From rotating atomic rings to quantum Hall states

Abstract

Considerable efforts are currently devoted to the preparation of ultracold neutral atoms in the strongly correlated quantum Hall regime. However, the necessary angular momentum is very large and in experiments with rotating traps this means spinning frequencies extremely near to the deconfinement limit; consequently, the required control on parameters turns out to be too stringent. Here we propose instead to follow a dynamic path starting from the gas initially confined in a rotating ring. The large moment of inertia of the ring-shaped fluid facilitates the access to large angular momenta, corresponding to giant vortex states. The trapping potential is then adiabatically transformed into a harmonic confinement, which brings the interacting atomic gas in the desired quantum-Hall regime. We provide numerical evidence that for a broad range of initial angular frequencies, the giant-vortex state is adiabatically connected to the bosonic ν = 1/2 Laughlin state.

Quantum Hall states of bosons in rotating anharmonic traps

“…Finally we discuss the connection between our approach and the experimental proposal of [11]. There it is argued that a convenient way of creating the Laughlin state in a cold Bose gas would be via a dynamical procedure.…”

“…With a careful tuning of parameters, one then ends up with a gas where interactions dominate the physics and thus strongly correlated states should emerge. Since the angular momentum is conserved during the adiabatic evolution, if one manages to first create a condensate with momentum N (N −1), the final evolved state should be the Laughlin state, and [11] mostly emphasizes this case. If one instead starts from a BEC with a larger momentum N (N − 1) + mN it is likely that the final evolved state will be the corresponding Laughlin times giant vortex (VI.1).…”

“…As in our approach an anharmonic trap is used, but this only in a first step. The main idea of [11] is to first use a "Mexican hat" anharmonic potential to create a rotating BEC with a large angular momentum concentrated in a giant vortex at the center of the trap. In a second step one would then stop the rotation and change adiabatically the trap from Mexican hat like to purely harmonic.…”

“…The theorems stated in Section IV are proved in Section V. In Section VI we discuss the determination of the one-body density in the strongly correlated trial states considered and its implications for the interpretation and improvement of the results of Section IV. A final Section VII summarizes our findings and discusses their relation to the recent paper [11].…”

“…Clearly this corresponds to a singular limit where the gas is no longer confined against centrifugal forces. This is the main source of difficulty that has to be overcome to create the Bose-Laughlin state (see [11] for a more quantitative discussion and [12,13] for state of the art experiments in this direction). A natural proposal [8,12,14] is to add a confining term that should be stronger than quadratic (i.e., stronger than the centrifugal force).…”