15 research outputs found

    Excitation spectroscopy of vortex lattices in a rotating Bose-Einstein condensate

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    Excitation spectroscopy of vortex lattices in rotating Bose-Einstein condensates is described. We numerically obtain the Bogoliubov-deGenne quasiparticle excitations for a broad range of energies and analyze them in the context of the complex dynamics of the system. Our work is carried out in a regime in which standard hydrodynamic assumptions do not hold, and includes features not readily contained within existing treatments.Comment: 4 pages, 4 figures. Submitted for publicatio

    Collective Oscillations of Vortex Lattices in Rotating Bose-Einstein Condensates

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    The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates (BEC) by solving the Bogoliubov-de Gennes (BdG) 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 (TDGP) equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both the BdG and TDGP approaches allows one to unambiguously identify every observed mode.Comment: 5 pages, 4 figure

    Collective Oscillations of Vortex Lattices in Rotating Bose-Einstein Condensates

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    The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates (BEC) by solving the Bogoliubov-de Gennes (BdG) 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 (TDGP) equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both the BdG and TDGP approaches allows one to unambiguously identify every observed mode.Comment: 5 pages, 4 figure

    Excitation spectrum of vortex lattices in rotating Bose-Einstein condensates

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    Using the coarse grain averaged hydrodynamic approach, we calculate the excitation spectrum of vortex lattices sustained in rotating Bose-Einstein condensates. The spectrum gives the frequencies of the common-mode longitudinal waves in the hydrodynamic regime, including those of the higher-order compressional modes. Reasonable agreement with the measurements taken in a recent JILA experiment is found, suggesting that one of the longitudinal modes reported in the experiment is likely to be the n=2n=2, m=0m=0 mode.Comment: 2 figures. Submitted to Physical Review A. v2 contains more references. No change in the main resul

    Vortex Synchronization in Bose-Einstein Condensates: A Time-Dependent Gross-Pitaevskii Equation Approach

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    In this work we consider vortex lattices in rotating Bose-Einstein Condensates composed of two species of bosons having different masses. Previously [1] it was claimed that the vortices of the two species form bound pairs and the two vortex lattices lock. Remarkably, the two condensates and the external drive all rotate at different speeds due to the disparity of the masses of the constituent bosons. In this paper we study the system by solving the full two-component Gross-Pitaevskii equations numerically. Using this approach we verify the stability of the putative locked state which is found to exist within a disk centered on the axis of rotation and which depends on the mass ratio of the two bosons. We also show that an analytic estimate of this locking radius based on a two-body force calculation agrees well with the numerical results.Comment: 6.1 pages, 3 figure

    Equatorial Waves in Rotating Bubble-Trapped Superfluids

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    As the Earth rotates, the Coriolis force causes several oceanic and atmospheric waves to be trapped along the equator, including Kelvin, Yanai, Rossby, and Poincar\'e modes. It has been demonstrated that the mathematical origin of these waves is related to the nontrivial topology of the underlying hydrodynamic equations. Inspired by recent observations of Bose-Einstein condensation (BEC) in bubble-shaped traps in microgravity ultracold quantum gas experiments, we show that equatorial modes are supported by a rapidly rotating condensate in a spherical geometry. Based on a zero-temperature coarse-grained hydrodynamic framework, we reformulate the coupled oscillations of the superfluid and the Abrikosov vortex lattice resulting from rotation by a Schr\"odinger-like eigenvalue problem. The obtained non-Hermitian Hamiltonian is topologically nontrivial. Furthermore, we solve the hydrodynamic equations for a spherical geometry and find that the rotating superfluid hosts Kelvin, Yanai, and Poincar\'e equatorial modes, but not the Rossby mode. Our predictions can be tested with state-of-the-art bubble-shaped trapped BEC experiments.Comment: 11 pages, 5 figure

    Rapidly Rotating Bose-Einstein Condensates in Strongly Anharmonic Traps

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    We study a rotating Bose-Einstein Condensate in a strongly anharmonic trap (flat trap with a finite radius) in the framework of 2D Gross-Pitaevskii theory. We write the coupling constant for the interactions between the gas atoms as 1/ϵ21/\epsilon^2 and we are interested in the limit ϵ0\epsilon\to 0 (TF limit) with the angular velocity Ω\Omega depending on ϵ\epsilon. We derive rigorously the leading asymptotics of the ground state energy and the density profile when Ω\Omega tends to infinity as a power of 1/ϵ1/\epsilon. If Ω(ϵ)=Ω0/ϵ\Omega(\epsilon)=\Omega_0/\epsilon a ``hole'' (i.e., a region where the density becomes exponentially small as 1/ϵ1/\epsilon\to\infty) develops for Ω0\Omega_0 above a certain critical value. If Ω(ϵ)1/ϵ\Omega(\epsilon)\gg 1/\epsilon the hole essentially exhausts the container and a ``giant vortex'' develops with the density concentrated in a thin layer at the boundary. While we do not analyse the detailed vortex structure we prove that rotational symmetry is broken in the ground state for const.logϵ<Ω(ϵ)const./ϵ{\rm const.}|\log\epsilon|<\Omega(\epsilon)\lesssim \mathrm{const.}/\epsilon.Comment: LaTex2e, 28 pages, revised version to be published in Journal of Mathematical Physic
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