials, produced by periodic or random spatial variations of the atomic scattering length. We obtain analytical results for the soliton motion, the radiation of matter wave, and the radiative soliton decay in such configurations of the Bose-Einstein condensate. The stable regimes of propagation are analyzed. The results are in remarkable agreement with the numerical simulations of the Gross-Pitaevskii equation with periodic or random spatial variations of the mean field interactions.
We consider a dark soliton in a Bose-Einstein condensate in the presence of a weak disorder potential. Deformation of the soliton shape is analyzed within the Bogoliubov approach and by employing an expansion in eigenstates of the P\"oschl-Teller Hamiltonian. Comparison of the results with the numerical simulations indicates that the linear response analysis reveals a good agreement even if the strength of disorder is of the order of the chemical potential of the system. In the second part of the paper we concentrate on the quantum nature of the dark soliton and demonstrate that the soliton may reveal Anderson localization in the presence of disorder. The Anderson-localized soliton may decay due to quasiparticle excitations induced by the disorder. However, we show that the corresponding lifetime is much longer than the condensate lifetime in a typical experiment.
We study the decay of a dark soliton in a homogeneous Bose-Einstein condensate. We give an analytical treatment of a decaying soliton, deriving an expression for the soliton velocity and decay time in the absence of thermal noise. We test the result against numerical simulations of a spatially confined system and find good agreement in the regime of low temperature (kBT≪μk_BT\ll μkB​T≪μ). Thermal fluctuations are found to slow the escape of the soliton, extending its lifetime beyond the predictions of the noise-free theory; the effect becomes significant at a characteristic temperature kBT∼μk_BT\sim μkB​T∼μ. This stabilization by noise allows us to infer an analytical lower bound for the dark soliton decay time.
We develop a systematic analytical approach to consider the dynamics of linear and nonlinear excitations in trapped quasi-one-dimensional Bose-Einstein condensates with repulsive atom-atom interactions. We show that, for a condensate strongly confined in two transverse directions, the ground state of the system involves the high-order eigenmodes of the transverse confining potential in the transverse directions and effective high-order Thomas-Fermi wave functions in the axial direction. The linear excitations of the system have a Bogoliubov-type spectrum with the excitation frequency varying slowly along the axial direction. We find that, in a weak nonlinear approximation, the amplitude of a nonlinear excitation is governed by a variable coefficient Korteweg--de Vries equation with additional terms contributed from the transverse structure and the inhomogeneity in the axial direction of the condensate, which results in varying amplitude, width, and velocity for dark solitons. Because of the inhomogeneity the dark solitons undergo deformation and emit radiations when traveling along the axial direction. We finally demonstrate that a dark soliton will disintegrate into several ones plus a residual wave train when passing over a steplike potential.