The Yrast Line of a Rapidly Rotating Bose Gas: Gross-Pitaevskii Regime

Abstract

We consider an ultracold rotating Bose gas in a harmonic trap close to the critical angular velocity so that the system can be considered to be confined to the lowest Landau level. With this assumption we prove that the Gross-Pitaevskii energy functional accurately describes the ground state energy of the corresponding $N$-body Hamiltonian with contact interaction provided the total angular momentum $L$ is much less than $N^2$. While the Gross-Pitaevskii energy is always an obvious variational upper bound to the ground state energy, a more refined analysis is needed to establish it as an exact lower bound. We also discuss the question of Bose-Einstein condensation in the parameter range considered. Coherent states together with inequalities in spaces of analytic functions are the main technical tools.

RevTeX4, 9 pages; references added; to appear in Phys. Rev. A

References in corpus (3)

• Many-Body Physics with Ultracold Gases
• Strongly correlated phases in rapidly rotating Bose gases
• Trial wave functions, molecular states, and ro-vibrational spectra in the lowest Landau level: A universal description for bosons and fermions

Cited by in corpus (17)

• Strongly correlated phases in rapidly rotating Bose gases
• Quantum Hall states of bosons in rotating anharmonic traps
• Critical Rotational Speeds for Superfluids in Homogeneous Traps
• Vortex nucleation in mesoscopic Bose superfluid and breaking of the parity symmetry
• Vortices in Bose-Einstein condensates - finite-size effects and the thermodynamic limit
• Solitary waves and yrast states in Bose-Einstein condensed gases of atoms
• Incompressibility Estimates for the Laughlin Phase
• Rotating Bose-Einstein condensates: Closing the gap between exact and mean-field solutions
• Quantal molecular description and universal aspects of the spectra of bosons and fermions in the lowest Landau level
• Beyond mean-field behavior of large Bose-Einstein condensates in double-well potentials
• Some contributions to many-body quantum mathematics
• Hot Topics in Cold Gases
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Asymptotically exact trial wave functions for yrast states of rotating Bose gases
• On the Third Critical Speed for Rotating Bose-Einstein Condensates
• Thomas-Fermi profile of a fast rotating Bose-Einstein condensate
• A two-state model for vortex nucleation in a rotating Bose-Einstein condensate