Measuring a dynamical topological order parameter in quantum walks

Xu, Xiao‐Ye; Wang, Qin-Qin; Heyl, Markus; Budich, Jan Carl; Pan, Weiwei; Chen, Zhe; Jan, Munsif; Sun, Kai; Xu, Jin‐Shi; Han, Yong‐Jian; Li, Chuan‐Feng; Guo, Guang-Can

doi:10.1038/s41377-019-0237-8

Cited by 69 publications

(38 citation statements)

References 68 publications

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“…Direct access to both walker position and quasimomentum could be exploited to study complex dynamics in the regime of spatial disorder. By combining topology and our dynamical control of the system parameters, we could investigate dynamical quantum phase transitions in quantum walks [44][45][46]. The demonstration of a new platform for 2D quantum walks opens the door to the experimental study of this simple yet rich quantum dynamics in two spatial dimensions, with potential applications to diverse scenarios like the topological physics of 2D periodically-driven systems [29,30].…”

Section: Discussionmentioning

confidence: 99%

Two-dimensional topological quantum walks in the momentum space of structured light

D’Errico¹,

Cardano²,

Maffei³

et al. 2020

Optica

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Quantum walks are powerful tools for building quantum algorithms, modeling transport phenomena, and designing topological systems. Here we present a photonic implementation of a quantum walk in two spatial dimensions, where the lattice of walker positions is encoded in the transversewavevector components of a paraxial light beam. The desired quantum dynamics is obtained by means of a sequence of liquid-crystal devices ("g-plates"), which apply polarization-dependent transverse kicks to the photons in the beam. We first characterize our setup, and then benchmark it by implementing a periodically-driven Chern insulator and probing its topological features. Our platform is compact, versatile and cost-effective: most evolution parameters are controlled dynamically, the walker distribution is detected in a single shot, and the input state can be tailored at will. These features offer exciting prospects for the photonic simulation of two-dimensional quantum systems. * AD'E and FC contributed equally to this work †

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Section: Discussionmentioning

confidence: 99%

Two-dimensional topological quantum walks in the momentum space of structured light

D’Errico¹,

Cardano²,

Maffei³

et al. 2020

Optica

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“…Because of their rich dynamics and flexibility, periodically driven systems have been extensively used to explore different phenomena such as topological insulators [27,28], nonequilibrium dynamics [29], and time crystals [30,31]. Generally, when a system is driven by the periodic Hamiltonian H(t) = H(t+T ) (where T is the period), its dynamics can be effectively described by the Floquet formalism [32][33][34], i.e., the Floquet equation…”

Section: Dynamics Of a Floquet Systemmentioning

confidence: 99%

Identifying the Riemann zeros by periodically driving a single qubit

Cui

et al. 2020

Phys. Rev. A

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The Riemann hypothesis, one of the most important open problems in pure mathematics, implies the most profound secret of prime numbers. One of the most interesting approaches to solve this hypothesis is to connect the problem with the spectrum of the physical Hamiltonian of a quantum system. However, none of the proposed quantum Hamiltonians have been experimentally feasible.Here, we report the first experiment to identify the first non-trivial zeros of the Riemann zeta function and the first two zeros of Pólya's fake zeta function, using a novel Floquet method, through properly designed periodically driving functions. According to this method, the zeros of these functions are characterized by the occurrence of crossings of quasi-energies when the dynamics of the system are frozen. The experimentally obtained zeros are in excellent agreement with their exact values. Our study provides the first experimental realization of the Riemann zeros, which may provide new insights into this fundamental mathematical problem.

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“…Among many other intriguing applications (see Ref. [19] for a review), DQPTs have become an important diagnostic tool for identifying topological insula- tor phases [27,28] in systems far from equilibrium, as has been demonstrated in recent experiments on various physical platforms, ranging from ultracold atomic gases [18], over superconducting qubit systems [29], and quantum walks in photonic systems [30,31], to nanomechanical settings [32]. The underlying conceptual insight is that changes in the topological properties over a quench generically imply the occurrence of DQPTs [14,15].…”

Section: Introductionmentioning

confidence: 99%

Stability of dynamical quantum phase transitions in quenched topological insulators: From multiband to disordered systems

Mendl

Budich

2019

Phys. Rev. B

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Dynamical quantum phase transitions (DQPTs) represent a counterpart in non-equilibrium quantum time evolution of thermal phase transitions at equilibrium, where real time becomes analogous to a control parameter such as temperature. In quenched quantum systems, recently the occurrence of DQPTs has been demonstrated, both with theory and experiment, to be intimately connected to changes of topological properties. Here, we contribute to broadening the systematic understanding of this relation between topology and DQPTs to multi-orbital and disordered systems. Specifically, we provide a detailed ergodicity analysis to derive criteria for DQPTs in all spatial dimensions, and construct basic counter-examples to the occurrence of DQPTs in multi-band topological insulator models. As a numerical case study illustrating our results, we report on microscopic simulations of the quench dynamics in the Harper-Hofstadter model. Furthermore, going gradually from multiband to disordered systems, we approach random disorder by increasing the (super) unit cell within which random perturbations are switched on adiabatically. This leads to an intriguing order of limits problem which we address by extensive numerical calculations on quenched one-dimensional topological insulators and superconductors with disorder. arXiv:1909.01402v1 [cond-mat.quant-gas]

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Measuring a dynamical topological order parameter in quantum walks

Cited by 69 publications

References 68 publications

Two-dimensional topological quantum walks in the momentum space of structured light

Two-dimensional topological quantum walks in the momentum space of structured light

Identifying the Riemann zeros by periodically driving a single qubit

Stability of dynamical quantum phase transitions in quenched topological insulators: From multiband to disordered systems

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