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

Non-integrable dynamics of matter-wave solitons in a density-dependent gauge theory

RJ Dingwall, M. J. Edmonds, JL Helm, BA Malomed, P Öhberg

Published Apr 1, 2018• 0 citations
Publisher

Abstract

We study interactions between bright matter-wave solitons which acquire chiral transport dynamics due to an optically-induced density-dependent gauge potential. Through numerical simulations, we find that the collision dynamics feature several non-integrable phenomena, from inelastic collisions including population transfer and radiation losses to the formation of short-lived bound states and soliton fission. An effective quasi-particle model for the interaction between the solitons is derived by means of a variational approximation, which demonstrates that the inelastic nature of the collision arises from a coupling of the gauge field to velocities of the solitons. In addition, we derive a set of interaction potentials which show that the influence of the gauge field appears as a short-range potential, that can give rise to both attractive and repulsive interactions.

DOI
10.25405/ncl.34353822

Related papers

Non-integrable dynamics of matter-wave solitons in a density-dependent gauge theory

Robert James Dingwall, Matthew Edmonds, J. L. Helm +2 more

We study interactions between bright matter-wave solitons which acquire chiral transport dynamics due to an optically-induced density-dependent gauge potential. Through numerical simulations, we find that the collision dynamics feature several non-integrable phenomena, from inelastic collisions including population transfer and radiation losses to the formation of short-lived bound states and soliton fission. An effective quasi-particle model for the interaction between the solitons is derived by means of a variational approximation, which demonstrates that the inelastic nature of the collision arises from a coupling of the gauge field to velocities of the solitons. In addition, we derive a set of interaction potentials which show that the influence of the gauge field appears as a short-range potential, that can give rise to both attractive and repulsive interactions.

arXiv:1709.08037•New Journal of Physics•Feb 27, 2018•38 citations

Interaction of chiral solitons in a Bose-Einstein Condensate under density-dependent gauge potential

Rui Gao, Xin Qiao, Yun-E Ma +3 more

Abstract The collision between two chiral solitons in a Bose-Einstein Condensate (BEC) under density-dependent gauge potential is studied. By means of Poincaré-Lighthill-Kuo (PLK) perturbation method, the different kinds of colliding chiral soliton pairs self-consistently excited upon the background of the system are obtained analytically. The coupling of the current nonlinearity induced by the gauge potential and mean-field atomic interaction results in rich collision dynamics of chiral soliton pairs. When the atomic interaction is repulsive, head-on collisions of dark-dark and dark-bright solitons are observed. However, when the atomic interaction is attractive, unidirectional chiral dark soliton pairs are excited, and overtaking collision between two chiral dark solitons takes place. The phase shifts following the collision of soliton pairs are derived analytically and confirmed numerically. Interestingly, due to the contribution of the density-dependent gauge potential, the phase shifts of the two interacting chiral solitons are different from each other. This is distinct from the case without the density-dependent gauge potential, where the phase shifts of the two colliding ordinary solitons are the same. Thus, phase shifts of interacting chiral soliton pairs can be used to identify the chiral properties of solitons in BEC under density-dependent gauge potential. Furthermore, both elastic and inelastic collisions of chiral solitons in the system are presented numerically. The phase diagram for occurrence of elastic and inelastic collisions of chiral soliton is obtained, which strongly depends on the strength of density-dependent gauge potential.

Europhysics Letters (EPL)•Feb 27, 2023•5 citations

Stability of matter-wave solitons in a density-dependent gauge theory

Robert James Dingwall, Patrik Öhberg

We consider the linear stability of chiral matter-wave solitons described by a density-dependent gauge theory. By studying the associated Bogoliubov--de Gennes equations both numerically and analytically, we find that the stability problem effectively reduces to that of the standard Gross-Pitaevskii equation, proving that the solitons are stable to linear perturbations. In addition, we formulate the stability problem in the framework of the Vakhitov-Kolokolov criterion and provide supplementary numerical simulations which illustrate the absence of instabilities when the soliton is initially perturbed. These results justify the production of chiral solitons in ultracold experiments and their potential application for practical transport dynamics in interferometry and atomtronics.

arXiv:1809.11154•Physical Review A•Feb 7, 2019•26 citations

Simulating an Interacting Gauge Theory with Ultracold Bose Gases

Matthew Edmonds, Manuel Valiente, Gediminas Juzeliūnas +2 more

We show how density dependent gauge potentials can be induced in dilute gases of ultracold atoms using light-matter interactions. We study the effect of the resulting interacting gauge theory and show how it gives rise to novel topological states in the ultracold gas. We find in particular that the onset of persistent currents in a ring geometry is governed by a critical number of particles. The density-dependent gauge potential is also found to support chiral solitons in a quasi-one-dimensional ultracold Bose gas.

arXiv:1212.0445•Physical Review Letters•Feb 19, 2013•100 citations

Soliton collisions in Bose-Einstein condensates with current-dependent interactions

Qian Jia, Haibo Qiu, Antonio Muñoz Mateo

We study general collisions between chiral solitons in Bose-Einstein condensates subject to combined attractive and current-dependent interatomic interactions. A simple analysis based on the linear superposition of the solitons allows us to determine the relevant time and space scales of the dynamics, which is illustrated by extensive numerical simulations. By varying the differential amplitude, the relative phase, the average velocity, and the relative velocity of the solitons, we characterize the different dynamical regimes that give rise to oscillatory and interference phenomena. Apart from the known inelastic character of the collisions, we show that the chiral dynamics involves an amplitude reduction with respect to the case of regular solitons. To compare these results with feasible ultracold-gas experiments, the influence of harmonic confinement is analyzed in both the emergence and the interaction of chiral solitons.

