Realizing Hopf Insulators in Dipolar Spin Systems.

Published on Jun 28, 2021in arXiv: Quantum Gases
· DOI :10.1103/PHYSREVLETT.127.015301
Thomas Schuster9
Estimated H-index: 9
,
Felix Flicker13
Estimated H-index: 13
+ 4 AuthorsNorman Y. Yao46
Estimated H-index: 46
Sources
Abstract
The Hopf insulator represents a topological state of matter that exists outside the conventional ten-fold way classification of topological insulators. Its topology is protected by a linking number invariant, which arises from the unique topology of knots in three dimensions. We predict that three-dimensional arrays of driven, dipolar-interacting spins are a natural platform to experimentally realize the Hopf insulator. In particular, we demonstrate that certain terms within the dipolar interaction elegantly generate the requisite non-trivial topology, and that Floquet engineering can be used to optimize dipolar Hopf insulators with large gaps. Moreover, we show that the Hopf insulator's unconventional topology gives rise to a rich spectrum of edge mode behaviors, which can be directly probed in experiments. Finally, we present a detailed blueprint for realizing the Hopf insulator in lattice-trapped ultracold dipolar molecules; focusing on the example of {}^{40}^{87}b, we provide quantitative evidence for near-term experimental feasibility.
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References70
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#1Thomas Schuster (University of California, Berkeley)H-Index: 9
#2Felix Flicker (University of Oxford)H-Index: 13
Last. Norman Y. Yao (LBNL: Lawrence Berkeley National Laboratory)H-Index: 46
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We present a quantitative, near-term experimental blueprint for the quantum simulation of topological insulators using lattice-trapped ultracold polar molecules. In particular, we focus on the so-called Hopf insulator, which represents a three-dimensional topological state of matter existing outside the conventional tenfold way and crystalline-symmetry-based classifications of topological insulators. Its topology is protected by a \emph{linking number} invariant, which necessitates long-range sp...
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#1Aris Alexandradinata (UIUC: University of Illinois at Urbana–Champaign)H-Index: 18
#2Aleksandra Nelson (UZH: University of Zurich)H-Index: 2
Last. Alexey A. Soluyanov (SPbU: Saint Petersburg State University)H-Index: 24
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The paradigm of topological insulators asserts that an energy gap separates conduction and valence bands with opposite topological invariants. Here, we propose that equal-energy bands with opposite Chern invariants can be spatially separated, onto opposite facets of a finite crystalline Hopf insulator. On a single facet, the number of Berry-curvature quanta is in one-to-one correspondence with the bulk homotopy invariant of the Hopf insulator; this originates from a bulk-to-boundary flow of Berr...
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#1Kyle Matsuda (NIST: National Institute of Standards and Technology)H-Index: 9
#2Luigi De Marco (NIST: National Institute of Standards and Technology)H-Index: 15
Last. Jun Ye (NIST: National Institute of Standards and Technology)H-Index: 126
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Full control of molecular interactions, including reactive losses, would open new frontiers in quantum science. We demonstrate extreme tunability of ultracold chemical reaction rates by inducing resonant dipolar interactions by means of an external electric field. We prepared fermionic potassium-rubidium molecules in their first excited rotational state and observed a modulation of the chemical reaction rate by three orders of magnitude as we tuned the electric field strength by a few percent ac...
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#1Giacomo Valtolina (NIST: National Institute of Standards and Technology)H-Index: 11
#2Kyle Matsuda (NIST: National Institute of Standards and Technology)H-Index: 9
Last. Jun Ye (NIST: National Institute of Standards and Technology)H-Index: 126
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The control of molecules is key to the investigation of quantum phases, in which rich degrees of freedom can be used to encode information and strong interactions can be precisely tuned1. Inelastic losses in molecular collisions2-5, however, have greatly hampered the engineering of low-entropy molecular systems6. So far, the only quantum degenerate gas of molecules has been created via association of two highly degenerate atomic gases7,8. Here we use an external electric field along with optical...
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#1Yan He (Sichuan University)H-Index: 16
#2Chih-Chun Chien (UCM: University of California, Merced)H-Index: 23
The Hopf insulator is a three-dimensional topological insulator outside the standard classification of topological insulators. Here we consider a non-Hermitian generalization of the Hopf insulator with a generalized expression of the Hopf index. The isolated gapless points of the Hermitian model are broadened into finite regimes in the non-Hermitian model. However, the modulus of the Hopf index remains quantized in the gapped regions. While the gapless regimes estimated from the system with peri...
