Validity of the Lowest Landau Level Approximation for Rotating Bose Gases

Abstract

The energy spectrum for an ultracold rotating Bose gas in a harmonic trap is calculated exactly for small systems, allowing the atoms to occupy several Landau levels. Two vortex-like states and two strongly correlated states (the Pfaffian and Laughlin) are considered in detail. In particular, their critical rotation frequencies and energy gaps are determined as a function of particle number, interaction strength, and the number of Landau levels occupied (up to three). For the vortex-like states, the Lowest Landau level (LLL) approximation is justified only if the interaction strength decreases with the number of particles; nevertheless, the constant of proportionality increases rapidly with the angular momentum per particle. For the strongly correlated states, however, the interaction strength can increase with particle number without violating the LLL condition. The results suggest that in large systems, the Pfaffian and Laughlin states might be stabilized at rotation frequencies below the centrifugal limit for sufficiently large interaction strengths, with energy gaps a significant fraction of the trap energy.

Ver. 3: Updated acknowledgements, minor corrections. 8 pages, 9 figures

References in corpus (4)

• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Edge excitations and Topological orders in rotating Bose gases
• Dynamical role of anyonic excitation statistics in rapidly rotating Bose gases

Cited by in corpus (6)

• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Quantum Hall physics in rotating Bose-Einstein condensates
• Rapidly rotating boson molecules with long or short range repulsion: an exact diagonalization study
• Gaussian potentials facilitate access to quantum Hall states in rotating Bose gases
• Fractional Spin Hall Effect in Atomic Bose Gases
• Topological Entropy of Quantum Hall States in Rotating Bose Gases