Modified interactions in a Floquet topological system on a square lattice and their impact on a bosonic fractional Chern insulator state

Račiūnas, Mantas; Žlabys, Giedrius; Eckardt, André; Anisimovas, Egidijus

doi:10.1103/physreva.93.043618

Cited by 20 publications

(16 citation statements)

References 69 publications

(99 reference statements)

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“…Numerical studies based on the exact diagonalization (Anisimovas et al, 2015;Račiūnas et al, 2016) suggest that this smearing out tends to have a negative impact on the possible stabilization of fractional-Chern-insulator states in Floquet topological band structures recently proposed by Grushin et al, 2014.…”

Section: Floquet Engineering Of Interactionsmentioning

confidence: 99%

Colloquium: Atomic quantum gases in periodically driven optical lattices

2017

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Time periodic forcing in the form of coherent radiation is a standard tool for the coherent manipulation of small quantum systems like single atoms. In the last years, periodic driving has more and more also been considered as a means for the coherent control of many-body systems. In particular, experiments with ultracold quantum gases in optical lattices subjected to periodic driving in the lower kilohertz regime have attracted a lot of attention. Milestones include the observation of dynamic localization, the dynamic control of the quantum phase transition between a bosonic superfluid and a Mott insulator, as well as the dynamic creation of strong artificial magnetic fields and topological band structures. This article reviews these recent experiments and their theoretical description. Moreover, fundamental properties of periodically driven many-body systems are discussed within the framework of Floquet theory, including heating, relaxation dynamics, anomalous topological edge states, and the response to slow parameter variations.

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Section: Floquet Engineering Of Interactionsmentioning

confidence: 99%

Colloquium: Atomic quantum gases in periodically driven optical lattices

2017

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“…We have also found that ramping up the interaction strengths, driving-induced heating is significantly enhanced, until a saturation value is reached roughly when the ratio U s /J s reaches values of 3. This saturation is a promising result regarding the possibility to use Floquet engineering for the preparation of strongly correlated states of matter such as fractional Chern insulators [46][47][48][49].…”

Section: Discussionmentioning

confidence: 99%

Optimal frequency window for Floquet engineering in optical lattices

Sun

Eckardt

2020

Phys. Rev. Research

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The concept of Floquet engineering is to subject a quantum system to time-periodic driving in such a way that it acquires interesting novel properties. It has successfully been employed in atomic quantum gases in driven optical lattices. Typically, Floquet engineering is based on two approximations. On the one hand, it is assuming that resonant excitations to high-lying states above some energy gap are suppressed for sufficiently low driving frequencies, so that the system can be described within some low-energy subspace (e.g. spanned by the lowest Bloch band of a lattice). On the other hand, the driving frequency is also assumed to still be large compared to the typical energy scale of this low-energy subspace, so that it does not resonantly create excitations within this space. Eventually, on some time scale τ , deviations from these approximations will make themselves felt as unwanted heating. Floquet engineering, thus, requires a window of driving frequencies, where both types of heating processes are suppressed on the experimentally relevant time scale. In this paper, we theoretically investigate the existence of such an optimal frequency window, using the example of interacting bosons in a shaken optical lattice. We find that the maximum value of τ , measured in the experimentally relevant unit of the tunneling time, increases with the lattice depth.

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“…An entire sub-domain of "Floquet Topological Insulators" [41] has emerged as a result, which constitutes those systems that exhibit topological ground states and edge phenomena in the presence of certain time-dependent periodic potentials [42]. They have offered unprecedented control and freedom to engineer new topological phases and edge state(in some cases Majorana modes) behaviors [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] as well as a knob to study topological phase transitions in cold-atom or photonic crystal setups [63][64][65][66][67][68][69]. The theoretical classification of Floquet topological insulators and the identification of valid topological invariants that correctly characterize the bulk-edge correspondence for these systems is an on-going effort [70][71][72][73][74][75][76][77].…”

Section: Introductionmentioning

confidence: 99%

“…The recent success in realizing the Haldane model experimentally [30] within the framework of ultracold atoms in optical lattices has opened a doorway to engineering various kinds of Chern insulators, using the paradigm of shaken optical lattices and the Floquet formalism, and studying topological transitions in them [67,69,86]. These realizations offer an appreciable degree of tunability and provide an encouraging platform arXiv:1709.08354v2 [cond-mat.mes-hall] 17 Jan 2018 for the study of Haldane systems under periodic driving.…”

Section: Introductionmentioning

confidence: 99%

Floquet topological phase transitions in a kicked Haldane-Chern insulator

et al. 2018

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We consider a periodically δ-kicked Haldane type Chern insulator with the kicking applied in theẑ direction. This is known to behave as an inversion symmetry breaking perturbation, since it introduces a time-dependent staggered sub-lattice potential. We study here the effects of such driving on the topological phase diagram of the original Haldane model of a Hall effect in the absence of a net magnetic field. The resultant Floquet band topology is again that of a Chern insulator with the driving parameters, frequency and amplitude, influencing the inversion breaking mass M of the undriven Haldane model. A family of such, periodically related, 'Semenoff masses' is observed to occur which support a periodic repetition of Haldane like phase diagrams along the inversion breaking axis of the phase plots. Out of these it is possible to identify two in-equivalent masses in the reduced zone scheme of the Floquet quasienergies, which form the centres of two inequivalent phase diagrams. Further, variation in the driving amplitude's magnitude alone is shown to effect the topological properties by linearly shifting the phase diagram of the driven model about the position of the undriven case. A phenomenon that allows the study of Floquet topological phase transitions in the system. Finally, we also discuss some issues regarding the modifications to Haldane's condition for preventing band overlaps at the Dirac point touchings in the Brillouin zone, in the presence of kicking. * tridev.mishra@pilani.bits-pilani.ac.in

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Modified interactions in a Floquet topological system on a square lattice and their impact on a bosonic fractional Chern insulator state

Cited by 20 publications

References 69 publications

Colloquium: Atomic quantum gases in periodically driven optical lattices

Colloquium: Atomic quantum gases in periodically driven optical lattices

Optimal frequency window for Floquet engineering in optical lattices

Floquet topological phase transitions in a kicked Haldane-Chern insulator

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