Control of transport in two-dimensional systems via dynamical decoupling of degrees of freedom with quasiperiodic driving fields

Cubero, David; Renzoni, Ferruccio

doi:10.1103/physreve.86.056201

Cited by 14 publications

(15 citation statements)

References 23 publications

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“…their mutual ratios are irrational. There are some approaches to analyse QPD systems by mappings to higher dimensions [35,37], constructing effective Hamiltonians to describe the system perturbatively [36], for analysing their asymptotic behaviour [38][39][40] or using them for enhanced performance of quantum simulations [41,42] and creation of Majorana edge modes [43]. While in general for QPD systems we are lacking efficient methods for calculating their full time evolution, the FTSs introduced here are a special class corresponding to periodic systems in a rotating frame.…”

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confidence: 99%

Floquet time spirals and stable discrete-time quasicrystals in quasiperiodically driven quantum many-body systems

2019

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We analyse quasi-periodically driven quantum systems that can be mapped exactly to periodically driven ones and find Floquet Time Spirals in analogy with spatially incommensurate spiral magnetic states. Generalising the mechanism to many-body systems we discover that a form of discrete time-translation symmetry breaking can also occur in quasi-periodically driven systems. We construct a discrete time quasi-crystal stabilised by many-body localisation. Crucially, it persists also under perturbations that break the equivalence with periodic systems. As such it provides evidence of a stable quasi-periodically driven many-body quantum system which does not heat up to the featureless infinite temperature state.The dynamics of a quantum system governed by a generic time-dependent Hamiltonian is generally hard to analyse because to reach a certain point in time the entire history of evolution is required. Hence, simulations quickly become computationally unfeasible, especially for many-body systems. There are some exceptions such as periodically driven (PD) systems, i.e. whose Hamiltonian is periodic in time H(t + T ) = H(t), for which Floquet theory significantly reduces the effort to simulate the dynamics by decomposing the wave function to Floquet modes periodic over one time period T up to phases. PD systems are of immense recent interest as they have been exploited extensively for engineering sought after Hamiltonians [1-5], controlling quantum systems [6][7][8][9][10][11][12][13][14]and realising non-equilibrium quantum phases [15][16][17]. For instance, the proper combination of periodic driving and many-body localisaton [18] gave birth to the discovery of discrete time crystals (DTCs) [19][20][21][22][23][24][25][26], a new quantum phase with broken discrete time translation symmetry.Here, we address the intriguing question whether quasi-periodically driven (QPD) quantum systems can show features similar to time-crystalline behaviour of periodically driven ones? Normally it is expected -apart for special integrable systems with momentum conservation [27] -that QPD systems generically heat up to featureless infinite-temperature states [28,29]. Hence, a related important question we address is whether there are interacting QPD quantum systems with a stable nontrivial steady state? Of course, generally such questions are hard to answer because Floquet theory, which provides an elegant framework for the analysis of PD quantum systems normally does not generalise to aperiodic time-dependencies. Here, we address the above questions by studying a class of QPD systems which can be efficiently treated within Floquet theory. This allows us to find QPD steady states with time-crystalline behaviour at special fine-tuned points whose stability to generic perturbations is studied with exact diagonalisation.The main idea is that special cases of originally QPD Hamiltonian H can be mapped exactly to a periodic(a) (b) Δθ 2Δθ FIG. 1. (a) Mapping a quasi-periodic magnetic spiral to a periodic ferromagnet. (b)Illustration of the tw...

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confidence: 99%

Floquet time spirals and stable discrete-time quasicrystals in quasiperiodically driven quantum many-body systems

2019

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“…driving with a time dependence characterised by several frequencies that can be irrationally related, promises substantially enhanced control over the quantum system at hand. As the use of quasi-periodic driving [31][32][33], however, implies that Floquet theorem is not applicable, the mathematical foundation is far less solid than in the case of periodic driving.…”

Section: Introductionmentioning

confidence: 99%

Quasi-Periodically Driven Quantum Systems

Verdeny

Puig

Mintert

2016

Zeitschrift Für Naturforschung A

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Floquet theory provides rigorous foundations for the theory of periodically driven quantum systems. In the case of non-periodic driving, however, the situation is not so well understood. Here, we provide a critical review of the theoretical framework developed for quasi-periodically driven quantum systems. Although the theoretical footing is still under development, we argue that quasiperiodically driven quantum systems can be treated with generalisations of Floquet theory in suitable parameter regimes. Moreover, we provide a generalisation of the Floquet-Magnus expansion and argue that quasi-periodic driving offers a promising route for quantum simulations.

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“…Our main results, expressed by Eqs. (8)- (12), are applicable to any system driven by a bifrequency forcing function and with a well-defined infinite-time average, independent of the initial conditions. With the help of Eq.…”

Section: Discussionmentioning

confidence: 99%

Universal asymptotic behavior in nonlinear systems driven by a two-frequency forcing

2013

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We examine the time-dependent behavior of a nonlinear system driven by a two-frequency forcing. By using a nonperturbative approach, we are able to derive an asymptotic expression, valid in the long-time limit, for the time average of the output variable which describes the response of the system. We identify several universal features of the asymptotic response of the system, which are independent of the details of the model. In particular, we determine an asymptotic expression for the width of the resonance observed by keeping one frequency fixed and varying the other one. We show that this width is smaller than the usually assumed Fourier width by a factor determined by the two driving frequencies, and independent of the model system parameters. Additional general features can also be identified depending on the specific symmetry properties of the system. Our results find direct application in the study of sub-Fourier signal processing with nonlinear systems.

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Control of transport in two-dimensional systems via dynamical decoupling of degrees of freedom with quasiperiodic driving fields

Cited by 14 publications

References 23 publications

Floquet time spirals and stable discrete-time quasicrystals in quasiperiodically driven quantum many-body systems

Floquet time spirals and stable discrete-time quasicrystals in quasiperiodically driven quantum many-body systems

Quasi-Periodically Driven Quantum Systems

Universal asymptotic behavior in nonlinear systems driven by a two-frequency forcing

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