Magnetic crystals and helical liquids in alkaline-earth fermionic gases

Abstract

The joint action of a magnetic field and of interactions is crucial for the appearance of exotic quantum phenomena, such as the quantum Hall effect. Owing to their rich nuclear structure, equivalent to an additional synthetic dimension, one-dimensional alkaline-earth(-like) fermionic gases with synthetic gauge potential and atomic contact repulsion may display similar related properties. Here we show the existence and the features of a hierarchy of fractional insulating and conducting states by means of analytical and numerical methods. We demonstrate that the gapped states are characterized by density and magnetic order emerging solely for gases with effective nuclear spin larger than 1/2, whereas the gapless phases can support helical modes. We finally argue that these states are related to an unconventional fractional quantum Hall effect in the thin-torus limit and that their properties can be studied in state-of-the-art laboratories.

Chiral currents in one-dimensional fractional quantum Hall states

“…1. On the other hand, the density should be small compared to unity, otherwise, lattice effects would take effect 20 . Therefore, we expect the behavior in Fig.…”

“…Upon increasing the range of interactions, we find that arbitrary Laughlin ν = 1/m states can be stabilized even at small inter-chain coupling. The required range of interactions increases 20 for low filling factors; the ν = 1/3 state already requires interactions between nearest neighbour rungs, while the ν = 1/2 bosonic state is stabilized for sufficiently strong but only on-rung interactions 9 . Interestingly, in the synthetic dimension realizations of quantum ladders, the interactions become non-local in the synthetic dimension 18,19,22 (along the rungs), allowing one to reach this bosonic FQH state.…”

“…Recently, an observation of chiral edge states was achieved using fermionic 18 and bosonic 19 1D gases with an extra synthetic dimension originating from nuclear spin degrees of freedom. This setup was theoretically envisioned to stabilise exotic states such as the fractional helical state, and numerically studied using density matrix renormalization group (DMRG) methods 20,21 .…”

Synthetic Dimensions and Spin-Orbit Coupling with an Optical Clock Transition

“…[14,15], where synthetic flux ladders have been implemented by using the spin degree of freedom, and has allowed the first observation of chiral edge states in ultracold atomic systems. Its extension has inspired several proposals, opening the way, e.g., to the observation of new quantum states [16,17], to the detection of fractional charge pumping [18,19], or to the observation of the four-dimensional quantum Hall effect [20].In this Letter, we demonstrate that SOC and SDs can be efficiently implemented by exploiting different degrees of freedom, specifically, the long-lived electronic state of alkaline-earth(-like) atoms. By using the technology developed in the context of optical atomic clocks, we induce a coherent coupling between the ground state g ¼ 1 S 0 and the metastable state e ¼ 3 P 0 (lifetime ∼20 s) of ultracold 173 Yb atoms.…”

“…[14,15], where synthetic flux ladders have been implemented by using the spin degree of freedom, and has allowed the first observation of chiral edge states in ultracold atomic systems. Its extension has inspired several proposals, opening the way, e.g., to the observation of new quantum states [16,17], to the detection of fractional charge pumping [18,19], or to the observation of the four-dimensional quantum Hall effect [20].…”