Non-Abelian Anyons from Degenerate Landau Levels of Ultracold Atoms in Artificial Gauge Potentials

Abstract

We show that non-abelian potentials acting on ultracold gases with two hyperfine levels can give rise to ground states with non-abelian excitations. We consider a realistic gauge potential for which the Landau levels can be exactly determined: the non-abelian part of the vector potential makes the Landau levels non-degenerate. In the presence of strong repulsive interactions, deformed Laughlin ground states occur in general. However, at the degeneracy points of the Landau levels, non-abelian quantum Hall states appear: these ground states, including deformed Moore-Read states (characterized by Ising anyons as quasi-holes), are studied for both fermionic and bosonic gases.The quest for states of matter having non-abelian excitations has been very intense in the past two decades, motivated by interest for the topological properties of such correlated states [1,2] and by their relevance for the implementation of topological quantum computation schemes [2].Quantum Hall systems provide a major arena in which investigating non-abelian anyons, and a huge amount of work has been devoted to characterize which quantum Hall states are non-abelian and to propose (mainly interferometric) experiments to test the non-abelian nature of such states A significant and complementary issue consists in finding other experimental systems suitable to simulate the quantum Hall physics and realize non-abelian anyons. In this respect, ultracold atomic systems provide a natural candidate [5,6], due to the possibility of using them as simulators of many-body systems [7]. Two essential (but in general not sufficient) ingredients are available in ultracold atomic systems. First, one can simulate artificial magnetic fields by using

Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices

“…The same gaps close also at q = 2π/3, at interchanged quasi-momenta k. From the analysis of the spectrum it is clear that this closing of the gap corresponds to a further Dirac cone appearing in the bulk of the system. However this does not correspond simply to a crossing of Landau levels, as we would expect in a similar system in the continuous limit [40,41]; instead, it is a topological phase transition which changes the Chern numbers of the involved bands, thus affecting the number of edge states in a geometry with boundaries. No change in the Chern number arises instead along the phase transition between a semimetal and an insulating phase.…”

Josephson physics of spin-orbit-coupled elongated Bose-Einstein condensates

“…We have reduced the problem from eight to six equations and checked that these equations give the same numerical results as Eqs. (17) and (18). Notice that if S ± , , andδ vanish, these equations give back those of the two-component two-well problem discussed in Ref.…”

“…Since we assumed that m 1 = m 2 = m, and therefore one can use the same localized function for the two components, we obtain that S = 0 and 1 = 2 , and consequently the corresponding terms are absent in Eqs. (17) and (18).…”

Vortex lattices for ultracold bosonic atoms in a non-Abelian gauge potential

“…There exists a variety of proposed ways to generate non-Abelian gauge potentials, both in the continuum [9,10] and in lattice-based systems [11][12][13] In this paper, we study the consequences of a U (2) non-Abelian gauge field on the groundstate of a weakly interacting atomic BEC. We focus on a gauge-field configuration in which the effective magnetic field is constant in space, and for which there exists a simple exact solution for the single particle wavefunctions [14][15][16][17]. In the case of a uniform Abelian magnetic field (or for uniform rotation of the gas) the spectrum has the Landau level structure.…”