Second Chern number of a quantum-simulated non-Abelian Yang monopole

Sugawa, Seiji; Salces-Carcoba, Francisco; Perry, Abigail R.; Yue, Yuchen; Spielman, I. B.

doi:10.1126/science.aam9031

Cited by 151 publications

(120 citation statements)

References 37 publications

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“…We hereby discuss possible experimental implementations of Floquetinduced nodal rings and nodal spheres in quantum matter. Inspired by a recent realization of the Yang monopole with ultracold atoms [61], we consider a four-level atomic system described by the following Hamiltonian…”

Section: < L a T E X I T S H A 1 _ B A S E 6 4 = " 2 + A R Q Y P Z 9 mentioning

confidence: 99%

Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric

Salerno

Goldman

Palumbo

2020

Phys. Rev. Research

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Semimetals exhibiting nodal lines or nodal surfaces represent a novel class of topological states of matter. While conventional Weyl semimetals exhibit momentum-space Dirac monopoles, these more exotic semimetals can feature unusual topological defects that are analogous to extended monopoles. In this work, we describe a scheme by which nodal rings and nodal spheres can be realized in synthetic quantum matter through well-defined periodic-driving protocols. As a central result of our work, we characterize these nodal defects through the quantum metric, which is a gauge-invariant quantity associated with the geometry of quantum states. In the case of nodal rings, where the Berry curvature and conventional topological responses are absent, we show that the quantum metric provides an observable signature for these extended topological defects. Besides, we demonstrate that quantum-metric measurements could be exploited to directly detect the topological charge associated with a nodal sphere. We discuss possible experimental implementations of Floquet nodal defects in few-level atomic systems, paving the way for the exploration of Floquet extended monopoles in quantum matter. arXiv:1912.00930v1 [cond-mat.mes-hall]

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Section: < L a T E X I T S H A 1 _ B A S E 6 4 = " 2 + A R Q Y P Z 9 mentioning

confidence: 99%

Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric

Salerno

Goldman

Palumbo

2020

Phys. Rev. Research

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“…Synthetic systems based purely on internal states suffer from limited state spaces, sensitivity to external noise for generic, field-sensitive states [16], and possible collisional relaxation [17] and three-body losses [18]. Furthermore, for isotropic scattering lengths as in 87 Rb [16] and alkaline earth atoms [19], interactions in the synthetic dimension are nearly all-to-all.…”

mentioning

confidence: 99%

Correlated Dynamics in a Synthetic Lattice of Momentum States

Meier

Ang’ong’a

et al. 2018

Phys. Rev. Lett.

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We study the influence of atomic interactions on quantum simulations in momentum-space lattices (MSLs), where driven atomic transitions between discrete momentum states mimic transport between sites of a synthetic lattice. Low energy atomic collisions, which are short ranged in real space, relate to nearly infinite-ranged interactions in momentum space. However, the distinguishability of the discrete momentum states coupled in MSLs gives rise to an added exchange energy between condensate atoms in different momentum orders, relating to an effectively attractive, finite-ranged interaction in momentum space. We explore the types of phenomena that can result from this interaction, including the formation of chiral self-bound states in topological MSLs. We also discuss the prospects for creating squeezed states in momentum-space double wells.Quantum simulation with ultracold atoms [1,2] has been a powerful tool in the study of many-body physics and nonequilibrium dynamics. There has been recent interest in extending quantum simulation studies from real-space potentials to synthetic lattice systems composed of discrete internal [3,4] or external [5] states. These synthetic dimensions enable many unique capabilities for quantum simulation, including new approaches to engineering nontrivial topology [4,6], access to higher dimensions [3], and potential insensitivity to finite motional temperature.The recent development of momentum-space lattices (MSLs), based on the use of discrete momentum states as effective sites, has introduced a fully synthetic approach to simulating lattice dynamics [7][8][9][10][11]. As compared to partially synthetic systems [12,13], fully synthetic lattices offer complete microscopic control of system parameters. While this level of control is analogous to that found in photonic simulators [14,15], matter waves of atoms can interact strongly with one another.However, fully synthetic systems also present apparent challenges for studying nontrivial atomic interactions. Synthetic systems based purely on internal states suffer from limited state spaces, sensitivity to external noise for generic, field-sensitive states [16], and possible collisional relaxation [17] and three-body losses [18]. Furthermore, for isotropic scattering lengths as in 87 Rb [16] and alkaline earth atoms [19], interactions in the synthetic dimension are nearly all-to-all. Similarly, s-wave contact interactions relate to nearly infinite-ranged momentumspace interactions at low energy, and should naively be decoupled from particle dynamics in MSLs.Here, we investigate the role of atomic interactions in MSLs, showing that finite-ranged interactions in momentum space result from the exchange energy of bosonic condensate atoms in distinguishable momentum states. We explore potential interaction-driven phenomena that can be studied in topological MSLs, showing that chiral propagating bound states can emerge in the presence of an artificial magnetic flux. We additionally discuss the use of momentum-space double wells for the gener...

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“…For instance, the integral of the Berry curvature over a closed two-dimensional manifold defines the first Chern number [10], which is a topological invariant to characterize quantized Hall conductivity and Chern insulators [11]. Recently, the Berry curvature has been directly measured in some engineered systems, such as cold atoms [9,[12][13][14][15], photonic lattices [16], and superconducting quantum circuits [17][18][19][20].…”

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confidence: 99%

Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit

et al. 2019

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Berry curvature is an imaginary component of the quantum geometric tensor (QGT) and is well studied in many branches of modern physics; however, the quantum metric as a real component of the QGT is less explored. Here, by using tunable superconducting circuits, we experimentally demonstrate two methods to directly measure the quantum metric tensor for characterizing the geometry and topology of underlying quantum states in parameter space. The first method is to probe the transition probability after a sudden quench, and the second one is to detect the excitation rate under weak periodic driving. Furthermore, based on quantum-metric and Berry-curvature measurements, we explore a topological phase transition in a simulated time-reversal-symmetric system, which is characterized by the Euler characteristic number instead of the Chern number. The work opens up a unique approach to explore the topology of quantum states with the QGT.

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Second Chern number of a quantum-simulated non-Abelian Yang monopole

Cited by 151 publications

References 37 publications

Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric

Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric

Correlated Dynamics in a Synthetic Lattice of Momentum States

Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit

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