Rapidly Rotating Bose-Einstein Condensates in Strongly Anharmonic Traps

Abstract

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 $1/{\epsilon }^2$ and we are interested in the limit $\epsilon \to 0$ (TF limit) with the angular velocity $\Omega$ depending on $\epsilon$. We derive rigorously the leading asymptotics of the ground state energy and the density profile when $\Omega$ tends to infinity as a power of $1/\epsilon$. If $\Omega (\epsilon )={\Omega }_0/\epsilon$ a ``hole'' (i.e., a region where the density becomes exponentially small as $1/\epsilon \to \infty$) develops for ${\Omega }_0$ above a certain critical value. If $\Omega (\epsilon )\gg 1/\epsilon$ 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 $const.|\log \epsilon |<\Omega (\epsilon )\lesssim const./\epsilon$.

LaTex2e, 28 pages, revised version to be published in Journal of Mathematical Physics

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Cited by in corpus (19)

• The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate
• Energy and Vorticity in Fast Rotating Bose-Einstein Condensates
• Rotating superfluids in anharmonic traps: From vortex lattices to giant vortices
• Ground-state multiquantum vortices in rotating two-species superfluids
• Critical Rotational Speeds for Superfluids in Homogeneous Traps
• Rapidly Rotating Bose-Einstein Condensates in Homogeneous Traps
• Vortex Rings in Fast Rotating Bose-Einstein Condensates
• The TF Limit for Rapidly Rotating Bose Gases in Anharmonic Traps
• On mathematical models for Bose-Einstein condensates in optical lattices (expanded version)
• Some contributions to many-body quantum mathematics
• Vortices in rotating Bose-Einstein condensates confined in homogeneous traps
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Vortex Phases of Rotating Superfluids
• On the Third Critical Speed for Rotating Bose-Einstein Condensates
• Surface Effects in Superconductors with Corners
• The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases
• The giant vortex state for a Bose-Einstein condensate in a rotating anharmonic trap : extreme rotation regimes
• Bosons in Rapid Rotation
• Rigorous derivation of the hydrodynamical equations for rotating superfluids