Strongly correlated states of trapped ultracold fermions in deformed Landau levels

Abstract

We analyze the strongly correlated regime of a two-component trapped ultracold fermionic gas in a synthetic non-Abelian U (2) gauge potential, that consists of both a magnetic field and a homogeneous spin-orbit coupling. This gauge potential deforms the Landau levels (LLs) with respect to the Abelian case and exchanges their ordering as a function of the spin-orbit coupling. In view of experimental realizations, we show that a harmonic potential combined with a Zeeman term, gives rise to an angular momentum term, which can be used to test the stability of the correlated states obtained through interactions. We derive the Haldane pseudopotentials (HPs) describing the interspecies contact interaction within a lowest LL approximation. Unlike ordinary fractional quantum Hall systems and ultracold bosons with short-range interactions in the same gauge potential, the HPs for sufficiently strong non-Abelian fields show an unconventional nonmonotonic behaviour in the relative angular momentum. Exploiting this property, we study the occurrence of new incompressible ground states as a function of the total angular momentum. In the first deformed Landau level (DLL) we obtain Laughlin and Jain states. Instead, in the second DLL three classes of stabilized states appear: Laughlin states, a series of intermediate strongly correlated states and finally vortices of the integer quantum Hall state. Remarkably, in the intermediate regime, the non-monotonic HPs of the second DLL induce two-particle correlations which are reminiscent of paired states such as the Haffnian state. Via exact diagonalization in the disk geometry, we compute experimentally relevant observables such as density profiles and correlations, and we study the entanglement spectra as a further tool to characterize the obtained strongly correlated states.

Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials

“…In previous works, theoretical investigations have shown that synthetic non-Abelian gauge potentials are an efficient way of implementing exotic quantum Hall systems [44][45][46][47][48][49][50] or topological phases [51][52][53][54][55] in two-dimensional lattices, and that laser assisted tunneling may provide useful tools for the simulation of particles like massless Dirac fermions [45], Wilson fermions [56] or Weyl fermions [57].…”

“…Beyond the tunability of the experimental parameters, another important advantage of considering ultracold atom systems is that in these setups one can also study generalizations of the Abelian π-flux model that involve artificial non-Abelian gauge potentials [36], including the effects of a spin-momentum coupling independent on the position. In previous works, theoretical investigations have shown that synthetic non-Abelian gauge potentials are an efficient way of implementing exotic quantum Hall systems [44][45][46][47][48][49][50] or topological phases [51][52][53][54][55] in two-dimensional lattices, and that laser assisted tunneling may provide useful tools for the simulation of particles like massless Dirac fermions [45], Wilson fermions [56] or Weyl fermions [57].…”

Bandwidth-resonant Floquet states in honeycomb optical lattices

“…For example, one can create quasi-periodic onedimensional systems (Amico et al 2005), realise p-band condensates (Wirth et al 2011(Wirth et al , Ölschläger et al 2013, or even do atomtronics (Seaman et al 2007), which aims at simulating electronic circuits. Due to this great flexibility, the recent realisation of topological states in condensed-matter systems (König et al 2007, Hasan and Kane 2010, Qi and Zhang 2010 has sparked a flurry of activities in the field of cold atoms, aiming at reproducing, engineering, and manipulating these fascinating quantum states in traps (Roncaglia et al 2011, Corman et al 2014, Burrello et al 2015 and in optical lattices (Hemmerich and Morais Smith 2007, Aidelsburger et al 2013, Miyake et al 2013, Jotzu et al 2014, Aidelsburger et al 2015, Chomaz et al 2015.…”

“…The recent realisation of topoplogical states in condensed-matter systems (König et al 2007, Hasan & Kane 2010, Qi & Zhang 2010 has sparked a flurry of activities in the field of cold atoms, aiming at reproducing, engineering, and manipulating these fascinating quantum states in traps (Roncaglia et al 2011, Corman et al 2014, Burrello et al 2015 and in optical lattices (Hemmerich & Morais Smith 2007, Aidelsburger et al 2013, Miyake et al 2013, Jotzu et al 2014, Aidelsburger et al 2015, Chomaz et al 2015.…”