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arXiv:1809.04493 · Physical Review Letters

Fractional Quantum Hall Phases of Bosons with Tunable Interactions: From the Laughlin Liquid to a Fractional Wigner Crystal

Tobias Graß, Przemysław Bienias, Michael J. Gullans, Rex Lundgren, Joseph Maciejko, Alexey Vyacheslavovich Gorshkov

Published Dec 18, 2018• 20 citations
arXivHTMLPDF

Abstract

Highly tunable platforms for realizing topological phases of matter are emerging from atomic and photonic systems and offer the prospect of designing interactions between particles. The shape of the potential, besides playing an important role in the competition between different fractional quantum Hall phases, can also trigger the transition to symmetry-broken phases, or even to phases where topological and symmetry-breaking order coexist. Here, we explore the phase diagram of an interacting bosonic model in the lowest Landau level at half filling as two-body interactions are tuned. Apart from the well-known Laughlin liquid, Wigner crystal, stripe, and bubble phases, we also find evidence of a phase that exhibits crystalline order at fractional filling per crystal site. The Laughlin liquid transits into this phase when pairs of bosons strongly repel each other at relative angular momentum 4ℏ. We show that such interactions can be achieved by dressing ground-state cold atoms with multiple different-parity Rydberg states.

DOI
10.1103/physrevlett.121.253403

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The fractional quantum Hall (FQH) nematic state is a conjectured state of matter in which FQH topological order coexists with spontaneously broken rotation symmetry. Recent experiments on GaAs quantum wells suggest this state, as well as the concomitant isotropic-nematic phase transition, may be realized in a two-dimensional electron gas at certain rational filling factors. Although effective field theories of the FQH nematic state have been constructed, there has been so far no explicit realization of this state as the ground state of a microscopic model of interacting electrons. The authors show via a variational approach and numerical exact diagonalization that tuning Haldane pseudopotentials in a model of interacting electrons in the lowest Landau level induces a quantum phase transition out of the isotropic Laughlin FQH liquid and into the FQH nematic state.
Recent proposals of topological flat band models have provided a new route to realize the fractional quantum Hall effect without Landau levels. We study hard-core bosons with short-range interactions in two representative topological flat band models, one of which is the well-known Haldane model (but with different parameters). We demonstrate that fractional quantum Hall states emerge with signatures of an even number of quasidegenerate ground states on a torus and a robust spectrum gap separating these states from the higher energy spectrum. We also establish quantum phase diagrams for the filling factor 1/2 and illustrate quantum phase transitions to other competing symmetry-breaking phases.
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Strongly interacting topological matter exhibits fundamentally new phenomena with potential applications in quantum information technology. Emblematic instances are fractional quantum Hall states, where the interplay of magnetic fields and strong interactions gives rise to fractionally charged quasi-particles, long-ranged entanglement, and anyonic exchange statistics. Progress in engineering synthetic magnetic fields has raised the hope to create these exotic states in controlled quantum systems. However, except for a recent Laughlin state of light, preparing fractional quantum Hall states in engineered systems remains elusive. Here, we realize a fractional quantum Hall (FQH) state with ultracold atoms in an optical lattice. The state is a lattice version of a bosonic ν=1/2ν=1/2ν=1/2 Laughlin state with two particles on sixteen sites. This minimal system already captures many hallmark features of Laughlin-type FQH states: we observe a suppression of two-body interactions, we find a distinctive vortex structure in the density correlations, and we measure a fractional Hall conductivity of σH/σ0=0.6(2)σ_\text{H}/σ_0= 0.6(2)σH​/σ0​=0.6(2) via the bulk response to a magnetic perturbation. Furthermore, by tuning the magnetic field we map out the transition point between the normal and the FQH regime through a spectroscopic probe of the many-body gap. Our work provides a starting point for exploring highly entangled topological matter with ultracold atoms.