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Bulletin of the American Physical Society

Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension

Sylvain Capponi, Heloise Nonne, Marion Moliner, P. Lecheminant, Keisuke Totsuka

Published Mar 18, 2013• 0 citations
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Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension

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We investigate the existence of symmetry-protected topological phases in one-dimensional alkaline-earth cold fermionic atoms with general half-integer nuclear spin I at halffilling. In this respect, some orbital degrees of freedom are required. They can be introduced by considering either the metastable excited state of alkaline-earth atoms or the p -band of the optical lattice. Using complementary techniques, we show that SU(2) Haldane topological phases are stabilised from these orbital degrees of freedom. On top of these phases, we find the emergence of topological phases with enlarged SU(2 I + 1) symmetry which depend only on the nuclear-spin degrees of freedom. The main physical properties of the latter phases are further studied using a matrix-product state approach. On the one hand, we find that these phases are symmetry-protected topological phases, with respect to inversion symmetry, when which is directly relevant to ytterbium and strontium cold fermions. On the other hand, for the other values of I (=half-odd integer), these topological phases are stabilised only in the presence of exact SU(2 I + 1) symmetry.

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Construction and classification of fermionic symmetry protected topological phases in 3D

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Symmetry-Protected Topological States for Interacting Fermions in Alkaline-Earth-Like Atoms

Xiaofan Zhou, Jian-Song Pan, Zheng-Xin Liu +4 more

We discuss the quantum simulation of symmetry-protected topological (SPT) states for interacting fermions in quasi-one-dimensional gases of alkaline-earth-like atoms such as ^{173}Yb. Taking advantage of the separation of orbital and nuclear-spin degrees of freedom in these atoms, we consider Raman-assisted spin-orbit couplings in the clock states, which, together with the spin-exchange interactions in the clock-state manifolds, give rise to SPT states for interacting fermions. We numerically investigate the phase diagram of the system, and study the phase transitions between the SPT phase and the symmetry-breaking phases. The interaction-driven topological phase transition can be probed by measuring local density distribution of the topological edge modes.

arXiv:1612.08880•Physical Review Letters•Nov 3, 2017•32 citations
We investigate the existence of symmetry-protected topological phases in one-dimensional alkaline-earth cold fermionic atoms with general half-integer nuclear spin I at halffilling. In this respect, some orbital degrees of freedom are required. They can be introduced by considering either the metastable excited state of alkaline-earth atoms or the p -band of the optical lattice. Using complementary techniques, we show that SU(2) Haldane topological phases are stabilised from these orbital degrees of freedom. On top of these phases, we find the emergence of topological phases with enlarged SU(2 I + 1) symmetry which depend only on the nuclear-spin degrees of freedom. The main physical properties of the latter phases are further studied using a matrix-product state approach. On the one hand, we find that these phases are symmetry-protected topological phases, with respect to inversion symmetry, when which is directly relevant to ytterbium and strontium cold fermions. On the other hand, for the other values of I (=half-odd integer), these topological phases are stabilised only in the presence of exact SU(2 I + 1) symmetry.
We discuss the quantum simulation of symmetry-protected topological (SPT) states for interacting fermions in quasi-one-dimensional gases of alkaline-earth-like atoms such as ^{173}Yb. Taking advantage of the separation of orbital and nuclear-spin degrees of freedom in these atoms, we consider Raman-assisted spin-orbit couplings in the clock states, which, together with the spin-exchange interactions in the clock-state manifolds, give rise to SPT states for interacting fermions. We numerically investigate the phase diagram of the system, and study the phase transitions between the SPT phase and the symmetry-breaking phases. The interaction-driven topological phase transition can be probed by measuring local density distribution of the topological edge modes.