Strongly correlated states of trapped ultracold fermions in deformed Landau levels

TL;DR

This paper investigates the emergence of novel strongly correlated quantum states in ultracold fermionic gases subjected to non-Abelian gauge potentials that deform Landau levels, revealing unconventional behaviors and new incompressible states.

Contribution

It introduces a detailed analysis of non-monotonic Haldane pseudopotentials in deformed Landau levels and identifies new correlated states, including intermediate and vortex states, in a trapped ultracold fermionic system.

Findings

Observation of Laughlin and Jain states in the first DLL

Discovery of intermediate strongly correlated states in the second DLL

Identification of vortex states and paired-like correlations

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 non-monotonic 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.