Real-space imaging of a topologically protected edge state with ultracold atoms in an amplitude-chirped optical lattice

Leder, Martin; Grossert, Christopher; Sitta, Lukas; Genske, Maximilian; Rosch, Achim; Weitz, Martin

doi:10.1038/ncomms13112

Cited by 113 publications

(78 citation statements)

References 34 publications

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“…Among the wide variety of topological models, the Su-Schrieffer-Heeger (SSH) model is the most basic and one of the most important models in describing band topology in condensed matter physics [66][67][68][69][70]. In order to study additional topological physics, various extended models have been proposed.…”

Section: Introductionmentioning

confidence: 99%

Topological characterizations of an extended Su–Schrieffer–Heeger model

et al. 2019

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The Su-Schrieffer-Heeger (SSH) model perhaps is the easiest and the most basic model for topological excitations. Many variations and extensions of the SSH model have been proposed and explored to better understand both fundamental and novel aspects of topological physics. The SSH4 model has been proposed theoretically as an extended SSH model with higher dimension (the internal dimension changes from two to four). It has been proposed that the winding number in this system can be determined through a higherdimensional extension of the mean chiral displacement measurement, however this has not yet been verified in experiment. Here we report the realization of this model with ultracold atoms in a momentum lattice.We verify the winding number through measurement of the mean chiral displacement in a system with higher internal dimension, we map out the topological phase transition in this system, and we confirm the topological edge state by observation of the quench dynamics when atoms are initially prepared at the system boundary. * yanbohang@zju.edu.cn 1 arXiv:1906.12019v1 [cond-mat.quant-gas]

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Section: Introductionmentioning

confidence: 99%

Topological characterizations of an extended Su–Schrieffer–Heeger model

et al. 2019

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“…A famous example of this correspondence can be found in the Quantum-Hall effect where the quantization of the Hall conductance is rooted in the current-carrying protected edge states [3][4][5]. The ensemble of (natural and artificial) topological insulators is steadily growing, and these have been by now synthetically engineered in a multitude of physical systems such as atomic [6][7][8][9][10][11], superconducting [12], photonic [13][14][15][16][17] and acoustic platforms [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Topological characterization of chiral models through their long time dynamics

et al. 2018

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We study chiral models in one spatial dimension, both static and periodically driven. We demonstrate that their topological properties may be read out through the long time limit of a bulk observable, the mean chiral displacement. The derivation of this result is done in terms of spectral projectors, allowing for a detailed understanding of the physics. We show that the proposed detection converges rapidly and it can be implemented in a wide class of chiral systems. Furthermore, it can measure arbitrary winding numbers and topological boundaries, it applies to all non-interacting systems, independently of their quantum statistics, and it requires no additional elements, such as external fields, nor filled bands.Topological phases of matter constitute a new paradigm by escaping the standard Ginzburg-Landau theory of phase transitions. These exotic phases appear without any symmetry breaking and are not characterized by a local order parameter, but rather by a global topological order. In the last decade, topological insulators have attracted much interest [1]. These systems are insulators in their bulk but exhibit current carrying edge states protected by the topology. A classification of topological insulators in terms of their discrete symmetries and their spatial dimensionality has been obtained in the celebrated periodic table of topological insulators and superconductors [2]. The topological invariant characterizing these models can be derived from the bulk Hamiltonian and allows one to recover the so called bulk-edge correspondence, namely that the number of topologically protected edge states is proportional to the topological invariant. A famous example of this correspondence can be found in the Quantum-Hall effect where the quantization of the Hall conductance is rooted in the current-carrying protected edge states [3][4][5]. The ensemble of (natural and artificial) topological insulators is steadily growing, and these have been by now synthetically engineered in a multitude of physical systems such as atomic [6][7][8][9][10][11], superconducting [12], photonic [13][14][15][16][17] and acoustic platforms [18][19][20].This work focuses on one-dimensional (1D) topological insulators possessing chiral symmetry. As a consequence of the chiral symmetry, the different sites of the unit cell can always be regarded as part of two sublattices. The topological invariant of the bulk, the winding number  , allows one to predict the number of zero energy edge states. 1D chiral topological insulators have been realized in numerous platforms as ultracold atoms [6,11], photonic crystals [15], photonic quantum walks [21][22][23][24][25]. Let us notice that the 1D chiral Hamiltonian can be static or the effective Hamiltonian of a Floquet system. In the latter case, the topology can be richer than its static counterpart [26][27][28][29]. In both cases, two different approaches to characterize the topology of such systems have been proposed and implemented experimentally. The first one is to look at intrinsic prope...

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“…the three legs of the ladders were associated with three internal states of an atom [79]). In addition, a very recent work [80] has reported on the observation of a point-like edge state, situated at the interface between two geometrically distinct regions, in a one-dimensional optical lattice reminiscent of the Su-Schrieffer-Heeger model [81]. Finally, we point out that topological structures were also identified in other engineered systems, such as photonic lattices [82][83][84][85][86][87], superconducting qubits [88,89], mechanical systems [90] and radio-frequency circuits [91,92].…”

Section: Introductionmentioning

confidence: 90%

“…In Ref. [80], a related type of localized state was created in a onedimensional lattice, by locally reversing the mass of a 1D Dirac point.…”

Section: Creating Topological Interfaces a The General Strategymentioning

confidence: 99%

Creating topological interfaces and detecting chiral edge modes in a two-dimensional optical lattice

et al. 2016

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We propose and analyze a general scheme to create chiral topological edge modes within the bulk of two-dimensional engineered quantum systems. Our method is based on the implementation of topological interfaces, designed within the bulk of the system, where topologically-protected edge modes localize and freely propagate in a unidirectional manner. This scheme is illustrated through an optical-lattice realization of the Haldane model for cold atoms [1], where an additional spatiallyvarying lattice potential induces distinct topological phases in separated regions of space. We present two realistic experimental configurations, which lead to linear and radial-symmetric topological interfaces, which both allows one to significantly reduce the effects of external confinement on topological edge properties. Furthermore, the versatility of our method opens the possibility of tuning the position, the localization length and the chirality of the edge modes, through simple adjustments of the lattice potentials. In order to demonstrate the unique detectability offered by engineered interfaces, we numerically investigate the time-evolution of wave packets, indicating how topological transport unambiguously manifests itself within the lattice. Finally, we analyze the effects of disorder on the dynamics of chiral and non-chiral states present in the system. Interestingly, engineered disorder is shown to provide a powerful tool for the detection of topological edge modes in cold-atom setups.

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Real-space imaging of a topologically protected edge state with ultracold atoms in an amplitude-chirped optical lattice

Cited by 113 publications

References 34 publications

Topological characterizations of an extended Su–Schrieffer–Heeger model

Topological characterizations of an extended Su–Schrieffer–Heeger model

Topological characterization of chiral models through their long time dynamics

Creating topological interfaces and detecting chiral edge modes in a two-dimensional optical lattice

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