We consider the persistent currents induced by an artificial gauge field applied to interacting ultra-cold bosonic atoms in a tight ring trap. Using both analytical and numerical methods, we study the scaling of the persistent current amplitude with
the size of the ring. In the strongly interacting regime we find a power-law scaling, in good agreement with the predictions of the Luttinger-liquid theory. By exploring all interaction regimes we find that the scaling is optimal, i.e. the current amplitude decreases slower with the system size, at intermediate interactions.
We study persistent currents for interacting one-dimensional bosons on a tight ring trap, subjected to a rotating barrier potential, which induces an artificial U(1) gauge field. We show that, at intermediate interactions, the persistent current resp
onse is maximal, due to a subtle interplay of effects due to the barrier, the interaction and quantum fluctuations. These results are relevant for ongoing experiments with ultracold atomic gases on mesoscopic rings.
Considerable efforts are currently devoted to the preparation of ultracold neutral atoms in the emblematic strongly correlated quantum Hall regime. The routes followed so far essentially rely on thermodynamics, i.e. imposing the proper Hamiltonian an
d cooling the system towards its ground state. In rapidly rotating 2D harmonic traps the role of the transverse magnetic field is played by the angular velocity. For particle numbers significantly larger than unity, the required angular momentum is very large and it can be obtained only for spinning frequencies extremely near to the deconfinement limit; consequently, the required control on experimental parameters turns out to be far too stringent. Here we propose to follow instead a dynamic path starting from the gas confined in a rotating ring. The large moment of inertia of the fluid facilitates the access to states with a large angular momentum, corresponding to a giant vortex. The initial ring-shaped trapping potential is then adiabatically transformed into a harmonic confinement, which brings the interacting atomic gas in the desired quantum Hall regime. We provide clear numerical evidence that for a relatively broad range of initial angular frequencies, the giant vortex state is adiabatically connected to the bosonic $ u=1/2$ Laughlin state, and we discuss the scaling to many particles.
