Dynamics of shallow dark solitons in a trapped gas of impenetrable bosons

Abstract

The dynamics of linear and nonlinear excitations in a Bose gas in the Tonks-Girardeau (TG) regime with longitudinal confinement are studied within a mean field theory of quintic nonlinearity. A reductive perturbation method is used to demonstrate that the dynamics of shallow dark solitons, in the presence of an external potential, can effectively be described by a variable-coefficient Korteweg-de Vries equation. The soliton oscillation frequency is analytically obtained to be equal to the axial trap frequency, in agreement with numerical predictions obtained by Busch {\it et al.} [J. Phys. B {\bf 36}, 2553 (2003)] via the Bose-Fermi mapping. We obtain analytical expressions for the evolution of both soliton and emitted radiation (sound) profiles.

4 pages, Phys. Rev. A (in press)

References in corpus (13)

• Exciting Collective Oscillations in a Trapped 1D Gas
• Collective oscillations of a 1D trapped Bose gas
• Ring Dark Solitons and Vortex Necklaces in Bose-Einstein Condensates
• One-dimensional Bosons in Three-dimensional Traps
• Soliton-sound interactions in quasi-one-dimensional Bose-Einstein condensates
• Dynamical transition from a quasi-one dimensional Bose-Einstein condensate to a Tonks-Girardeau gas
• Energy dependent scattering and the Gross-Pitaevskii Equation in two dimensional Bose-Einstein condensates
• Density Functional Theory of Bosons in a Trap
• Low-density, one-dimensional quantum gases in a split trap
• Deformation of dark solitons in inhomogeneous Bose-Einstein condensates
• Shock waves in ultracold Fermi (Tonks) gases
• A density-functional approach to fermionization in the 1D Bose gas
• Dynamics of Lieb-Liniger Gases

Cited by in corpus (15)

• Dark solitons in atomic Bose-Einstein condensates: from theory to experiments
• Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques
• Bright-Dark Soliton Complexes in Spinor Bose-Einstein Condensates
• Gap-Townes solitons and localized excitations in low dimensional Bose Einstein condensates in optical lattices
• Dark solitons as quasiparticles in trapped condensates
• Oscillations of dark solitons in trapped Bose-Einstein condensates
• Solitons in Tonks-Girardeau gas with dipolar interactions
• Bose-Einstein condensation: Twenty years after
• Shock waves in a one-dimensional Bose gas: from a Bose-Einstein condensate to a Tonks gas
• Dark soliton oscillations in Bose-Einstein condensates with multi-body interactions
• Interactions of bright and dark solitons with localized $\mathcal{P}\mathcal{T}$-symmetric potentials
• Domain walls and bubble-droplets in immiscible binary Bose gases
• Solitary waves in elongated clouds of strongly-interacting bosons
• The single-particle density matrix and the momentum distribution of dark "solitons" in a Tonks-Girardeau gas
• Interfaces between Bose-Einstein and Tonks-Girardeau atomic gases