Simulation of higher-order topological phases and related topological phase transitions in a superconducting qubit

Niu, Jingjing; Yan, Tongxing; Zhou, Yuxuan; Tao, Ziyu; Li, Xiaole; Liu, Weiyang; Zhang, Libo; Jia, Hao; Liu, Song; Yan, Zhongbo; Chen, Yuanzhen; Yu, Dapeng

doi:10.1016/j.scib.2021.02.035

Cited by 44 publications

(18 citation statements)

References 76 publications

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“…Compared with previous quench measurements [17,[32][33][34][35][36][37][38][39][40][41], the present PPQM has three distinct features. Firstly, optical lattices are not applied during the state preparation before the quench.…”

mentioning

confidence: 75%

Realization of Qi-Wu-Zhang model in spin-orbit-coupled ultracold fermions

Liang¹,

Wei²,

Zhang³

et al. 2021

Preprint

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Based on the optical Raman lattice technique, we experimentally realize the Qi-Wu-Zhang model for quantum anomalous Hall phase in ultracold fermions with two-dimensional (2D) spin-orbit (SO) coupling. We develop a novel protocol of pump-probe quench measurement to probe, with minimal heating, the resonant spin flipping on particular quasi-momentum subspace called band-inversion surfaces. With this protocol we demonstrate a continuous crossover between 1D and 2D SO couplings by tuning the relative phase between two coherent Raman couplings, and detect the non-trivial topological band structures by varying the twophoton detuning. The non-trivial band topology is also observed by slowly loading the atoms into optical Raman lattices and measuring the spin textures. Our results show solid evidence for the realization of the minimal SO-coupled quantum anomalous Hall model, which can provide a feasible platform to investigate novel topological physics including the correlation effects with SO-coupled ultracold fermions.

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mentioning

confidence: 75%

Realization of Qi-Wu-Zhang model in spin-orbit-coupled ultracold fermions

Liang¹,

Wei²,

Zhang³

et al. 2021

Preprint

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“…Thirdly, our topological characterization does not require any additional crystal symmetry to facilitate the investigations. Among the several experimental platforms where BISs have been examined, nested BISs can be dynamically detected in solid-state qubit systems [45][46][47][48], where momentum space can be simulated by the highly tunable parameter space of certain qubit Hamiltonians. In ultracold atom systems, time-averaged pseudospin textures can be also readily measured with timeof-flight imaging [41][42][43][44].…”

Section: Discussionmentioning

confidence: 99%

“…the winding number of a 2D vector along a 1D loop) [34,[38][39][40]. The topological invariant defined this way is of genuine appeal, because it can be directly detected through the dynamics by measuring the time-averaged pseudospin texture after a sudden quench, a feat already demonstrated in several experimental platforms involving ultracold atom systems [41][42][43][44], solid-state spin systems [45][46][47], and superconducting circuits [48].…”

Section: Introductionmentioning

confidence: 99%

Direct dynamical characterization of higher-order topological insulators with nested band inversion surfaces

Li,

Zhu,

Gong

2020

Preprint

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Higher-order topological insulators (HOTIs) are systems with topologically protected in-gap boundary states localized at their (d − n)-dimensional boundaries, with d the system dimension and n the order of the topology. This work proposes a rather universal dynamics-based characterization of one large class of Z-type HOTIs without specifically relying on any symmetry considerations.The key element of our innovative approach is to connect quantum quench dynamics with nested configurations of the so-called band inversion surfaces (BISs) of momentum-space Hamiltonians as a sum of operators from the Clifford algebra (a condition that can be relaxed), thereby making it possible to dynamically detect each and every order of topology on an equal footing. Given that experiments on synthetic topological matter can directly measure the winding of certain pseudospin texture to determine topological features of BISs, the topological invariants defined through nested BISs are all within reach of ongoing experiments. Further, the necessity of having nested BISs in defining higher-order topology offers a unique perspective to investigate and engineer higher-order topological phase transitions.

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“…Quantum simulators have been proven to be powerful platforms to experimentally study novel topological phases. During the past decade, there have been great advances in simulating various topological phases via different quantum simulators including cold atom systems [34][35][36][37][38], solid-state spin systems [39][40][41][42][43] and superconducting circuits [44][45][46][47]. Trapped ions provide an alternative flexible platform to perform quantum simulations due to its state-of-the-art technologies to control and measure [48,49], enabling us to use it to simulate exotic topological phases and directly probe their intriguing topological properties through measurements with high precision.…”

Section: Introductionmentioning

confidence: 99%

Observation of topological Euler insulators with a trapped-ion quantum simulator

Zhao¹,

Yang²,

Jiang³

et al. 2022

Preprint

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Symmetries play a crucial role in the classification of topological phases of matter. Although recent studies have established a powerful framework to search for and classify topological phases based on symmetry indicators, there exists a large class of fragile topology beyond the description. The Euler class characterizing the topology of two-dimensional real wave functions is an archetypal fragile topology underlying some important properties, such as non-Abelian braiding of crossing nodes and higher-order topology. However, as a minimum model of fragile topology, the twodimensional topological Euler insulator consisting of three bands remains a significant challenge to be implemented in experiments. Here, we experimentally realize a three-band Hamiltonian to simulate a topological Euler insulator with a trapped-ion quantum simulator. Through quantum state tomography, we successfully evaluate the Euler class, Wilson loop flow and entanglement spectra to show the topological properties of the Hamiltonian. We also measure the Berry phases of the lowest energy band, illustrating the existence of four crossing points protected by the Euler class. The flexibility of the trapped-ion quantum simulator further allows us to probe dynamical topological features including skyrmion-antiskyrmion pairs and Hopf links in momentum-time space from quench dynamics. Our results show the advantage of quantum simulation technologies for studying exotic topological phases and open a new avenue for investigating fragile topological phases in experiments.

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Simulation of higher-order topological phases and related topological phase transitions in a superconducting qubit

Cited by 44 publications

References 76 publications

Realization of Qi-Wu-Zhang model in spin-orbit-coupled ultracold fermions

Realization of Qi-Wu-Zhang model in spin-orbit-coupled ultracold fermions

Direct dynamical characterization of higher-order topological insulators with nested band inversion surfaces

Observation of topological Euler insulators with a trapped-ion quantum simulator

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