Stroboscopic symmetry-protected topological phases

Iadecola, Thomas; Santos, Luiz; Chamon, Claudio

doi:10.1103/physrevb.92.125107

Cited by 42 publications

(59 citation statements)

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“…Despite these advantages, and owing to the complexity of typical model SPT Hamiltonians, it remains difficult to engineer and stabilize SPT phases in coldatom systems. One approach to this challenge is to emulate the complex interactions giving rise to static, equilibrium SPT (ESPT) phases by periodically driving a simpler Hamiltonian at frequencies much larger than its intrinsic energy scales [22]. In addition to this approach, seminal results on classifying driven (Floquet) phases [23][24][25][26][27][28] have also shown that there exist Floquet-SPT (FSPT) phases which are inherently dynamical and have no static analog.…”

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“…1). Driving the interaction term of a transversefield Ising model (TFIM) enables the emulation of an ESPT phase whose edge modes are protected by an emergent Z 2 × Z 2 symmetry [22]. This phase remains stable only within a parametric time scale controlled by the driving frequency, beyond which its topological features break down.…”

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“…Crucially, the λ 1 , λ 2 -dimerization of the Ising interaction enables us to arbitrarily tune the correlation length of the edge mode (inset of Fig. 2a), leading to coherent dynamics with significantly higher fidelity than those of the undimerized TFIM [22].To characterize the edge coherence, we introduce the trace fidelity F α (t) = 1 Z Tr e −βH(t) Σ α (t)Σ α (0) as a function of time, where Z is the partition function, β = 1/k B T , and Σ α are the zero correlation length edge operators Σ x = σ x 1 σ z 2 , Σ y = σ y 1 σ z 2 , and Σ z = σ z 1 . This autocorrelation function at infinite temperature will serve as a proxy for the coherence time.…”

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“…Alternatively, toggling between Hamiltonians with solely Ising interactions or purely transverse fields yields an intrinsically dynamical FSPT phase which has no equilibrium analog. We explore the stability of both phases to long-range interactions and provide a detailed experimental blueprint using Rydberg-dressed atoms.ESPT phase-Inspired by pioneering work on emulating static phases in driven systems [22,32,33,[64][65][66][67][68], we first consider the realization of a many-body localized version of the Haldane phase [69]. This SPT phase can be protected by a discrete dihedral symmetry, Z 2 × Z 2 , and exhibits boundary modes that are odd under the symmetry; these edge modes behave as decoupled spin-1/2 degrees of freedom that are robust to any perturbation which preserves the symmetry.…”

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Floquet Symmetry-Protected Topological Phases in Cold-Atom Systems

et al. 2017

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We propose and analyze two distinct routes toward realizing interacting symmetry-protected topological (SPT) phases via periodic driving. First, we demonstrate that a driven transversefield Ising model can be used to engineer complex interactions which enable the emulation of an equilibrium SPT phase. This phase remains stable only within a parametric time scale controlled by the driving frequency, beyond which its topological features break down. To overcome this issue, we consider an alternate route based upon realizing an intrinsically Floquet SPT phase that does not have any equilibrium analog. In both cases, we show that disorder, leading to many-body localization, prevents runaway heating and enables the observation of coherent quantum dynamics at high energy densities. Furthermore, we clarify the distinction between the equilibrium and Floquet SPT phases by identifying a unique micromotion-based entanglement spectrum signature of the latter. Finally, we propose a unifying implementation in a one-dimensional chain of Rydbergdressed atoms and show that protected edge modes are observable on realistic experimental time scales.The discovery of topological insulators-materials which are insulating in their interior but can conduct on their surface-has led to a multitude of advances at the interface of condensed matter physics and materials engineering [1][2][3][4][5]. At their core, such insulators are characterized by the existence of nontrivial topology in their underlying single-particle electronic band structure [6, 7]. Generalizing our understanding of topological phases to the presence of strong many-body interactions represents one of the central questions in modern physics. Some of the simplest generalizations that have emerged along this direction are symmetry-protected topological (SPT) phases [8][9][10], which represent the minimal extension of topological band insulators to include many-body correlations. Featuring short-range entanglement, SPT phases do not exhibit anyonic excitations in their bulk, but nevertheless possess protected edge modes on their surface; as a result, they represent a particularly fertile ground for studying the interplay between symmetry, topology, and interactions.While indirect signatures of certain ground state SPTs have been observed in the solid state [11][12][13], directly probing the quantum coherence of their underlying edge modes represents an outstanding experimental challenge. In principle, cold-atom quantum simulations could offer a powerful additional tool set-including locally-resolved measurements and interferometric protocols-for probing the robustness of edge modes and systematically exploring their stability to specific perturbations [14][15][16][17][18]. Moreover, such platforms could also enable the controlled storage and transmission of quantum information [19][20][21]. Despite these advantages, and owing to the complexity of typical model SPT Hamiltonians, it remains difficult to engineer and stabilize SPT phases in coldatom systems. One approach to t...

