Geometrically protected triple-point crossings in an optical lattice

We show how to realize topologically protected crossings of three energy bands, integer-spin analogs of Weyl fermions, in three-dimensional optical lattices. Our proposal only involves ultracold atom techniques that have already been experimentally demonstrated and leads to isolated triple-point crossings (TPCs) which are required to exist by a novel combination of lattice symmetries. The symmetries also allow for a new type of topological object, the type-II, or tilted, TPC. Our Rapid Communication shows that spin-1 Weyl points, which have not yet been observed in the bandstructure of crystals, are within reach of ultracold atom experiments.Comment: 5 pages, 2 figures + 3 pages, 3 figures supplemental material. Added appendix on model symmetries, fixed typos and added references. This is the final, published versio

Braiding of non-Abelian anyons using pairwise interactions

The common approach to topological quantum computation is to implement quantum gates by adiabatically moving non-Abelian anyons around each other. Here we present an alternative perspective based on the possibility of realizing the exchange (braiding) operators of anyons by adiabatically varying pairwise interactions between them rather than their positions. We analyze a system composed by four anyons whose couplings define a T-junction and we show that the braiding operator of two of them can be obtained through a particular adiabatic cycle in the space of the coupling parameters. We also discuss how to couple this scheme with anyonic chains in order to recover the topological protection.Comment: 8 pages, 7 figures. Errors corrected, clarifications and comments adde

Effects of disorder on Coulomb-assisted braiding of Majorana zero modes

Majorana zero modes in one-dimensional topological superconductors obey non-Abelian braiding statistics. Braiding manipulations can be realized by controlling Coulomb couplings in hybrid Majorana-transmon devices. However, strong disorder may induce accidental Majorana modes, which are expected to have detrimental effects on braiding statistics. Nevertheless, we show that the Coulomb-assisted braiding protocol is efficiently realized also in the presence of accidental modes. The errors occurring during the braiding cycle are small if the couplings of the computational Majorana modes to the accidental ones are much weaker than the maximum Coulomb coupling.Comment: 7 pages, 4 figures, this is the final, published versio

Reaching the quantum Hall regime with rotating Rydberg-dressed atoms

Despite the striking progress in the field of quantum gases, one of their much anticipated applications-the simulation of quantum Hall states-remains elusive: all experimental approaches so far have failed in reaching a sufficiently small ratio between atom and vortex densities. In this paper we consider rotating Rydberg-dressed atoms in magnetic traps: these gases offer strong and tunable nonlocal repulsive interactions and very low densities; hence they provide an exceptional platform to reach the quantum Hall regime. Based on the Lindemann criterion and the analysis of the interplay of the length scales of the system, we show that there exists an optimal value of the dressing parameters that minimizes the ratio between the filling factor of the system and its critical value to enter the Hall regime, thus making it possible to reach this strongly correlated phase for more than 1000 atoms under realistic conditions