Exploring 2D Synthetic Quantum Hall Physics with a Quasiperiodically Driven Qubit

Boyers, Eric; Crowley, Philip J. D.; Chandran, Anushya; Sushkov, Alexander O.

doi:10.1103/physrevlett.125.160505

Cited by 42 publications

(25 citation statements)

References 56 publications

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“…Despite the nonadiabatic nature of this gapless system, it was shown that the energy pumping power can be characterized by some universal scaling forms, and the short-time topological energy pumping becomes half-integer quantized at the gapless point. This result was even demonstrated experimentally [30].…”

Section: Introductionmentioning

confidence: 57%

“…In fact, the concept of synthetic dimensions has recently emerged as a powerful way to emulate topological phases of matter, which are now of great interest across many areas of physics [21]. Among various approaches to engineer synthetic dimensions, the idea based on quasiperiodic drives was pursued and generalized by several theorists [22][23][24][25][26][27][28][29], as well as realized in experiments [30,31].…”

Section: Introductionmentioning

confidence: 99%

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Universal nonadiabatic energy pumping in a quasiperiodically driven extended system

2021

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The paradigm of Floquet engineering of topological states of matter can be generalized into the timequasiperiodic scenario, where a lower-dimensional time-dependent system maps onto a higher-dimensional one by combining the physical dimensions with additional synthetic dimensions generated by multiple incommensurate driving frequencies. Differently from most previous works in which gapped topological phases were considered, we propose an experimentally realizable, one-dimensional chain driven by two frequencies, which maps onto a gapless Weyl semimetal in a synthetic dimension. Based on analytical reasoning and numerical simulations, we find that the nonadiabatic quantum dynamics of this system exhibit energy pumping behaviors characterized by universal functions. We also numerically find that such behaviors are robust against a considerable amount of spatial disorder.

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Section: Introductionmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Universal nonadiabatic energy pumping in a quasiperiodically driven extended system

2021

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“…For example, as mentioned earlier, they arise naturally in inverse scattering problems [242], where the presence of measured scatted data nonlocal boundary conditions are typical, and advanced data-based methodologies, such as deep learning schemes [215], may be required. Other substantial sources are provided by open driven systems, and in particular driven quantum systems [50,158,[243][244][245], including those for Floquet engineering [246], quantum information control with quantum computing applications [247], as well as various nonlinear problems such as those described by Rabi's models, providing, among other things, new perspectives on the entanglement via the von Neumann entropy [248,249]. It is envisaged that in dealing with such systems, communication complexity will play a progressively growing role.…”

Section: Discussion and Generalizationsmentioning

confidence: 99%

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Sytnyk

Melnik

2021

MCA

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Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot. While spatial nonlocalities have received considerable attention in the research community, the same cannot be said about nonlocality in time, in particular when nonlocal initial conditions are present. This paper aims at filling this gap, providing an overview of the current status of nonlocal models and focusing on the mathematical treatment of such models when nonlocal initial conditions are at the heart of the problem. Specifically, our representative example is given for a nonlocal-in-time problem for the abstract Schrödinger equation. By exploiting the linear nature of nonlocal conditions, we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of the complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem’s well-posedness and the existence of its solution under different regularities. Furthermore, we present new sufficient conditions for the existence of the solution that extend the existing results in this field to the case when some nonlocal parameters are unbounded. Two further examples demonstrate the developed methodology and highlight the importance of its computer algebra component in the reduction procedures and parameter estimations for nonlocal models. Finally, a connection of the considered models and developed analysis is discussed in the context of other reduction techniques, concentrating on the most promising from the viewpoint of data-driven modelling environments, and providing directions for further generalizations.

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“…While the model from Ref. [31] has been experimentally implemented and studied [35,36], actual observation of topological frequency conversion is still lacking. The reasons are two fold: First, in the magnetic realm, topological frequency conversion in the desirable frequency regime of THz and above requires extremely high amplitudes of the oscillating magnetic field (of about 1 Tesla and above, corresponding to radiation intensities of more than 240 MW/mm 2 ).…”

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confidence: 99%

Topological frequency conversion in Weyl semimetals

Nathan¹,

Martin²,

Refael³

2022

Preprint

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FIG. 2. (a): Energy bands of the linearized Hamiltonian in Eq. (1) in the plane ky = 0, with ε0 = 0, Rij = δij3.87 • 10 5 m/s, and v = (0, 0, 3.1 • 10 5 m/s). The red line shows an example of the Fermi surface (with Fermi energy −115 meV) when projected into the same plane. (b): Trajectory of eA(t)/ resulting from two modes with circular polarization in the xz and yz planes with amplitudes E1 = 0.74 MV/m, E2 = 1 MV/m and frequencies, f2 = 1, THz, f1 = √ 5−1 2 f2 (blue). Also shown is the surface B0 (gray). See main text for further details. (c): Cross-section of B0 for the same parameters as in (b). Within the red and blue sub-surfaces W (k) takes value 1 and −1, respectively, while W (k) = 0 outside the surface. (d): Trajectory of eA(t)/ for the same values of E2 and f2 as in (b), and with E1 = 0.72 MV/m, f1 = 2 3 f2 (resulting in a commenusrate frequency ratio). The different value of E1 is chosen to ensure that the vector potential of mode 1 has the same amplitude in panels (b) and (d), such that the topological phase boundary B0 is the same for panels (b-d).

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Exploring 2D Synthetic Quantum Hall Physics with a Quasiperiodically Driven Qubit

Cited by 42 publications

References 56 publications

Universal nonadiabatic energy pumping in a quasiperiodically driven extended system

Universal nonadiabatic energy pumping in a quasiperiodically driven extended system

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Topological frequency conversion in Weyl semimetals

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