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arXiv:1904.02380 · Physical Review A

Transverse instability and disintegration of a domain wall of a relative phase in coherently coupled two-component Bose-Einstein condensates

Kousuke Ihara, Kenichi Kasamatsu

Published Jul 31, 2019• 22 citations
arXivHTMLPDF

Abstract

We study transverse instability and disintegration dynamics of a domain wall of a relative phase in two-component Bose-Einstein condensates with a coherent Rabi coupling. We obtain analytically the stability phase diagram of the stationary solution of the domain wall for the one-dimensional coupled Gross-Pitaevskii equations in the plane of the Rabi frequency and the intercomponent coupling constant. Outside the stable region, the domain wall is dynamically unstable for the transverse modulation along the direction perpendicular to the phase kink. The nonlinear evolution associated with the instability is demonstrated through numerical simulations for both the domain wall without edges and that with edges formed by the quantized vortices.

DOI
10.1103/physreva.100.013630

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We study transverse instability and disintegration dynamics of a domain wall of a relative phase in two-component Bose-Einstein condensates with a coherent Rabi coupling. We obtain analytically the stability phase diagram of the stationary solution of the domain wall for the one-dimensional coupled Gross-Pitaevskii equations in the plane of the Rabi frequency and the intercomponent coupling constant. Outside the stable region, the domain wall is dynamically unstable for the transverse modulation along the direction perpendicular to the phase kink. The nonlinear evolution associated with the instability is demonstrated through numerical simulations for both the domain wall without edges and that with edges formed by the quantized vortices.
We investigate nonlinear dynamics induced by the modulation instability of a two-component mixture in an atomic Bose-Einstein condensate. The nonlinear dynamics is examined using numerical simulations of the time-dependent coupled Gross-Pitaevskii equations. The unstable modulation grows from initially miscible condensates into various types of vector solitary waves, depending on the combinations of the sign of the coupling constants (intracomponent and intercomponent). We discuss the detailed features of the modulation instability, dynamics of solitary wave formation, and an analogy with the collapsing dynamics in a single-component condensate with attractive interactions.
The dynamic behavior of vortex pairs in two-component coherently (Rabi) coupled Bose-Einstein condensates is investigated in the presence of harmonic trapping. We discuss the role of the surface tension associated with the domain wall connecting two vortices in condensates of atoms occupying different spin states and its effect on the precession of the vortex pair. The results, based on the numerical solution of the Gross-Pitaevskii equations, are compared with the predictions of an analytical macroscopic model and are discussed as a function of the size of the pair, the Rabi coupling, and the intercomponent interaction. We show that the increase of the Rabi coupling results in the disintegration of the domain wall into smaller pieces, connecting vortices of newly created vortex pairs. The resulting scenario is the analog of quark confinement and string breaking in quantum chromodynamics.
The dynamics of multiple domain formation caused by the modulation instability of two-component Bose-Einstein condensates in an axially symmetric trap are studied by numerically integrating the coupled Gross-Pitaevskii equations. The modulation instability induced by the intercomponent mean-field coupling occurs in the out-of-phase fluctuation of the wave function and leads to the formation of multiple domains that alternate from one domain to another, where the phase of one component jumps across the density dips where the domains of the other exist. This behavior is analogous to a soliton train, which explains the origin of the long lifetime of the spin domains observed by Miesner et al. [Phys. Rev. Lett. 82, 2228 (1999)]].
We study rotating two-component Bose–Einstein condensates with equal particle numbers and strong intercomponent repulsion located in a harmonic potential by numerically solving two-dimensional coupled Gross–Pitaevskii equations. The condensates are observed as a dramatic departure, forming a pair of shells located symmetrically in the trap with a small spatial overlap. Projecting the system into a pseudospin space, a spin domain wall is formed at the interface of the two components. The complex and spatial periodic spin texture is formed on the domain-wall region. We discuss the dependence of the spin texture of the domain wall on the angular velocity in detail. The relation among the number of the vortices, the topological charge and the angular momentum, as an extension of Feynman's rule in the two-component Bose–Einstein condensates, is given, based on the spin texture carrying the angular momentum of the condensates.
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.
The dynamical instability of weakly interacting two-component Bose-Einstein condensates with coaxial quantized vortices is analytically investigated in a two-dimensional isotopic harmonic potential. We examine whether complex eigenvalues appear on the Bogoliubov--de Gennes equation, implying dynamical instability. Rather than solving the Bogoliubov--de Gennes equation numerically, we rely on a perturbative expansion with respect to the coupling constant which enables a simple, analytic approach. For each pair of winding numbers and for each magnetic quantum number, the ranges of intercomponent coupling constant where the system is dynamically unstable are exhaustively obtained. Corotating and counter-rotating systems show distinctive behaviors. The latter is much more complicated than the former with respect to dynamical instability, particularly because radial excitations contribute to complex eigenvalues in counter-rotating systems.