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Floquet Symmetry-Protected Topological Phases in Cold-Atom Systems

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“…(18)] to other Floquet spin models. A multifrequency modulation may be more effective than a single-frequency modulation in terms of realizing topological phases [43,44].…”

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Floquet engineering from long-range to short-range interactions

Lee

2016

Phys. Rev. A

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Quantum simulators based on atoms or molecules often have long-range interactions due to dipolar or Coulomb interactions. We present a method based on Floquet engineering to turn a long-range interaction into a short-range one. By modulating a magnetic-field gradient with one or a few frequencies, one reshapes the interaction profile, such that the system behaves as if it only had nearest-neighbor interactions. Our approach works in both one and two dimensions and for both spin-1/2 and spin-1 systems. It does not require individual addressing, and it is applicable to all experimental systems with long-range interactions: trapped ions, polar molecules, Rydberg atoms, nitrogen-vacancy centers, and cavity QED. Our approach allows one achieve a short-range interaction without relying on Hubbard superexchange. DOI: 10.1103/PhysRevA.94.040701Introduction. A quantum simulator is a quantum system that is engineered to implement a particular quantum model [1,2]. A quantum simulator with a large number of particles would be able to simulate quantum many-body systems beyond what a classical computer could handle [3]. One goal of quantum simulation is to implement models that describe solid-state systems and thereby gain direct insight into phenomena like high-T c superconductivity.There has been a lot of progress on quantum simulation using cold atoms [1,2]. A common feature of such systems is the presence of long-range interactions that decay with a power law in distance due to dipolar or Coulomb interactions [4][5][6][7][8][9]. On the one hand, long-range interactions can lead to qualitatively new physics [10]. On the other hand, solid-state systems usually have short-range interactions because Wannier functions are exponentially localized [11][12][13]. Thus, for the sake of directly simulating solid-state models, it can be preferable for quantum simulators to have short-range interactions.For ultracold atoms in an optical lattice, the on-site interaction arising from s-wave scattering allows one, in principle, to achieve a nearest-neighbor spin model via superexchange [14,15]. However, the nearest-neighbor interaction is small, and it is hard to cool the atoms to sufficiently low temperatures. This has motivated many experimental groups to create quantum simulators based on dipolar or Coulomb interactions [4][5][6][7][8][9]. The advantages of these setups are that the interaction strength is large and that the atoms do not have to be very cold. However, these setups have long-range interactions, so it would be beneficial to somehow remove the longrange tail while otherwise preserving the magnitude of the interactions.In this Rapid Communication, we show how to use Floquet engineering [16,17] to reshape a long-range interaction into a short-range one. Although we focus on making the interaction as short range as possible, our approach can be used to engineer other interaction profiles. Starting from a spin model with long-range XX interactions, we modulate a magnetic-field gradient periodically in time, so that in a rota...

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