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arXiv:1303.4469 · Journal of Physics Condensed Matter

D-brane solitons and boojums in field theory and Bose–Einstein condensates

Kenichi Kasamatsu, Hiromitsu Takeuchi, Muneto Nitta

Published Sep 11, 2013• 22 citations
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Abstract

In certain field theoretical models, composite solitons consisting of a domain wall and vortex lines attached to the wall have been referred to as 'D-brane solitons'. We show that similar composite solitons can be realized in phase-separated two-component Bose-Einstein condensates. We discuss the similarities and differences between topological solitons in the Abelian-Higgs model and those in two-component Bose-Einstein condensates. On the basis of the formulation of gauge theory, we introduce the 'boojum charge' to characterize the D-brane soliton in Bose-Einstein condensates.

DOI
10.1088/0953-8984/25/40/404213

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In certain field theoretical models, composite solitons consisting of a domain wall and vortex lines attached to the wall have been referred to as 'D-brane solitons'. We show that similar composite solitons can be realized in phase-separated two-component Bose-Einstein condensates. We discuss the similarities and differences between topological solitons in the Abelian-Higgs model and those in two-component Bose-Einstein condensates. On the basis of the formulation of gauge theory, we introduce the 'boojum charge' to characterize the D-brane soliton in Bose-Einstein condensates.
We study composite solitons, consisting of domain walls and vortex lines attaching to the walls in two-component Bose-Einstein condensates. When the total density of the two components is homogeneous, the system can be mapped to the O(3) nonlinear $\ensuremath{\sigma}$ model for the pseudospin representing the two-component order parameter, and the analytical solutions of the composite solitons can be obtained. Based on the analytical solutions, we discuss the detailed structure of the composite solitons in two-component condensates by employing the generalized nonlinear $\ensuremath{\sigma}$ model, where all degrees of freedom of the original Gross-Pitaevskii theory are active. The domain wall pulled by a vortex is logarithmically bent as a membrane pulled by a pin. It bends more flexibly than the domain wall in the $\ensuremath{\sigma}$ model, because the density inhomogeneity results in a reduction of the domain wall tension from that in the $\ensuremath{\sigma}$ model limit. We find, however, that the curvature of the wall bending pulled by a vortex is still greater than that expected from the reduced tension due to only the density inhomogeneity. Finally, we study the composite soliton structure for actual experimental situations with trapped immiscible condensates under rotation, through numerical simulations of the coupled Gross-Pitaevskii equations.
We theoretically study the vortex formation from the collision of the domain walls in phase-separated two-component Bose-Einstein condensates. The collision process mimics the tachyon condensation for the annihilation of D-brane and anti-D-brane in string theory. A pair annihilation leaves the quantized vortices with superflow along their core, namely `superflowing cosmic strings'. It is revealed that the line density and the core size of the vortices depend on the initial distance between the walls.
We study the topological objects in two-component Bose-Einstein condensates. We compare two competing theories of two-component Bose-Einstein condensates, the popular Gross-Pitaevskii theory, and the recently proposed gauge theory of two-component Bose-Einstein condensate which has an induced vorticity interaction. We show that two theories produce very similar topological objects, in spite of the obvious differences in dynamics. Furthermore we show that the gauge theory of two-component Bose-Einstein condensates, with the U(1)U(1)U(1) gauge symmetry, is remarkably similar to the Skyrme theory. Just like the Skyrme theory this theory admits the non-Abelian vortex, the helical vortex, and the vorticity knot. We construct the lightest knot solution in two-component Bose-Einstein condensates numerically, and discuss how the knot can be constructed in the spin-12\frac{1}{2}21​ condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms.
The creation and interaction of dark solitons in a two-component Bose-Einstein condensate is investigated. For a miscible case, the interaction of dark solitons in different components is studied. Various possible scenarios are presented, including the formation of a soliton-soliton bound pair. We also analyze the soliton propagation in the presence of domains, and show that a dark soliton can be transferred from one component to the other at the domain wall when it exceeds a critical velocity. For lower velocities multiple reflections within the domain are observed, where the soliton is evaporated and accelerated after each reflection until it finally escapes from the domain.
We report the numerical realization of robust two-component structures in 2D and 3D Bose-Einstein condensates with nontrivial topological charge in one component. We identify a stable symbiotic state in which a higher-dimensional bright soliton exists even in a homogeneous setting with defocusing interactions, due to the effective potential created by a stable vortex in the other component. The resulting vortex-bright-solitons, generalizations of the recently experimentally observed dark-bright solitons, are found to be very robust both in the homogeneous medium and in the presence of external confinement.
The creation, interaction, observation and stability of dark solitons in two-component condensates are investigated. As a first scenario, we consider the case of miscible components, analysing the creation of solitons in different components via phase-imprinting, and the soliton-soliton interaction in different situations, which include the formation of a soliton-soliton binary system and free single solitons accompanied by a filling of the other component. The different regimes of interaction are analysed numerically, and compared with a variational calculation. The observability of the solitons and their stability are also analysed. In a second scenario, we study the soliton propagation in the presence of domains, and show that a dark soliton can be transferred from one component to the other at the domain wall when exceeding a critical velocity.