2017/12/31 by I. Morera, Ivan Morera, A. Muñoz Mateo +4
Chemistry · Physics and Astronomy · #Adiabatic process #Bifurcation #Bifurcation theory #Bose–Einstein condensate #Cold Atom Physics and Bose-Einstein Condensates #Excitation #Instability #Mathematical physics #Nonlinear system #Omega #Physics #Pitchfork bifurcation #Quantum electrodynamics #Quantum mechanics #Scalar (mathematics) #Soliton #Spectroscopy and Laser Applications #Strong Light-Matter Interactions #Superposition principle #cond-mat.quant-gas #nlin.PS
paper · pdf · doi:10.1103/physreva.97.043621
published as Phys. Rev. A 97, 043621 (2018)
arxiv created 2017/12/31 · openalex publication_date 2018/04/20 · arxiv updated 2018/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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>0). By using an adiabatic perturbation theory in the parameter g12/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. As a result, the relative motion of dark solitons with equal chemical potential \ensuremathμ is well approximated by harmonic oscillations of angular frequency wr=(\ensuremathμ/\ensuremathℏ)√(8/15)g12/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\ensuremathΩ) the solitons are driven by the superposition of two harmonic motions at a frequency given by w2=(\mathrm\ensuremathΩ/√(2))2+wr2. When g12<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.