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arXiv:1308.5601 · Physical Review Letters

Emergent Kinetics and Fractionalized Charge in 1D Spin-Orbit Coupled Flatband Optical Lattices

Fei Lin, Chuanwei Zhang, V. W. Scarola

Published Mar 18, 2014• 24 citations
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Abstract

Recent ultracold atomic gas experiments implementing synthetic spin-orbit coupling allow access to flatbands that emphasize interactions. We model spin-orbit coupled fermions in a one-dimensional flatband optical lattice. We introduce an effective Luttinger-liquid theory to show that interactions generate collective excitations with emergent kinetics and fractionalized charge, analogous to properties found in the two-dimensional fractional quantum Hall regime. Observation of these excitations would provide an important platform for exploring exotic quantum states derived solely from interactions.

DOI
10.1103/physrevlett.112.110404

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Recent ultracold atomic gas experiments implementing synthetic spin-orbit coupling allow access to flatbands that emphasize interactions. We model spin-orbit coupled fermions in a one-dimensional flatband optical lattice. We introduce an effective Luttinger-liquid theory to show that interactions generate collective excitations with emergent kinetics and fractionalized charge, analogous to properties found in the two-dimensional fractional quantum Hall regime. Observation of these excitations would provide an important platform for exploring exotic quantum states derived solely from interactions.
Recent ultracold atomic gas experiments implementing synthetic spin-orbit coupling allow access to flat bands that emphasize interactions. We model spin-orbit coupled fermions in a one-dimensional flat band optical lattice. We introduce an effective Luttinger liquid theory to show that interactions generate collective excitations with emergent kinetics and fractional charge, analogous to emergence of Fermi-liquid properties in the fractional quantum Hall regime. Observation of these excitations would provide an important platform for exploring exotic quantum states derived solely from interactions.
Artificial spin-orbit coupling in optical lattices can be engineered to tune band structure into extreme regimes where the single-particle band flattens leaving only interparticle interactions to define many-body states of matter. Lin et al. [F. Lin, C. Zhang, and V. W. Scarola, Phys. Rev. Lett. 112, 110404 (2014)] showed that under such conditions interactions lead to a Wigner crystal of fermionic atoms under approximate conditions: no bandwidth or band mixing. The excitations were shown to possess emergent kinetics with fractionalized charge derived entirely from interactions. In this work we use numerical exact diagonalization to study a more realistic model with nonzero bandwidth and band mixing. We map out the stability phase diagram of the Wigner crystal. We find that emergent properties of the Wigner crystal excitations remain stable for realistic experimental parameters. Our results validate the approximations made by Lin et al. and define parameter regimes where strong interaction effects generate emergent kinetics in optical lattices.
This work theoretically studies spin-1 bosons with antiferromagnetic interactions and synthetic spin-orbit coupling in a one-dimensional lattice, showing the appearance of a robust superfluid spin-liquid phase and a correlated charge density wave. Signatures of these states can be observed in ultracold gases of 23{}^{23}23Na in an optical lattice within experimentally accessible parameters.
At low temperatures bosons typically condense to minimize their single-particle kinetic energy while interactions stabilize superfluidity. Optical lattices with artificial spin-orbit coupling challenge this paradigm, because here kinetic energy can be quenched in an extreme regime where the single-particle band flattens. To probe the fate of superfluidity in the absence of kinetics we construct and numerically solve interaction-only tight-binding models in flatbands. We find that superfluid states arise entirely from interactions operating in quenched kinetic energy bands, thus revealing a distinct and unexpected condensation mechanism. Our results have important implications for the identification of quantum condensed phases of ultracold bosons beyond conventional paradigms.
Ultracold atoms in optical lattices serve as a tool to model different physical phenomena appearing originally in condensed matter. To study magnetic phenomena one needs to engineer synthetic fields as atoms are neutral. Appropriately shaped optical potentials force atoms to mimic charged particles moving in a given field. We present the realization of artificial gauge fields for the observation of anomalous Hall effect. Two species of attractively interacting ultracold fermions are considered to be trapped in a shaken two dimensional triangular lattice. A combination of interaction induced tunneling and shaking can result in an emergent Dice lattice. In such a lattice the staggered synthetic magnetic flux appears and it can be controlled with external parameters. The obtained synthetic fields are non-Abelian. Depending on the tuning of the staggered flux we can obtain either anomalous Hall effect or its quantized version. Our results are reminiscent of Anomalous Hall conductivity in spin-orbit coupled ferromagnets.
Recently it has been theoretically proposed and experimentally demonstrated that a spin-orbit coupled multicomponent gas in a 1D lattice can be viewed as a spinless gas in a synthetic 2D lattice with a magnetic flux. In this Letter we consider interaction effects in such a Fermi gas, and propose these effects can be easily detected in a charge pumping experiment. Using 1/3 filling of the lowest 2D band as an example, in the strongly interacting regime, we show that the charge pumping value gradually approaches a universal fractional value for large spin components and low filling of the 1D lattice, indicating a fractional quantum Hall-type behavior, while the charge pumping value is zero if the 1D lattice filling is commensurate, indicating a Mott insulator behavior. The charge-density-wave order is also discussed.