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arXiv:cond-mat/0412743

Nucleation of solitary wave complexes in two-component mixture Bose-Einstein condensates

Natalia G. Berloff

Published Dec 29, 2004• 2 citations
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Abstract

Two-component mixtures of Bose-Einstein condensates are shown to support solitary wave complexes that move with a constant velocity preserving their form. I obtain the families of such solitary wave complexes in two-dimensional two-component mixture condensates. These solutions are classified according to the structure of the wavefunction in each component. I show that these complexes nucleate from the surface of the disk when it moves supercritically, therefore, suggesting a mechanism by which these waves can be obtained in condensates by a moving laser beam. The condition for such a nucleation is derived analytically. The flow for supercritical disk velocities is computed numerically. The process of a boundary layer separation with emission of either vortex pairs in each component or a vortex pair in one component and a ``slaved wave'' in the other component is elucidated.

DOI
10.48550/arxiv.cond-mat/0412743

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Two-component mixtures of Bose-Einstein condensates are shown to support solitary wave complexes that move with a constant velocity preserving their form. I obtain the families of such solitary wave complexes in two-dimensional two-component mixture condensates. These solutions are classified according to the structure of the wavefunction in each component. I show that these complexes nucleate from the surface of the disk when it moves supercritically, therefore, suggesting a mechanism by which these waves can be obtained in condensates by a moving laser beam. The condition for such a nucleation is derived analytically. The flow for supercritical disk velocities is computed numerically. The process of a boundary layer separation with emission of either vortex pairs in each component or a vortex pair in one component and a ``slaved wave'' in the other component is elucidated.
Axisymmetric three-dimensional solitary waves in uniform two-component mixture Bose-Einstein condensates are obtained as solutions of the coupled Gross-Pitaevskii equations with equal intracomponent but varying intercomponent interaction strengths. Several families of solitary wave complexes are found: (1) vortex rings of various radii in each of the components; (2) a vortex ring in one component coupled to a rarefaction solitary wave of the other component; (3) two coupled rarefaction waves; (4) either a vortex ring or a rarefaction pulse coupled to a localized disturbance of a very low momentum. The continuous families of such waves are shown in the momentum-energy plane for various values of the interaction strengths and the relative differences between the chemical potentials of two components. Solitary wave formation, their stability, and solitary wave complexes in two dimensions are discussed.
Generation of wave structures by a two-dimensional (2D) object (laser beam) moving in a 2D two-component Bose-Einstein condensate with a velocity greater than the two sound velocities of the mixture is studied by means of analytical methods and systematic simulations of the coupled Gross-Pitaevskii equations. The wave pattern features three regions separated by two Mach cones. Two branches of linear patterns similar to the so-called ``ship waves'' are located outside the corresponding Mach cones, and oblique dark solitons are found inside the wider cone. An analytical theory is developed for the linear patterns. A particular dark-soliton solution is also obtained, its stability is investigated, and two unstable modes of transverse perturbations are identified. It is shown that for a sufficiently large flow velocity, this instability has a convective character in the reference frame attached to the moving body, which makes the dark soliton effectively stable. The analytical findings are corroborated by numerical simulations.
The phase separation and vortex states in two-component Bose-Einstein condensate consisting of |F = 1,mf = −1> and |2,1> internal spin states of 87Rb atoms are considered in the framework of Thomas-Fermi approximation. It is shown that in nonrotating system the atoms in the state |1, −1> form a shell about the atoms in the state |2,1>. The critical angular velocity for each state is calculated. These velocities depend drastically on the relative concentrations of the components, the critical angular velocity of the outer component being less than the angular velocity of the inner one. It is shown that the atoms in the |1, −1> state can form a rotating ring about the resting core of the atoms in the state |2,1>. PACS:03.75.Fi; 05.30.Jp; 32.80.Pj. The realization of Bose-Einstein Condensation (BEC) in dilute atomic gases offers new opportunities for studying quantum degenerate fluids [1]. These condensates, which contain thousands of atoms confined to microscale clouds, have similarities to superfluidity and laser,
Axisymmetric disturbances that preserve their form as they move along the vortex lines in uniform Bose-Einstein condensates are obtained numerically by the solution of the Gross-Pitaevskii equation. A continuous family of such solitary waves is shown in the momentum (ppp)-substitution energy ($\stackrel{^}{\mathcal{E}}$) plane with $p\ensuremath{\rightarrow}0.09\ensuremath{\rho}{\ensuremath{\kappa}}^{3}/{c}^{2}$, $\stackrel{^}{\mathcal{E}}\ensuremath{\rightarrow}0.091\ensuremath{\rho}{\ensuremath{\kappa}}^{3}/c$ as $U\ensuremath{\rightarrow}c$, where $\ensuremath{\rho}$ is the density, ccc is the speed of sound, $\ensuremath{\kappa}$ is the quantum of circulation, and UUU is the solitary wave velocity. It is shown that collapse of a bubble captured by a vortex line leads to the generation of such solitary waves in condensates. The various stages of collapse are elucidated. In particular, it is shown that during collapse the vortex core becomes significantly compressed, and after collapse two solitary wave trains moving in opposite directions are formed on the vortex line.
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.