Strongly correlated phases in rapidly rotating Bose gases
arXiv:0906.0741 · doi:10.1007/s10955-009-9833-y
Abstract
We consider a system of trapped spinless bosons interacting with a repulsive potential and subject to rotation. In the limit of rapid rotation and small scattering length, we rigorously show that the ground state energy converges to that of a simplified model Hamiltonian with contact interaction projected onto the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles, we also prove convergence of states; in particular, in a certain regime we show convergence towards the bosonic Laughlin wavefunction. This is the first rigorous justification of the effective FQHE Hamiltonian for rapidly rotating Bose gases. We review previous results on this effective Hamiltonian and outline open problems.
AMSLaTeX, 23 pages
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Cited by in corpus (22)
- Coulomb and Riesz gases: The known and the unknown
- Quantum Hall phases and plasma analogy in rotating trapped Bose gases
- The Yrast Line of a Rapidly Rotating Bose Gas: Gross-Pitaevskii Regime
- Quantum Hall states of bosons in rotating anharmonic traps
- Critical Rotational Speeds for Superfluids in Homogeneous Traps
- Local incompressibility estimates for the Laughlin phase
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- Rotating Bose-Einstein condensates: Closing the gap between exact and mean-field solutions
- Some contributions to many-body quantum mathematics
- Hot Topics in Cold Gases
- Quantum statistics transmutation via magnetic flux attachment
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- Holomorphic quantum Hall states in higher Landau levels
- Vortex Phases of Rotating Superfluids
- Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
- Stability of the Laughlin phase against long-range interactions
- Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states
- Thomas-Fermi profile of a fast rotating Bose-Einstein condensate
- On a bulk gap strategy for quantum lattice models