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arXiv:cond-mat/0609642 · Physical Review A

Dynamics of vortex matter in rotating two-species Bose-Einstein condensates

Sungjong Woo, Seok Jin Choi, Leslie O. Baksmaty, N. P. Bigelow

Published Mar 27, 2007• 21 citations
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Abstract

In a rotating two-component Bose-Einstein condensate (BEC), the traditional triangular vortex lattice can be replaced by a rectangular vortex lattice or even a structure characterized in terms of vortex sheets, depending on the interspecies interactions. We study the dynamics of this system by analyzing the Bogoliubov excitation spectrum. Excitations familiar to BEC vortex systems are found such as Tkachenko modes, hydrodynamic modes, and surface waves, however, the complex two-component morphology also gives rise to phenomena including shear flow between vortex sheets.

DOI
10.1103/physreva.75.031604

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In a rotating two-component Bose-Einstein condensate (BEC), the traditional triangular vortex lattice can be replaced by a rectangular vortex lattice or even a structure characterized in terms of vortex sheets, depending on the interspecies interactions. We study the dynamics of this system by analyzing the Bogoliubov excitation spectrum. Excitations familiar to BEC vortex systems are found such as Tkachenko modes, hydrodynamic modes, and surface waves, however, the complex two-component morphology also gives rise to phenomena including shear flow between vortex sheets.
The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates by solving the Bogoliubov-de Gennes equation, yielding, e.g., the Tkachenko mode recently observed at JILA. The totally symmetric subset of these modes includes the transverse shear, common longitudinal, and differential longitudinal modes. We also solve the time-dependent Gross-Pitaevskii equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both approaches allows one to unambiguously identify every observed mode.
We consider a rapidly rotating two-component Bose-Einstein condensate (BEC) containing a vortex lattice. We calculate the dispersion relation for small oscillations of vortex positions (Tkachenko modes) in the mean-field quantum Hall regime, taking into account the coupling of these modes with density excitations. Using an analytic form for the density of the vortex lattice, we numerically calculate the elastic constants for different lattice geometries. We also apply this method to calculate the elastic constant for the single-component triangular lattice. For a two-component BEC, there are two kinds of Tkachenko modes, which we call acoustic and optical in analogy with phonons. For all lattice types, acoustic Tkachenko mode frequencies have quadratic wave-number dependence at long wavelengths, while the optical Tkachenko modes have linear dependence. For triangular lattices the dispersion of the Tkachenko modes are isotropic, while for other lattice types the dispersion relations show directional dependence consistent with the symmetry of the lattice. Depending on the intercomponent interaction there are five distinct lattice types, and four structural phase transitions between them. Two of these transitions are second order and are accompanied by the softening of an acoustic Tkachenko mode. The remaining two transitions are first order and while one of them is accompanied by the softening of an optical mode, the other does not have any dramatic effect on the Tkachenko spectrum. We also find an instability of the vortex lattice when the intercomponent repulsion becomes stronger than the repulsion within components.
This report addresses our recent study on pattern formation in two-component Bose-Einstein condensates(BECs), focusing on the dynamics of multiple-domain formation and the structure of vortex states in rotating condensates. Cross-phase modulation instability gives rise to formation of multiple domains that alternate two components, which are consistent with the experimental observation by the MIT group. Rotating two-component BECs exhibit a rich variety of vortex states such as square lattices and vortex sheets, which depend on the strength of intercomponent interaction and rotation frequency.
We investigate the structure of vortex states in rotating two-component Bose-Einstein condensates with equal intracomponent but varying intercomponent-coupling constants. A phase diagram in the intercomponent-coupling versus rotation-frequency plane reveals rich equilibrium structures of vortex states. As the ratio of intercomponent to intracomponent couplings increases, the interlocked vortex lattices undergo phase transitions from triangular to square, to double-core lattices, and eventually develop interwoven "serpentine" vortex sheets with each component made up of chains of singly quantized vortices.
We study the dynamics of rotating two-component Bose-Einstein condensates(BECs) toward vortex lattice formation by numerically solving the two-dimensional Gross-Pitaevskii equations.The dynamics are similar to that of single-component BEC, and the whole changes of physical quantities in two cases are qualitatively similar.However, there are some differences between two cases.First, the characteristic time toward vortex entering depends on the inter-component interaction.The time toward vortex entering becomes shorter with increasing the inter-component interaction.Second, the angular momenta exchange between two components with keeping the total angular momentum.