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arXiv:1607.07842 · Physical Review Letters

Topological Fractional Pumping with Alkaline-Earth-Like Atoms in Synthetic Lattices

Luca Taddia, Eyal Cornfeld, Davide Rossini, Leonardo Mazza, Eran Sela, Rosario Fazio

Published Jun 8, 2017• 99 citations
arXivHTMLPDF

Abstract

Alkaline-earth(-like) atoms, trapped in optical lattices and in the presence of an external gauge field, can form insulating states at given fractional fillings. We will show that, by exploiting these properties, it is possible to realize a topological fractional pump. Our analysis is based on a many-body adiabatic expansion, on simulations with time-dependent matrix product states, and, for a specific form of atom-atom interaction, on an exactly solvable model of fractional pump. The numerical simulations allow us to consider a realistic setup amenable of an experimental realization. As a further consequence, the measure of the center-of-mass shift of the atomic cloud would constitute the first measurement of a many-body Chern number in a cold-atom experiment.

DOI
10.1103/physrevlett.118.230402

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Alkaline-earth(-like) atoms, trapped in optical lattices and in the presence of an external gauge field, can form insulating states at given fractional fillings. We will show that, by exploiting these properties, it is possible to realize a topological fractional pump. Our analysis is based on a many-body adiabatic expansion, on simulations with time-dependent matrix product states, and, for a specific form of atom-atom interaction, on an exactly solvable model of fractional pump. The numerical simulations allow us to consider a realistic setup amenable of an experimental realization. As a further consequence, the measure of the center-of-mass shift of the atomic cloud would constitute the first measurement of a many-body Chern number in a cold-atom experiment.
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The realization of interacting topological states of matter such as fractional Chern insulators (FCIs) in cold atom systems has recently come within experimental reach due to the engineering of optical lattices with synthetic gauge fields providing the required topological band structures. However, detecting their occurrence might prove difficult since transport measurements akin to those in solid state systems are challenging to perform in cold atom setups and alternatives have to be found. We show that for a ν=1/2 FCI state realized in the lowest band of a Harper-Hofstadter model of interacting bosons confined by a harmonic trapping potential, the fractionally quantized Hall conductivity σ_{xy} can be accurately determined by the displacement of the atomic cloud under the action of a constant force which provides a suitable experimentally measurable signal for detecting the topological nature of the state. Using matrix-product state algorithms, we show that, in both cylinder and square geometries, the movement of the particle cloud in time under the application of a constant force field on top of the confining potential is proportional to σ_{xy} for an extended range of field strengths.
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We present a setup with Rydberg atoms for the realization of a bosonic fractional Chern insulator in artificial matter. The suggested setup relies on Rydberg atoms arranged in a honeycomb lattice, where excitations hop through the lattice by dipolar exchange interactions and can be interpreted as hard-core bosons. The quantum many-body Hamiltonian is studied within exact diagonalization and the density-matrix renormalization group. We identify experimentally accessible parameters where all signatures indicate the appearance of a fractional state with the same topological properties as the ν=1/2 bosonic Laughlin state. We demonstrate an adiabatic ramping procedure, which allows for the preparation of the topological state in a finite system, and demonstrate an experimentally accessible smoking-gun signature for the fractional excitations.