Quantum Hall states of bosons in rotating anharmonic traps

Abstract

We study a model of bosons in the lowest Landau level in a rotating trap where the confinement potential is a sum of a quadratic and a quartic term. The quartic term improves the stability of the system against centrifugal deconfinement and allows to consider rotation frequencies beyond the frequency of the quadratic part. The interactions between particles are modeled by a Dirac delta potential. We derive rigorously conditions for ground states of the system to be strongly correlated in the sense that they are confined to the kernel of the interaction operator, and thus contain the correlations of the Bose-Laughlin state. Rigorous angular momentum estimates and trial state arguments indicate a transition from a pure Laughlin state to a state containing in addition a giant vortex at the center of the trap (Laughlin quasi-hole). There are also indications of a second transition where the density changes from a flat profile in a disc or an annulus to a radial Gaussian confined to a thin annulus.

References in corpus (3)

• Composite fermion theory of rapidly rotating two-dimensional bosons
• Lowest Landau Level vortex structure of a Bose-Einstein condensate rotating in a harmonic plus quartic trap
• Gaussian potentials facilitate access to quantum Hall states in rotating Bose gases

Cited by in corpus (14)

• Emergence of fractional statistics for tracer particles in a Laughlin liquid
• Quantum Hall phases and plasma analogy in rotating trapped Bose gases
• Local incompressibility estimates for the Laughlin phase
• Higher Dimensional Coulomb Gases and Renormalized Energy Functionals
• Incompressibility Estimates for the Laughlin Phase
• Linear and nonlinear edge dynamics of trapped fractional quantum Hall droplets
• Some contributions to many-body quantum mathematics
• Quantum statistics transmutation via magnetic flux attachment
• The Laughlin liquid in an external potential
• Stability of the Laughlin phase against long-range interactions
• Fragility of the Laughlin state in an anharmonically-trapped Bose-Einstein condensate
• Effect of non-local interactions on the vortex solution in Bose-Einstein Condensates
• Equidistribution of jellium energy for Coulomb and Riesz Interactions
• Transition from the mean-field to the bosonic Laughlin state in a rotating Bose-Einstein condensate