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arXiv:cond-mat/0409123 · Physical Review A

Static and rotating domain-wall cross patterns in Bose-Einstein condensates

Boris A. Malomed, Hector E. Nistazakis, D. J. Frantzeskakis, P. G. Kevrekidis

Published Oct 18, 2004• 60 citations
arXivHTMLPDF

Abstract

For a Bose-Einstein condensate (BEC) in a two-dimensional (2D) trap, we introduce cross patterns, which are generated by the intersection of two domain walls (DWs) separating immiscible species, with opposite signs of the wave functions in each pair of sectors filled by the same species. The cross pattern remains stable up to the zero value of the immiscibility parameter $\ensuremath{\mid}\ensuremath{\Delta}\ensuremath{\mid}$, while simpler rectilinear (quasi-1D) DWs exist only for values of $\ensuremath{\mid}\ensuremath{\Delta}\ensuremath{\mid}$ essentially exceeding those in BEC mixtures (two spin states of the same isotope) currently available to the experiment. Both symmetric and asymmetric cross configurations are investigated, with equal or different numbers ${N}_{1,2}$ of atoms in the two species. In rotating traps, ``propellers'' (stable revolving crosses) are found too. A full stability region for the crosses and propellers in the system's parameter space is identified, unstable crosses evolving into arrays of vortex-antivortex pairs. Stable rotating rectilinear DWs are found too, at larger values of $\ensuremath{\mid}\ensuremath{\Delta}\ensuremath{\mid}$. All the patterns produced by the intersection of three or more DWs are unstable, rearranging themselves into ones with two DWs. Optical ``propellers'' are also predicted in a twisted nonlinear photonic-crystal fiber carrying two different wavelengths or circular polarizations, which can be used for applications to switching and routing.

DOI
10.1103/physreva.70.043616

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The existence and stability of domain walls (DWs) and bubble-droplet (BD) states in binary mixtures of quasi-one-dimensional ultracold Bose gases with inter- and intraspecies repulsive interactions is considered. Previously, DWs were studied by means of coupled systems of Gross-Pitaevskii equations (GPEs) with cubic terms, which model immiscible binary Bose-Einstein condensates (BECs). We address immiscible BECs with two- and three-body repulsive interactions, as well as binary Tonks--Girardeau (TG) gases, using systems of GPEs with cubic and quintic nonlinearities for the binary BEC, and coupled nonlinear Schr\"odinger equations with quintic terms for the TG gases. Exact DW solutions are found for the symmetric BEC mixture, with equal intraspecies scattering lengths. Stable asymmetric DWs in the BEC mixtures with dissimilar interactions in the two components, as well as of symmetric and asymmetric DWs in the binary TG gas, are found by means of numerical and approximate analytical methods. In the BEC system, DWs can be easily put in motion by phase imprinting. Combining a DW and anti-DW on a ring, we construct BD states for both the BEC and TG models. These consist of a dark soliton in one component (the ``bubble''), and a bright soliton (the ``droplet'') in the other. In the BEC system, these composite states are mobile, too.
We study spin-polarized states and their stability in the antiferromagnetic phase of spinor (F=1)(F=1)(F=1) quasi-one-dimensional Bose-Einstein condensates. Using analytical approximations and numerical methods, we find various types of polarized states, including patterns of the Thomas-Fermi type, structures featuring a pulse in one component inducing a hole in the other components, states with holes in all three components, and domain walls (DWs). The stability analysis based on the Bogoliubov--de Gennes equations reveals intervals of weak oscillatory instability in families of these states, except for the DWs, which are always stable. The development of the instabilities is examined by means of direct simulations.
A domain wall of relative phase in a flattened harmonically trapped Bose-Einstein condensed mixture of two atomic hyperfine states, subject to a stationary Rabi coupling of intensity $\mathrm{\ensuremath{\Omega}}$, is predicted to decay through two different mechanisms. For small values of $\mathrm{\ensuremath{\Omega}}$ the instability has an energetic nature and is associated with the formation of a vortex-antivortex pair of the same atomic hyperfine states, the motion of which inside the trap causes the emergence of magnetization, the bending of the domain wall, and its consequent fragmentation. For large values of $\mathrm{\ensuremath{\Omega}}$ the domain wall instead undergoes a dynamic snake instability, caused by the negative value of its effective mass, and results in the fast fragmentation of the wall into smaller domain walls confining vortex pairs of different atomic species. Numerical predictions are given by solving the time-dependent Gross-Pitaevskii equation in experimentally available configurations of mixtures of sodium atomic gases.
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Abstract We numerically investigate the collision dynamics of a dark soliton with a domain wall in an immiscible, two-component Bose-Einstein condensate confined in a quasi-two-dimensional harmonic trap. The role of the inter-species interaction strength δ=g12/g11\delta = g_{12}/g_{11}δ=g12​/g11​ and the soliton's initial displacement Δx\Delta_xΔx​ is investigated thoroughly. Our results reveal a clear bifurcation into two distinct dynamical regimes: a penetrationregimepenetration regimepenetrationregime, where the soliton decays into vortex pairs that cross the interface, and a non−penetrationregimenon-penetration regimenon−penetrationregime, where the soliton's energy is dissipated at the interface through sound emission and vortex annihilation. We present a phase diagram that maps these outcomes across the (δ,Δx)(\delta, \Delta_x)(δ,Δx​) parameter space. Furthermore, within the non-penetration regime, we identify a complex excited state characterized by the combination of component breakup in one component and vortex formation in the other. This work provides the systematic study of dark soliton-domain wall interactions in a 2D phase-separated binary BEC, offering new insights into interfacial dynamics and non-equilibrium transport in multi-component quantum fluids.