arXiv:2208.09972•Physical Review A•Dec 19, 2022•9 citations

Dynamical evolutions of matter-wave bright solitons in an inverted parabolic potential

Guishu Chong, Wenhua Hai

A family of analytical solutions to a quasi one-dimensional time-dependent Gross–Pitaevskii equation with inverted parabolic potentials and time-varying nonlinear two-body interactions are presented, which simulate the dynamical evolutions of nonlinear matter-wave bright solitons. Synchronous behaviour between the variations of nonlinear interaction and compression or expansion of the solitons is demonstrated. For the case of higher order solitons, collision features are investigated. For travelling two solitons, different kinds of collisions are discussed for π and 0 phase difference between the two solitons at the collision point. Furthermore, a moving two-soliton 'bound' state is demonstrated. During the propagation, the solitons oscillate and collide many times.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 20, 2006•14 citations
We study interactions between bright matter-wave solitons which acquire chiral transport dynamics due to an optically-induced density-dependent gauge potential. Through numerical simulations, we find that the collision dynamics feature several non-integrable phenomena, from inelastic collisions including population transfer and radiation losses to the formation of short-lived bound states and soliton fission. An effective quasi-particle model for the interaction between the solitons is derived by means of a variational approximation, which demonstrates that the inelastic nature of the collision arises from a coupling of the gauge field to velocities of the solitons. In addition, we derive a set of interaction potentials which show that the influence of the gauge field appears as a short-range potential, that can give rise to both attractive and repulsive interactions.
We study interactions between bright matter-wave solitons which acquire chiral transport dynamics due to an optically-induced density-dependent gauge potential. Through numerical simulations, we find that the collision dynamics feature several non-integrable phenomena, from inelastic collisions including population transfer and radiation losses to the formation of short-lived bound states and soliton fission. An effective quasi-particle model for the interaction between the solitons is derived by means of a variational approximation, which demonstrates that the inelastic nature of the collision arises from a coupling of the gauge field to velocities of the solitons. In addition, we derive a set of interaction potentials which show that the influence of the gauge field appears as a short-range potential, that can give rise to both attractive and repulsive interactions.
Abstract The collision between two chiral solitons in a Bose-Einstein Condensate (BEC) under density-dependent gauge potential is studied. By means of Poincaré-Lighthill-Kuo (PLK) perturbation method, the different kinds of colliding chiral soliton pairs self-consistently excited upon the background of the system are obtained analytically. The coupling of the current nonlinearity induced by the gauge potential and mean-field atomic interaction results in rich collision dynamics of chiral soliton pairs. When the atomic interaction is repulsive, head-on collisions of dark-dark and dark-bright solitons are observed. However, when the atomic interaction is attractive, unidirectional chiral dark soliton pairs are excited, and overtaking collision between two chiral dark solitons takes place. The phase shifts following the collision of soliton pairs are derived analytically and confirmed numerically. Interestingly, due to the contribution of the density-dependent gauge potential, the phase shifts of the two interacting chiral solitons are different from each other. This is distinct from the case without the density-dependent gauge potential, where the phase shifts of the two colliding ordinary solitons are the same. Thus, phase shifts of interacting chiral soliton pairs can be used to identify the chiral properties of solitons in BEC under density-dependent gauge potential. Furthermore, both elastic and inelastic collisions of chiral solitons in the system are presented numerically. The phase diagram for occurrence of elastic and inelastic collisions of chiral soliton is obtained, which strongly depends on the strength of density-dependent gauge potential.
We consider the linear stability of chiral matter-wave solitons described by a density-dependent gauge theory. By studying the associated Bogoliubov--de Gennes equations both numerically and analytically, we find that the stability problem effectively reduces to that of the standard Gross-Pitaevskii equation, proving that the solitons are stable to linear perturbations. In addition, we formulate the stability problem in the framework of the Vakhitov-Kolokolov criterion and provide supplementary numerical simulations which illustrate the absence of instabilities when the soliton is initially perturbed. These results justify the production of chiral solitons in ultracold experiments and their potential application for practical transport dynamics in interferometry and atomtronics.
We show how density dependent gauge potentials can be induced in dilute gases of ultracold atoms using light-matter interactions. We study the effect of the resulting interacting gauge theory and show how it gives rise to novel topological states in the ultracold gas. We find in particular that the onset of persistent currents in a ring geometry is governed by a critical number of particles. The density-dependent gauge potential is also found to support chiral solitons in a quasi-one-dimensional ultracold Bose gas.
We study general collisions between chiral solitons in Bose-Einstein condensates subject to combined attractive and current-dependent interatomic interactions. A simple analysis based on the linear superposition of the solitons allows us to determine the relevant time and space scales of the dynamics, which is illustrated by extensive numerical simulations. By varying the differential amplitude, the relative phase, the average velocity, and the relative velocity of the solitons, we characterize the different dynamical regimes that give rise to oscillatory and interference phenomena. Apart from the known inelastic character of the collisions, we show that the chiral dynamics involves an amplitude reduction with respect to the case of regular solitons. To compare these results with feasible ultracold-gas experiments, the influence of harmonic confinement is analyzed in both the emergence and the interaction of chiral solitons.
A family of analytical solutions to a quasi one-dimensional time-dependent Gross–Pitaevskii equation with inverted parabolic potentials and time-varying nonlinear two-body interactions are presented, which simulate the dynamical evolutions of nonlinear matter-wave bright solitons. Synchronous behaviour between the variations of nonlinear interaction and compression or expansion of the solitons is demonstrated. For the case of higher order solitons, collision features are investigated. For travelling two solitons, different kinds of collisions are discussed for π and 0 phase difference between the two solitons at the collision point. Furthermore, a moving two-soliton 'bound' state is demonstrated. During the propagation, the solitons oscillate and collide many times.