Related papers: Tkachenko waves in rapidly rotating Bose-Einstein …
We directly image Tkachenko waves in a vortex lattice in a dilute-gas Bose-Einstein condensate. The low (sub-Hz) resonant frequencies are a consequence of the small but nonvanishing elastic shear modulus of the vortex-filled superfluid. The…
We calculate the in-plane modes of the vortex lattice in a rotating Bose condensate from the Thomas-Fermi to the mean-field quantum Hall regimes. The Tkachenko mode frequency goes from linear in the wavevector, $k$, for lattice rotational…
We calculate the frequencies of the Tkachenko oscillations of a vortex lattice in a harmonically trapped superfluid Fermi gas. We use the elasto-hydrodynamic theory by properly accounting for the elastic constants, the Thomas-Fermi density…
The present paper suggests the continuum theory of Tkachenko modes in a rotating 2D Bose-Einstein condensate taking into account density inhomogeneity and compressibility of the condensate. The problem requires solution of coupled…
We have calculated the low-lying elementary excitations of three-dimensional few-vortex arrays in trapped Bose-Einstein condensates. The number of different Kelvin-Tkachenko vortex wave branches matches the number of vortices in the…
After delineating the physical regimes which vortex lattices encounter in rotating Bose-Einstein condensates as the rotation rate, $\Omega$, increases, we derive the normal modes of the vortex lattice in two dimensions at zero temperature.…
We consider a periodic vortex lattice in a rotating Bose-Einstein condensed gas, where the centrifugal potential is exactly compensated by the external harmonic trap. By introducing a gauge transformation which makes the Hamiltonian…
This is a short review of theoretical and experimental studies of Tkachenko waves starting from their theoretical prediction by Tkachenko about 50 years ago up to their unambiguous experimental observation in the Bose--Einstein condensate…
We review the theory of vortices in trapped dilute Bose-Einstein condensates and compare theoretical predictions with existing experiments. Mean-field theory based on the time-dependent Gross-Pitaevskii equation describes the main features…
The elastic oscillations of the vortex lattice of a cold Bose gas (Tkachenko modes) are shown to play a crucial role in the saturation of the compressibility sum rule, as a consequence of the hybridization with the longitudinal degrees of…
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…
We have calculated collective mode spectra for three-dimensional, rotating Bose-Einstein condensates in oblate harmonic traps using the microscopic Bogoliubov-deGennes field theory. For condensates with $N_v$ vortices, $N_v$…
I review the basic physics of ultracold dilute trapped atomic gases, with emphasis on Bose-Einstein condensation and quantized vortices. The hydrodynamic form of the Gross-Pitaevskii equation (a nonlinear Schr{\"o}dinger equation)…
We establish the general equations of motion for the modes of a vortex lattice in a rapidly rotating Bose-Einstein condensate in three dimensions, taking into account the elastic energy of the lattice and the vortex line bending energy. As…
We construct an effective field theory describing the collective Tkachenko oscillation mode of a vortex lattice in a two-dimensional rotating Bose-Einstein condensate in the long-wavelength regime. The theory has the form of a…
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…
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…
Using path integral formalism, we show that the Abrikosov-Tkachenko vortex lattice may equivalently be understood as an array of Josephson junctions. The Tkachenko modes are found to be basically equivalent to the low energy excitations…
The dynamics of a ring of vortices in two-dimensional Bose-Einstein condensates (with and without an additional vortex at the center) is studied for (1) a uniform condensate in a rigid cylinder and (2) a nonuniform trapped condensate in the…
We have calculated low-lying quasiparticle excitation spectra of rotating three-dimensional Bose-Einstein condensates. As opposed to the prediction of hydrodynamic continuum theories, we find a minimum in the Tkachenko mode spectrum at…