Role of real-space micromotion for bosonic and fermionic Floquet fractional Chern insulators

Anisimovas, Egidijus; Žlabys, Giedrius; Anderson, Brandon; Juzeliūnas, Gediminas; Eckardt, André

doi:10.1103/physrevb.91.245135

Cited by 56 publications

(63 citation statements)

References 82 publications

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“…Moreover, in Refs. [185,186] it was shown that Floquet Chern insulators with sufficiently strong nearest-neighbour interactions exhibit the phenomenon fractionalisation at fractional fillings. Cold atom experiments managed to realize a fermionic system with topological bands in the laboratory [49].…”

Section: 2mentioning

confidence: 99%

Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering

Bukov

D’Alessio

Polkovnikov

2015

Advances in Physics

1,169

1,291

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We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian. These classes cover systems, such as the Kapitza pendulum, the Harper-Hofstadter model of neutral atoms in a magnetic field, the Haldane Floquet Chern insulator and others. In all setups considered, we discuss both the infinite-frequency limit and the leading finite-frequency corrections to the Floquet Hamiltonian. We provide a short overview of Floquet theory focusing on the gauge structure associated with the choice of stroboscopic frame and the differences between stroboscopic and non-stroboscopic dynamics. In the latter case one has to work with dressed operators representing observables and a dressed density matrix. We also comment on the application of Floquet Theory to systems described by static Hamiltonians with well-separated energy scales and, in particular, discuss parallels between the inverse-frequency expansion and the Schrieffer-Wolff transformation extending the latter to driven systems. PACS

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Section: 2mentioning

confidence: 99%

Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering

Bukov

D’Alessio

Polkovnikov

2015

Advances in Physics

1,169

1,291

View full text Add to dashboard Cite

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“…Similar schemes can be envisaged to produce synthetic spin-orbit couplings, uniform magnetic fields and topological insulating states with shaken optical lattices [100]. Recently, and in direct analogy with solid-state-physics Floquet topological states [104,105,107,109,375], it has been suggested that (circularly) shaken hexagonal optical lattices could reproduce the physics of graphene subjected to circularly polarized light [see Sect. 2.2 and Refs.…”

Section: Other Relevant Schemesmentioning

confidence: 99%

Light-induced gauge fields for ultracold atoms

et al. 2014

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Abstract. Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our universe is ruled by gravity, whose gauge structure suggests the existence of a particle -the graviton-that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms "feeling" laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials -both Abelian and non-Abelian -in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms.arXiv:1308.6533v3 [cond-mat.quant-gas]

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“…In addition to this aspect, we now have to measure observables that are affected by micromotion describing the dynamics of the Floquet system within a driving period. Whilst this micromotion tends to become negligible for infinite driving frequencies, it alters the states significantly for near-resonant and low-frequency modulation [1,2,4,[28][29][30][31].In this work, we address the previously mentioned challenges in a tractable way by realizing a periodically driven array of double wells [32] occupied by pairs of interacting atoms [33][34][35][36], which allows for a full control of the Floquet state population [27]. The symmetric double well consists of two sites containing two opposite spins, and can be described by a Hubbard model with a tunneling amplitude t, and an on-site interaction U .…”

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confidence: 99%

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Controlling the Floquet state population and observing micromotion in a periodically driven two-body quantum system

et al. 2017

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Near-resonant periodic driving of quantum systems promises the implementation of a large variety of novel quantum states, though their preparation and measurement remains challenging. We address these aspects in a model system consisting of interacting fermions in a periodically driven array of double wells created by an optical lattice. The singlet and triplet fractions and the double occupancy of the Floquet states are measured, and their behavior as a function of the interaction strength is analyzed in the high-and low-frequency regimes. We demonstrate full control of the Floquet state population and find suitable ramping protocols and time-scales which adiabatically connect the initial ground state to different targeted Floquet states. The micromotion which exactly describes the time evolution of the system within one driving cycle is observed. Additionally, we provide an analytic description of the model and compare it to numerical simulations.Floquet engineering aims to create novel quantum states through periodic driving, by realising effective Hamiltonians beyond the reach of static systems [1][2][3]. These effective Hamiltonians have been implemented with photons [4,5], solids [6] and ultracold gases in optical lattices [3]. However, preparing and controlling a specific quantum state in a driven system remains in general a challenge. This is particularly the case for many interesting schemes which were realised by driving at low frequencies [4,7] or even close to a characteristic energy scale of the underlying static Hamiltonian. Indeed, driving near-resonantly to the band structure was used to modify kinetic terms in the Hamiltonian [8][9][10][11][12][13][14][15], and modulating close to the interaction energy was proposed to engineer novel interaction terms [16][17][18][19][20]. For all these schemes, the periodic drive strongly couples the static eigenstates, which makes the full control of the population of the different Floquet states and the analysis of their exact time evolution demanding.One important aspect lies in the fundamental differences between Floquet-engineered systems and static Hamiltonians. For example, a periodically driven system is described by a periodic quasi-energy spectrum, and thus has no ground state. Its absence raises an important experimental challenge: How to adiabatically connect the ground state of the initial static Hamiltonian to the targeted Floquet eigenstate? Theory suggests that the population of Floquet states has a non-trivial dependence on the ramp speed and on the exact trajectory which is used in parameter-space [21][22][23][24][25][26], particularly in the case of near-resonant driving which leads to the formation of avoided crossings between quasi-energy levels [27]. In addition to this aspect, we now have to measure observables that are affected by micromotion describing the dynamics of the Floquet system within a driving period. Whilst this micromotion tends to become negligible for infinite driving frequencies, it alters the states significantly for nea...

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Role of real-space micromotion for bosonic and fermionic Floquet fractional Chern insulators

Cited by 56 publications

References 82 publications

Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering

Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering

Light-induced gauge fields for ultracold atoms

Controlling the Floquet state population and observing micromotion in a periodically driven two-body quantum system

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