2004/05/31 by S. Andrew Gifford, Gordon Baym · 22 citations
Physics and Astronomy · #Bose–Einstein condensate #Classical mechanics #Coherence length #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Instability #Lattice (music) #Mechanics #Physics #Physics of Superconductivity and Magnetism #Strong Light-Matter Interactions #Superconductivity #Transverse plane #Vortex #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreva.70.033602
published in Physical Review A 70(3) (American Physical Society) · 10 pages, 2 figures, Changes include the addition of the particle density - vortex density coupling and the correct value of the shear modulus
openalex publication_date 2004/09/02 · arxiv created 2008/06/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 in two dimensions, the vortex lattice supports Tkachenko and gapped sound modes. In contrast, in three dimensions the Tkachenko mode frequency at long wavelengths becomes linear in the wave vector for any propagation direction out of the transverse plane. We compute the correlation functions of the vortex displacements and the superfluid order parameter for a homogeneous Bose gas of bounded extent in the axial direction. At zero temperature the vortex displacement correlations are convergent at large separation, but at finite temperatures, they grow with separation. The growth of the vortex displacements should lead to observable melting of vortex lattices at higher temperatures and somewhat lower particle number and faster rotation than in current experiments. At zero temperature a system of large extent in the axial direction maintains long range order-parameter correlations for large separation, but at finite temperatures the correlations decay with separation.