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Physical Review A

Dynamics of two-dimensional dark quasisolitons in a smoothly inhomogeneous Bose-Einstein condensate

Lev A. Smirnov, V. A. Mironov

Published May 16, 2012• 18 citations
Publisher

Abstract

We develop an asymptotic theory describing the dynamics of two-dimensional dark quasisolitons in a smoothly inhomogeneous Bose-Einstein condensate (BEC) with repulsive interaction between atoms. It is shown that the trajectories of such quasisolitons coincide with the geometric-optical rays in an equivalent isotropic medium characterized by the effective refractive index dependent on both the density of the undisturbed condensate and the energy of the structures. An expression for this effective refractive index is found and specific features of the refraction of quasisolitons with different initial energies by the condensate inhomogeneities are studied. The obtained results are confirmed by direct numerical simulation using the Gross-Pitaevskii (GP) equation.

DOI
10.1103/physreva.85.053620

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We develop an asymptotic theory describing the dynamics of two-dimensional dark quasisolitons in a smoothly inhomogeneous Bose-Einstein condensate (BEC) with repulsive interaction between atoms. It is shown that the trajectories of such quasisolitons coincide with the geometric-optical rays in an equivalent isotropic medium characterized by the effective refractive index dependent on both the density of the undisturbed condensate and the energy of the structures. An expression for this effective refractive index is found and specific features of the refraction of quasisolitons with different initial energies by the condensate inhomogeneities are studied. The obtained results are confirmed by direct numerical simulation using the Gross-Pitaevskii (GP) equation.
An asymptotic theory has been developed to describe the propagation and annihilation of vortex pairs in a smoothly inhomogeneous Bose-Einstein condensate with the repulsive interaction between atoms. It has been shown that the trajectories of vortex pairs coincide with geometric-optical rays in an equivalent isotropic medium with the refractive index depending both on the density of the unperturbed inhomogeneous condensate and on the energy of structures under study. The transformation of vortex pairs to vortex-free quasisolitons and back has been described.
We study the process of scattering of two-dimensional dark solitons, and their vortex-antivortex pairs as a specific case, by a single quantum vortex in a Bose-Einstein condensate with repulsive interaction between atoms. An asymptotic theory describing the dynamics of such solitonlike structures in a smoothly inhomogeneous flow of ultracold Bose gas is developed. An analytical expression for the angle of scattering of two-dimensional dark solitons (including vortex pairs) by a single-phase singularity is obtained in the limit of large impact parameters. All theoretical concepts are confirmed by numerical calculations performed directly within the Gross-Pitaevskii equation. It is shown that for small impact parameters, the considered solitonlike structures interact inelastically with the core of a single quantum vortex, scattering over large angles and radiating sound waves.
Abstract: In this thesis we experimentally observe the dynamics of dark solitons in elongated Bose-Einstein condensates (BEC) in the crossover regime between 1D and 3D. Dark solitons are dynamically stable in this regime. This allows the observation of the collisional and oscillational dynamics of two dark solitons in a harmonically confined BEC over several oscillation periods. We can detect the repulsive intersolitonic interaction as an increase of the oscillation frequency of the two solitons strongly depending on their mean distance. Thereby we give the first experimental evidence of the theoretically predicted repulsive interaction between the solitons. We compare our experimental findings to numerical simulations of the Gross-Pitaevskii equation and effective 1D equations. Additionally we develop a model in which the solitons are approximated by repulsively interacting classical particles. This model is based on a soliton interaction potential suggested by [Kiv1995] and can describe the essentials of the soliton dynamics. We observe well agreement between the soliton oscillation frequencies measured in the experiment, the numerical simulations and the results of the particle model. Besides we verify the theoretical prediction that the oscillation frequency of dark solitons in a harmonically confined BEC should be slower than the trap frequency.
We study the interaction of dark solitons with a localized impurity in Bose-Einstein condensates. We apply the soliton perturbation theory developed earlier in optics for describing the soliton dynamics and soliton-impurity interaction analytically, and then verify the results by direct numerical simulations of the Gross-Pitaevskii equation. We find that a dark soliton can be reflected from or transmitted through a repulsive impurity in a controllable manner, while near the critical point the soliton can be quasitrapped by the impurity. Additionally, we demonstrate that an immobile soliton may be captured and dragged by an adiabatically moving attractive impurity.
Abstract We study the statics and dynamics of anisotropic, stable, bright and dark-in-bright dipolar quasi-two-dimensional Bose–Einstein condensate (BEC) solitons on a one-dimensional (1D) optical-lattice (OL) potential. These solitons mobile in a plane perpendicular to a 1D OL trap can have both repulsive and attractive contact interactions. Dark-in-bright solitons are the excited states of bright solitons. The solitons, when subjected to a small perturbation, exhibit sustained breathing oscillation. Dark-in-bright solitons can be created by phase imprinting a bright soliton. At medium velocities the collision between two solitons is found to be quasi-elastic. Results are demonstrated by a numerical simulation of the three-dimensional mean-field Gross–Pitaevskii equation in three spatial dimensions employing realistic interaction parameters for a dipolar 164 Dy BEC.
We study the one-dimensional dynamics of dark-dark solitons in the miscible regime of two density-coupled Bose-Einstein condensates having repulsive interparticle interactions within each condensate (g>0g>0g>0). By using an adiabatic perturbation theory in the parameter g12/g{g}_{12}/gg12​/g, we show that, contrary to the case of two solitons in scalar condensates, the interactions between solitons are attractive when the interparticle interactions between condensates are repulsive g12>0{g}_{12}>0g12​>0. As a result, the relative motion of dark solitons with equal chemical potential $\ensuremath{\mu}$ is well approximated by harmonic oscillations of angular frequency ${w}_{r}=(\ensuremath{\mu}/\ensuremath{\hbar})\sqrt{(8/15){g}_{12}/g}$. We also show that, in finite systems, the resonance of this anomalous excitation mode with the spin-density mode of lowest energy gives rise to alternating dynamical instability and stability fringes as a function of the perturbative parameter. In the presence of harmonic trapping (with angular frequency $\mathrm{\ensuremath{\Omega}}$) the solitons are driven by the superposition of two harmonic motions at a frequency given by ${w}^{2}={(\mathrm{\ensuremath{\Omega}}/\sqrt{2})}^{2}+{w}_{r}^{2}$. When g12<0{g}_{12}<0g12​<0, these two oscillators compete to give rise to an overall effective potential that can be either single well or double well through a pitchfork bifurcation. All our theoretical results are compared with numerical solutions of the Gross-Pitaevskii equation for the dynamics and the Bogoliubov equations for the linear stability. A good agreement is found between them.