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arXiv:1005.4760 · Physical Review Letters

Texture Control in a Pseudospin Bose-Einstein Condensate

Gary Ruben, Michael J. Morgan, David M. Paganin

Published Nov 24, 2010• 16 citations
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Abstract

We describe a wave function engineering approach to the formation of textures in nonrotated multicomponent Bose-Einstein condensates. With numerical simulations of a viable two-component condensate experiment, we demonstrate the formation of a ballistically expanding regular lattice texture, composed of half-quantum vortices and spin-2 textures. The formation is described by a linear interference process in which the geometry and phase of three initially separated wave packets provide deterministic control over the resulting lattice texture.

DOI
10.1103/physrevlett.105.220402

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We describe a wave function engineering approach to the formation of textures in nonrotated multicomponent Bose-Einstein condensates. With numerical simulations of a viable two-component condensate experiment, we demonstrate the formation of a ballistically expanding regular lattice texture, composed of half-quantum vortices and spin-2 textures. The formation is described by a linear interference process in which the geometry and phase of three initially separated wave packets provide deterministic control over the resulting lattice texture.
We investigate half-vortex sheets and domain-wall trains of rotating two-component Bose-Einstein condensates in spin-dependent optical lattices. The two-component condensates undergo phase separation in the form of stripes arranged alternately. The vortices of one component are aligned in lines in the low-density regions and filled with the other component, which results in a stable vortex configuration, straight half-vortex sheets. A train of domain walls, with spatially periodic eyebrowlike spin textures embedded on them, are formed at the interfaces of the two components. We reveal that these spatially periodic textures on the domain walls result from the linear gradient of the relative phase, which is induced by the alternating arrangement of the vortex sheets in the two components. An accurate manipulation of the textures can be realized by adjusting the intercomponent interaction strength, the rotating angular frequency, and the period of the optical lattices. Under external disturbances, some interesting phenomena, including collective movement of vortices along the sheets and spin-wave propagation along the domain walls, as well as local spin precession, are observed.
Numerical simulations of the interference of a three-way segmented nonrotating Bose-Einstein condensate reveal the production of a honeycomb vortex lattice containing significant numbers of vortices and antivortices. If confined within a trap, the lattice subsequently melts, exhibiting a rich assortment of vortex-antivortex interactions. In contrast with nonlinear vortex production mechanisms previously described for Bose-Einstein condensates, the process here is shown to be primarily one of linear superposition, with initial vortex locations approximately described by a linear theory of wave packet interference.
We investigate two kinds of coreless vortices with axisymmetric and nonaxisymmetric configurations in rotating two-component Bose-Einstein condensates. Starting from the Gross-Pitaevskii energy functional in a rotating frame, we derive a nonlinear sigma model generalized to the two-component condensates. In terms of a pseudospin representation, an axisymmetric vortex and a nonaxisymmetric one correspond to spin textures referred to as a ``skyrmion'' and a ``meron-pair,'' respectively. A variational method is used to investigate the dependence of the sizes of the stable spin textures on system parameters, and the optimized variational function is found to reproduce well the numerical solution. In the SU(2) symmetric case, the optimal skyrmion and meron-pair are degenerate and transform to each other by a rotation of the pseudospin. An external rf field that couples coherently the hyperfine states of two components breaks the degeneracy in favor of the meron-pair texture due to an effective transverse pseudomagnetic field. The difference between the intracomponent and intercomponent interactions yields a longitudinal pseudomagnetic field and a ferromagnetic or an antiferromagnetic pseudospin interaction, leading to a meron-pair texture with an anisotropic distribution of vorticity.
In this thesis the features that arise from the interference of simple coherent waves are described, namely the topological defects of phase known as phase vortices permeating such wavefields. Phase vortices are associated with the rotation of energy and mass and arise naturally in regions containing coherent light and/or matter. The simplest possible system exhibiting these defects is that of three linearly interfering plane waves, described using the classical theory of monochromatic complex scalar wavefields. We explore the related case of three outgoing waves produced by point sources, such as a laser-illuminated screen that has been punctured by three pinholes. We develop a description of the resulting vortex structure in the optical far-field, and relate this to the source arrangement and parameters. This allows an estimate of the number and positions of the vortices, and leads to connections to particular results from information theory and number theory. Numerical simulations of the near-field defect structure are also presented. Findings from this study are then applied to the time evolution of a nonlinear Bose-Einstein condensate of atoms, which shares the property of coherence that enables its description by a related model of interfering Gaussian wavepackets. Numerical modelling of the nonlinear system is performed for both trapped and untrapped Bose-Einstein condensates (BECs) in two and three spatial dimensions, for BEC pieces initially positioned at the three corners of an equilateral triangle. We demonstrate the production of a distorted honeycomb vortex-antivortex lattice, due to wavepacket interference. The wavepacket expansion is halted by the presence of a magnetic trap, causing the lattice to melt and providing a population of mobile vortices and antivortices. The addition of nonlinearity in this system over the linear case leads to the formation of vortex clusters, whose dynamics we investigate. A model of a Laguerre-Gauss (LG) laser beam, which carries a phase vortex along its axis, is studied following its interaction with a ground-glass plate. We present preliminary results showing that the beam acquires interference-generated vortices whose number density evolves as a function of propagation distance and beam topological charge, due to interaction with the roughened glass. Beyond the nonlinear coherent wavefields applied to the description of Bose-condensed gases, a pseudo-spinor system described as a nonlinear coupled system of two complex scalar fields is studied. Such systems admit the existence of texture defects similar to those that exist in ferromagnetic systems. We numerically model a pseudo-spinor system that we arrange to generate carefully aligned honeycomb vortex-antivortex lattices in the coupled components. We find that this corresponds to a texture defect lattice and identify its constituent texture defects as merons and a type of planar defect. Following the analogy with the single component BEC, we also study texture defects and clusters in the trapped pseudo-spinor system.
We provide a detailed description of our previously proposed scheme for topological interface engineering with constructed defects and textures perforating across coherent interfaces between different broken symmetries [Borgh and Ruostekoski, Phys. Rev. Lett. 109, 015302 (2012)]. We consider a spin-1 Bose-Einstein condensate, in which polar and ferromagnetic phases are prepared in spatially separated regions. We show that a stable coherent interface is established between the two phases, allowing defects of different topology to connect continuously across the boundary. We provide analytic constructions of interface-crossing defect solutions that could be experimentally phase imprinted using existing technology. By numerically minimizing the energy, we calculate the core structures of interface-crossing defect configurations. We demonstrate nontrivial core deformations to considerably more complex structures, such as the formation of an arch-shaped half-quantum line defect, an Alice arch, at the interface, with the topological charge of a point defect, whose emergence may be understood by the ``hairy ball'' theorem. Another example of an energetically stable object is the connection of a coreless vortex to a pair of half-quantum vortices. We show that rotation leads to spontaneous nucleation of defects in which a coreless vortex continuously transforms to a half-quantum vortex across the interface.