Energy and Vorticity in Fast Rotating Bose-Einstein Condensates

Abstract

We study a rapidly rotating Bose-Einstein condensate confined to a finite trap in the framework of two-dimensional Gross-Pitaevskii theory in the strong coupling (Thomas-Fermi) limit. Denoting the coupling parameter by $1/\eps^2$ and the rotational velocity by $\Omega$, we evaluate exactly the next to leading order contribution to the ground state energy in the parameter regime $|\log\eps|\ll Ω\ll 1/(\eps^2|\log\eps|)$ with $\eps\to 0$. While the TF energy includes only the contribution of the centrifugal forces the next order corresponds to a lattice of vortices whose density is proportional to the rotational velocity.

19 pages, LaTeX; typos corrected, clarifying remarks added, some rearrangements in the text

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• Quantum Hall phases and plasma analogy in rotating trapped Bose gases
• Critical Rotational Speeds for Superfluids in Homogeneous Traps
• Local density approximation for the almost-bosonic anyon gas
• Critical Rotational Speeds in the Gross-Pitaevskii Theory on a Disc with Dirichlet Boundary Conditions
• Higher Dimensional Coulomb Gases and Renormalized Energy Functionals
• Inhomogeneous Vortex Patterns in Rotating Bose-Einstein Condensates
• Vortex Rings in Fast Rotating Bose-Einstein Condensates
• Vortex density models for superconductivity and superfluidity
• Local Density Approximation for Almost-Bosonic Anyons
• Lieb-Robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems
• Fluctuations in the two-dimensional one-component plasma and associated fourth-order phase transition
• On compound vortices in a two-component Ginzburg-Landau functional
• Vortex Phases of Rotating Superfluids
• On the Third Critical Speed for Rotating Bose-Einstein Condensates
• Surface Effects in Superconductors with Corners
• Effects of Corners in Surface Superconductivity
• Equidistribution of jellium energy for Coulomb and Riesz Interactions
• The giant vortex state for a Bose-Einstein condensate in a rotating anharmonic trap : extreme rotation regimes
• Bosons in Rapid Rotation
• Energy of a rotating Bose-Einstein condensate in a harmonic trap
• Annular Bose-Einstein Condensates in the Lowest Landau Level