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arXiv:1504.02263 · Physical Review Letters

Charge Pumping of Interacting Fermion Atoms in the Synthetic Dimension

Tian-Sheng Zeng, Ce Wang, Hui Zhai

Published Aug 28, 2015• 90 citations
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Abstract

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.

DOI
10.1103/physrevlett.115.095302

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We study a model of a two-dimensional ultracold atomic gas subjected to an ``optical flux lattice'': a laser configuration where Raman-dressed atoms experience a strong artificial magnetic field. This leads to a band structure of narrow energy bands with nonzero Chern numbers. We consider the case of two-level (spin-1/21/21/2) fermionic atoms in this lattice, interacting via a repulsive sss-wave contact interaction. Atoms restricted to the lowest band are described by an effective model of spinless fermions with interactions that couple states in a momentum-dependent manner across the Brillouin zone; a consequence of the Raman dressing of the two spin states. We present the results of detailed exact diagonalization studies of the many-body states for a range of filling factors, $\ensuremath{\nu}$. First, we present evidence for the existence of a phase with coupled ferromagnetic-nematic ordering, which was previously suggested by a mean-field analysis. Second, we present evidence indicating the presence of a Laughlin-like fractional quantum Hall state occurring at filling factor $\ensuremath{\nu}=1/3$. Finally, we observe a charge-density wave state at $\ensuremath{\nu}=1/2$, which we are able to cleanly distinguish from the Laughlin-like state by its translational symmetry breaking and relatively low participation ratio.
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.
Synthetic ladders pierced by a magnetic field realized with one-dimensional alkaline-earth(-like) fermionic gases represent a promising environment for the investigation of quantum-Hall physics with ultracold atoms. We unveil the existence of a hierarchy of insulating and conducting states which appear at fractional filling factors by means of both analytical and numerical methods based on the density-matrix renormalization group algorithm. Analogously to the original quantum Hall effect, we show that such states can be exploited for constructing a topological Thouless pump where the charge transported after one cycle is quantized to fractional values and demonstrate this behavior with a full many-body time-dependent calculation. We conclude with some results on Laughlin-like states in both fermionic and bosonic systems.
We study NNN-component interacting particles (hardcore bosons and fermions) loaded in topological lattice models with SU(N)\mathrm{SU}(N)SU(N)-invariant interactions based on exact diagonalization and density matrix renormalization group method. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that a class of SU(N)\mathrm{SU}(N)SU(N) fractional quantum Hall states can emerge at fractional filling factors $\ensuremath{\nu}=N/(N+1)$ for bosons [$\ensuremath{\nu}=N/(2N+1)$ for fermions] in the lowest Chern band, characterized by the nontrivial fractional Hall responses and the fractional charge pumping. Moreover, we establish a topological characterization based on the K\mathbf{K}K matrix and discuss the close relationship to the fractional quantum Hall physics in topological flat bands with Chern number NNN.
We study the many-body ground states of three-component quantum particles in two prototypical topological lattice models under strong intercomponent and intracomponent repulsions. At band filling $\ensuremath{\nu}=3/4$ for hard-core bosons, we demonstrate the emergence of the three-component fractional quantum Hall (FQH) effect characterized by the K\mathbf{K}K matrix, through an exact diagonalization study of fourfold quasidegenerate ground states with a robust spectrum gap and the combined density-matrix renormalization group calculation of fractional drag charge pumping. Further, we formulate the topological characterization of FQH states of three-component Bose-Fermi mixtures at various fillings by the K\mathbf{K}K matrix. Finally, we discuss the possible generalization of our approach to identify non-Abelian three-component spin-singlet FQH states.