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#1Haiping Hu (GMU: George Mason University)H-Index: 13
#2Chao Yang (NTU: Nanyang Technological University)H-Index: 1
Last. Erhai Zhao (GMU: George Mason University)H-Index: 22
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Hopf insulators are exotic topological states of matter outside the standard ten-fold way classification based on discrete symmetries. Its topology is captured by an integer invariant that describes the linking structures of the Hamiltonian in the three-dimensional momentum space. In this paper, we investigate the quantum dynamics of Hopf insulators across a sudden quench and show that the quench dynamics is characterized by a \mathbb{Z}_2invariant \nuwhich reveals a rich interplay between...
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#1Thomas Schuster (University of California, Berkeley)H-Index: 9
#2Snir Gazit (University of California, Berkeley)H-Index: 13
Last. Norman Y. Yao (University of California, Berkeley)H-Index: 46
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We predict the existence of a novel Floquet topological insulator in three-dimensional two-band systems, the Floquet Hopf insulator, which possesses two distinct topological invariants. One is the Hopf \mathbb{Z}invariant, a linking number characterizing the (non-driven) Hopf topological insulator. The second invariant is an intrinsically Floquet \mathbb{Z}_2invariant, and represents a condensed matter realization of the topology underlying the Witten anomaly in particle physics. Both inva...
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#1F. Nur Ünal (MPG: Max Planck Society)H-Index: 10
#2André Eckardt (MPG: Max Planck Society)H-Index: 28
Last. Robert-Jan Slager (Harvard University)H-Index: 19
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This paper shows that the dynamics of two-band systems can be characterized by Hopf maps, where the winding numbers are cast as linking numbers. This finding opens the doors towards both the investigation of Hopf insulators in experiments with ultracold atoms in driven optical lattices and the measurement of Floquet topological invariants via the observation of post quench-dynamics
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#1Sylvain de Léséleuc (Université Paris-Saclay)H-Index: 14
#2Vincent Lienhard (Université Paris-Saclay)H-Index: 15
Last. Antoine Browaeys (Université Paris-Saclay)H-Index: 49
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The concept of topological phases is a powerful framework for characterizing ground states of quantum many-body systems that goes beyond the paradigm of symmetry breaking. Topological phases can appear in condensed-matter systems naturally, whereas the implementation and study of such quantum many-body ground states in artificial matter require careful engineering. Here, we report the experimental realization of a symmetry-protected topological phase of interacting bosons in a one-dimensional la...
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#1Yan He (Sichuan University)H-Index: 16
#2Chih-Chun Chien (UCM: University of California, Merced)H-Index: 23
We present a class of three dimensional (3D) two-band Floquet topological insulators constructed from two-dimensional Floquet topological insulators with a Ztopological index. It is shown that the 3D two-band Floquet topological insulator has a Z_2topological index, whose value can be obtained by numerical calculations or by using a relation to the winding number. The classification of the 3D Z_2Floquet topological insulator, however, cannot be attributed to the stable homotopy groups. ...
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Pontrjagin's seminal topological classification of two-band Hamiltonians in three momentum dimensions is hereby enriched with the inclusion of a crystallographic rotational symmetry. The enrichment is attributed to a new topological invariant which quantifies a 2\piquantized change in the Berry-Zak phase between a pair of rotation-invariant lines in the bulk, three-dimensional Brillouin zone; because this change is reversed on the complementary section of the Brillouin zone, we refer to this ...
We present a series of models of three-dimensional rotation-symmetric fragile topological insulators in class AI (time-reversal symmetric and spin-orbit-free systems), which have gapless surface states protected by time-reversal (T and nfold rotation (C_n symmetries (n=2,4,6. Our models are generalizations of Fu's model of a spinless topological crystalline insulator, in which orbital degrees of freedom play the role of pseudo-spins. We consider minimal surface Hamiltonian with C_n..
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#1Thomas Schuster (University of California, Berkeley)H-Index: 9
#2Felix Flicker (University of Oxford)H-Index: 13
Last. Norman Y. Yao (LBNL: Lawrence Berkeley National Laboratory)H-Index: 46
view all 7 authors...
We present a quantitative, near-term experimental blueprint for the quantum simulation of topological insulators using lattice-trapped ultracold polar molecules. In particular, we focus on the so-called Hopf insulator, which represents a three-dimensional topological state of matter existing outside the conventional tenfold way and crystalline-symmetry-based classifications of topological insulators. Its topology is protected by a \emph{linking number} invariant, which necessitates long-range sp...
Source
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