Dark solitons in atomic Bose-Einstein condensates: from theory to experiments

Abstract

This review paper presents an overview of the theoretical and experimental progress on the study of matter-wave dark solitons in atomic Bose-Einstein condensates. Upon introducing the general framework, we discuss the statics and dynamics of single and multiple matter-wave dark solitons in the quasi one-dimensional setting, in higher-dimensional settings, as well as in the dimensionality crossover regime. Special attention is paid to the connection between theoretical results, obtained by various analytical approaches, and relevant experimental observations.

82 pages, 13 figures. To appear in J. Phys. A: Math. Theor.

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• Dynamical Instability Induced by Zero Mode Under Symmetry Breaking External Perturbation
• Modified non-linear Schrödinger models, $\mathcal{C}{\mathcal{P}}_s{\mathcal{T}}_d$ invariant $N-$bright solitons and infinite towers of anomalous charges
• Stable and mobile two-dimensional dipolar ring-dark-in-bright Bose-Einstein condensate soliton
• Topology of Quantum Grey Soliton in Multi-Component Inhomogeneous Bose-Einstein Condensates
• Singular and regular vortices on top of a background pulled to the center
• Modified AKNS model, Riccati-type pseudo-potential approach and infinite towers of quasi-conservation laws
• Signatures of rigidity and second sound in dipolar supersolids
• Nonlinear Waves in an Experimentally Motivated Ring-shaped Bose-Einstein Condensate Setup
• Interactions and Collisions of Discrete Breathers in Two-Species Bose-Einstein Condensates in Optical Lattices
• Probing non-locality of interactions in a Bose-Einstein Condensate using solitons
• Vortex rings and vortex ring solitons in shaken Bose-Einstein condensate
• Novel soliton in dipolar BEC caused by the quantum fluctuations
• Negative radiation pressure in Bose-Einstein condensates
• Dynamic instabilities and turbulence of merged rotating Bose-Einstein condensates
• Accurate one-dimensional effective description of realistic matter-wave gap solitons
• Manakov system on metric graphs: Modeling the reflectionless propagation of vector solitons in networks
• Study of implosion in an attractive Bose-Einstein condensate
• Excitation spectrum of a toroidal spin-1 Bose-Einstein condensate
• Observation of Breathers in an Attractive Bose Gas
• Dynamical generation of dark-bright solitons through the domain wall of two immiscible Bose-Einstein condensates
• Interacting multiple zero mode formulation and its application to a system consisting of a dark soliton in a condensate
• Some results on topological currents in field theory
• Dynamical Instability of 3d Stationary and Traveling Planar Dark Solitons
• Nonlinear Schrodinger solitons in massive Yang-Mills theory and partial localization of Dirac matter
• An instability criterion for nonlinear standing waves on nonzero backgrounds
• Superfluid vortex multipoles and soliton stripes on a torus
• Positive normalized solutions to nonlinear elliptic systems in ${\mathbb{R}}^4$ with critical Sobolev exponent
• Some properties of small perturbations against a stationary solution of the nonlinear Schrodinger equation
• Exact solutions to the four Goldstone modes around a dark soliton of the nonlinear Schroedinger equation
• Black holes will break up solitons and white holes may destroy them
• Rayleigh-Taylor, Kelvin-Helmholtz and immiscible to miscible quenching instabilities in binary Bose-Einstein condensates
• Detecting Topological Phase Transition in Superconductor-Semiconductor Hybrids by Electronic Raman Spectroscopy
• Quenched dynamics of two-dimensional solitons and vortices in the Gross-Pitaevskii equation
• Dark solitons in a trapped gas of long-range interacting bosons
• Many-body dark solitons in one-dimensional hard-core Bose gases
• Phase Characters of Optical Dark Solitons with the Third-order Dispersion and Delayed Nonlinear Response
• Collisional dynamics of multiple dark solitons in a toroidal Bose-Einstein condensate: Quasiparticle picture
• Collective modes in Fulde-Ferrell-Larkin-Ovchinnikov superconductors: The role of long-range Coulomb interaction and signatures in density response
• Performing Hong-Ou-Mandel-type Numerical Experiments with Repulsive Condensates: The case of Dark and Dark-bright Solitons
• Finite-temperature dynamics of matter-wave dark solitons in linear and periodic potentials: an example of an anti-damped Josephson junction
• Integrability of the hyperbolic reduced Maxwell-Bloch equations for strongly correlated Bose-Einstein condensates
• Characterizing far from equilibrium states of the one-dimensional nonlinear Schr{ö}dinger equation
• Symmetry of components, Liouville-type theorems and classification results for some nonlinear elliptic systems
• Modulated harmonic wave in series connected discrete Josephson transmission line: the discrete calculus approach
• The Krein Matrix: General Theory and Concrete Applications in Atomic Bose-Einstein Condensates
• Soliton Diffusion as a Signature of Hawking Radiation in Bose-Einstein Condensates
• Solitons and their ghosts in PT-symmetric systems with defocusing nonlinearities
• Analytic Vortex Dynamics in an Annular Bose-Einstein Condensate
• Solitons in a hard-core bosonic system: Gross-Pitaevskii type and beyond
• Bohmian analysis of dark solutions in interfering Bose-Einstein condensates: The dynamical role of underlying velocity fields
• Multiple fluxon analogues and dark solitons in linearly coupled Bose-Einstein condensates
• Spectral Properties of Confining Superexponential Potentials
• Breakdown of the mean field for dark solitons of dipolar bosons in a one-dimensional harmonic trap
• Generation, propagation and control of quantized vortices and dark solitons in polariton superfluids
• Dynamics of a solitonic vortex in an anisotropically trapped superfluid
• Variational Approach to the Snake Instability of a Bose-Einstein Condensate Soliton
• Characterising arbitrary dark solitons in trapped one-dimensional Bose-Einstein condensates
• Optical creation of dark-bright soliton lattices in one-dimensional multicomponent Bose-Einstein condensates
• Stability and dynamics of dark-bright soliton bound states away from the integrable limit
• Negative radiation pressure in the abelian Higgs model