Dark solitons as quasiparticles in trapped condensates

Abstract

We present a theory of dark soliton dynamics in trapped quasi-one-dimensional Bose-Einstein condensates, which is based on the local density approximation. The approach is applicable for arbitrary polynomial nonlinearities of the mean-field equation governing the system as well as to arbitrary polynomial traps. In particular, we derive a general formula for the frequency of the soliton oscillations in confining potentials. A special attention is dedicated to the study of the soliton dynamics in adiabatically varying traps. It is shown that the dependence of the amplitude of oscillations {\it vs} the trap frequency (strength) is given by the scaling law $X_0\propto {\omega }^{-\gamma }$ where the exponent $\gamma$ depends on the type of the two-body interactions, on the exponent of the polynomial confining potential, on the density of the condensate and on the initial soliton velocity. Analytical results obtained within the framework of the local density approximation are compared with the direct numerical simulations of the dynamics, showing remarkable match. Various limiting cases are addressed. In particular for the slow solitons we computed a general formula for the effective mass and for the frequency of oscillations.

arXiv comment16 pages, 4 figures. To appear in Phys. Rev. A

References in corpus (12)

• Theory of Bose-Einstein condensation in trapped gases
• Formation and Propagation of Matter Wave Soliton Trains
• Dark Solitons in Bose-Einstein Condensates
• Effective wave-equations for the dynamics of cigar-shaped and disc-shaped Bose condensates
• Motion of dark solitons in trapped Bose-Einstein condensates
• Low-dimensional Bose liquids: beyond the Gross-Pitaevskii approximation
• Landau dynamics of a grey soliton in a trapped condensate
• One-dimensional Bosons in Three-dimensional Traps
• Dissipative dynamics of a kink state in a Bose-condensed gas
• Stable and unstable vector dark solitons of coupled nonlinear Schrödinger equations. Application to two-component Bose-Einstein condensates
• Oscillations of dark solitons in trapped Bose-Einstein condensates
• Dynamics of shallow dark solitons in a trapped gas of impenetrable bosons

Cited by in corpus (22)

• Dark solitons in atomic Bose-Einstein condensates: from theory to experiments
• Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques
• The impact of ultra-light axion self-interactions on the large scale structure of the Universe
• An Adiabatic Invariant Approach to Transverse Instability: Landau Dynamics of Soliton Filaments
• Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics
• Strong Collapse Turbulence in Quintic Nonlinear Schrödinger Equation
• One-dimension cubic-quintic Gross-Pitaevskii equation in Bose-Einstein condensates in a trap potential
• Dark solitons generation and their instability dynamics in two dimensional condensates
• Dark soliton oscillations in Bose-Einstein condensates with multi-body interactions
• Dark solitons dynamics and snake instability in superfluid Fermi gases trapped by an anisotropic harmonic potential
• Quantum fluctuations in the image of a Bose gas
• Dark solitons in cigar-shaped Bose-Einstein condensates in double-well potentials
• A direct derivation of the dark soliton excitation energy
• Complex plane representations and stationary states in cubic and quintic resonant systems
• Observation of self-patterned defect formation in atomic superfluids -- from ring dark solitons to vortex dipole necklaces
• Anomalous oscillations of dark solitons in trapped dipolar condensates
• Adiabatic invariant analysis of dark and dark-bright soliton stripes in two-dimensional Bose-Einstein condensates
• Intermittency in generalized NLS equation with focusing six-wave interactions
• Self-Adapted Josephson Oscillation of Dark-Bright Solitons under Constant Forces
• Finite-temperature dynamics of matter-wave dark solitons in linear and periodic potentials: an example of an anti-damped Josephson junction
• Stochastic longevity of a dark soliton in a finite-temperature Bose-Einstein condensate
• Contour dynamics of two-dimensional dark solitons