Effective time-independent analysis for quantum kicked systems

Bandyopadhyay, Jayendra N.; Sarkar, Tapomoy Guha

doi:10.1103/physreve.91.032923

Cited by 16 publications

(17 citation statements)

References 41 publications

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“…Here, T is the chosen stroboscopic time step and T is the time-ordering operator. Exotic Floquet Hamiltonians [43][44][45][46][47][48][49] which are inaccessible in static systems can be engineered from equation (1.1) and a range of novel physical phenomena, such as Floquet topological physics [50][51][52][53], phase space crystals [54,55], Anderson localization in time domain [56][57][58] and spontaneous breaking of discrete time-translation symmetry (Floquet time crystals) [59][60][61][62][63][64][65][66][67], can be created by Floquet engineering [68][69][70]. While most work focus on the singleparticle physics of (dissipative) Floquet systems, the possible new physics by Floquet many-body engineering has become an active research direction in recent years.…”

Section: Introductionmentioning

confidence: 99%

Floquet many-body engineering: topology and many-body physics in phase space lattices

2018

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Hamiltonians which are inaccessible in static systems can be engineered in periodically driven manybody systems, i.e., Floquet many-body systems. We propose to use interacting particles in a onedimensional (1D) harmonic potential with periodic kicking to investigate two-dimensional topological and many-body physics. Depending on the driving parameters, the Floquet Hamiltonian of single kicked harmonic oscillator has various lattice structures in phase space. The noncommutative geometry of phase space gives rise to the topology of the system. We investigate the effective interactions of particles in phase space and find that the point-like contact interaction in quasi-1D real space becomes a long-rang Coulomb-like interaction in phase space, while the hardcore interaction in pure-1D real space becomes a confinement quark-like potential in phase space. We also find that the Floquet exchange interaction does not disappear even in the classical limit, and can be viewed as an effective long-range spin-spin interaction induced by collision. Our proposal may provide platforms to explore new physics and exotic phases by Floquet many-body engineering.

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Section: Introductionmentioning

confidence: 99%

Floquet many-body engineering: topology and many-body physics in phase space lattices

2018

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“…Lets set

t_{i} = 0

, then

H_{e f f}

and

F (t)

can be expanded as,

\begin{matrix} true \\ right H_{e f f} = \sum_{n = 0}^{\infty} \frac{1}{ω^{n}} H_{e f f}^{n}, scriptF (t) = \sum_{n = 1}^{\infty} \frac{1}{ω^{n}} F^{n} \end{matrix}

A generic quantum δ‐kick can be implemented with following perturbation,

\begin{matrix} true \\ right H_{k i c k} (t) = α normalΛ (\vec{k}) \sum_{n = - \infty}^{\infty} δ (t - n T) \end{matrix}

where

T = 2 π / ω

, α is the kicking strength and

Λ (\vec{k})

is the matrix representation of a perturbation, which in general can be a function of momentum,

\overset{k}{true}

, and could be used to mimic a nonuniform kicking. Following a perturbative expansion the effective Hamiltonian for δ‐kick, with

H_{k i c k, n} = α Λ false(\overset{k}{true} false) / T for all n

, can be obtained as

\begin{matrix} true \\ right H_{e f f}^{k i c k} = & left H_{L} + \frac{α normalΛ false(\overset{k}{true} false)}{T} \end{matrix}

…”

Section: Model and Formalismmentioning

confidence: 99%

“…Using the periodic -function kicks can typically simplify theoretical studies by allowing to perform calculations analytically to a large extent (in contrast to sinusoidal driving or elliptical/circular light). [47,57] However, for the sake of comparison we also briefly discuss the smooth driving case to show that some of the features of our discussion can be held up in smooth driving setup as long as the perturbation breaks inversion (uniaxially) and time-reversal symmetries but preserve their combinations. In this paper, we show two examples of such perturbations which along with an external magnetic field induce various hybrid Dirac and Weyl phases, including a new hybrid dispersion Dirac semimetal.…”

Section: Doi: 101002/andp201900336mentioning

confidence: 99%

“…In this work, we tackle this issue by an alternative way of periodic driving, in particular the periodic kicking. Using the periodic δ‐function kicks can typically simplify theoretical studies by allowing to perform calculations analytically to a large extent (in contrast to sinusoidal driving or elliptical/circular light) . However, for the sake of comparison we also briefly discuss the smooth driving case to show that some of the features of our discussion can be held up in smooth driving setup as long as the perturbation breaks inversion (uniaxially) and time‐reversal symmetries but preserve their combinations.…”

Section: Introductionmentioning

confidence: 99%

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Hybrid Dispersion Dirac Semimetal and Hybrid Weyl Phases in Luttinger Semimetals: A Dynamical Approach

Ghorashi

2019

Annalen der Physik

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It is shown that hybrid Dirac and Weyl semimetals can be realized in a 3D Luttinger semimetal with quadratic band touching (QBT). This is illustrated using a periodic kicking scheme. In particular, the focus is on a momentum‐dependent driving (nonuniform driving) and the realization of various hybrid Dirac and Weyl semimetals is demonstrated. A unique hybrid dispersion Dirac semimetal with two nodes is identified, where one of the nodes is linear while the other is dispersed quadratically. Next, it is shown that by tilting QBT via periodic driving and in the presence of an external magnetic field, one can realize various single/double hybrid Weyl semimetals depending on the strength of external field. Finally, it is noted that in principle, phases that are found in this work can also be realized by employing the appropriate electronic interactions.

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“…This kind of kicking layout can be hard to be reached in experimental conditions, therefore, we discuss the experimental feasibility of our model in a special section (see section VII), therein, we also study a more realistic kind of driving: harmonic driving. However it is worth mentioning that many theoretical papers consider a quite similar kind of kicking 41,[47][48][49][50][51][52] . From here, we will study the t 1 → T limit, then the driving protocol can be written as…”

Section: Periodically Driven Strain Graphenementioning

confidence: 99%

Topological flat bands in time-periodically driven uniaxial strained graphene nanoribbons

Roman‐Taboada

Naumis

2017

Phys. Rev. B

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We study the emergence of electronic non-trivial topological flat bands in time-periodically driven strained graphene within a tight binding approach based on the Floquet formalism. In particular, we focus on uniaxial spatially periodic strain since it can be mapped onto an effective one-dimensional system. Also, two kinds of time-periodic driving are considered: a short pulse (delta kicking) and a sinusoidal variation (harmonic driving). We prove that for special strain wavelengths, the system is described by a two level Dirac Hamiltonian. Even though the study case is gapless, we find that topologically non-trivial flat bands emerge not only at zero-quasienergy but also at ±π quasienergy, the latter being a direct consequence of the periodicity of the Floquet space. Both kind of flat bands are thus understood as dispersionless bands joining two inequivalent touching band points with opposite Berry phase. This is confirmed by explicit evaluation of the Berry phase in the touching band points' neighborhood. Using that information, the topological phase diagram of the system is built. Additionally, the experimental feasibility of the model is discussed and two methods for the experimental realization of our model are proposed.

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Effective time-independent analysis for quantum kicked systems

Cited by 16 publications

References 41 publications

Floquet many-body engineering: topology and many-body physics in phase space lattices

Floquet many-body engineering: topology and many-body physics in phase space lattices

Hybrid Dispersion Dirac Semimetal and Hybrid Weyl Phases in Luttinger Semimetals: A Dynamical Approach

Topological flat bands in time-periodically driven uniaxial strained graphene nanoribbons

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