Tight-binding couplings in microwave artificial graphene

Bellec, Matthieu; Kuhl, Ulrich; Montambaux, Gilles; Mortessagne, Fabrice

doi:10.1103/physrevb.88.115437

Cited by 114 publications

(190 citation statements)

References 35 publications

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“…The honeycomb or hexagonal lattice geometry has now been studied theoretically and experimentally in many different photonic systems including metamaterials and photonic crystals [15][16][17], plasmonic nanoparticles [18,19], photonic lattices [20][21][22], and microwave resonator arrays [23][24][25][26], eg. Fig.…”

Section: Designmentioning

confidence: 99%

Conical intersections for light and matter waves

Leykam

Desyatnikov

2016

Advances in Physics: X

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We review the design, theory, and applications of two dimensional periodic lattices hosting conical intersections in their energy-momentum spectrum. The best known example is the Dirac cone, where propagation is governed by an effective Dirac equation, with electron spin replaced by a "fermionic" half-integer pseudospin. However, in many systems such as metamaterials, modal symmetries result in the formation of higher order conical intersections with integer or "bosonic" pseudospin. The ability to engineer lattices with these qualitatively different singular dispersion relations opens up many applications, including superior slab lasers, generation of orbital angular momentum, zeroindex metamaterials, and quantum simulation of exotic phases of relativistic matter.

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Section: Designmentioning

confidence: 99%

Conical intersections for light and matter waves

Leykam

Desyatnikov

2016

Advances in Physics: X

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“…It seems more promising to use the impact of second-order coupling on the eigenmodes of the system for experimental access. Indeed, second-and even third-order coupling in square and honeycomb lattices of microwave resonators have been unambiguously identia) Electronic mail: robert.keil@uibk.ac.at fied from their frequency spectra 19 . In optics, however, a direct measurement of waveguide eigenmodes is more challenging and requires interferometric techniques.…”

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confidence: 99%

“…Numerical simulations of the three-site system suggest a strong dependence of the inhibition on the precise form of the refractive index profiles. Therefore, an extended experimental study with different fabrication parameters as well as analogue investigations in different physical systems, such as lithographic arrays [13][14][15] , fiber waveguides 28 or microwave resonators 19 , could provide more insight in this respect. A suppression of coupling by a buffer structure could perhaps be exploited to reduce undesired cross-talk at waveguide array junctions 29 or waveguide crossings 30-32 within three-dimensional photonic routing networks.…”

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confidence: 99%

Direct measurement of second-order coupling in a waveguide lattice

Keil

Pressl

Heilmann

et al. 2015

Applied Physics Letters

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We measure the next-nearest-neighbour coupling in an array of coupled optical waveguides directly via an integrated eigenmode interferometer. In contrast to light propagation experiments, the technique is insensitive to nearest-neighbour dynamics. Our results show that second-order coupling in a linear configuration can be suppressed well below the level expected from the exponential decay of the guided modes.50 years past its proposition 1 , evanescent coupling between optical waveguides has become a standard part in the optical engineer's toolbox and is now widely applied in science and industry 2 . Extended lattices of coupled waveguides have been used for various fundamental studies and applications, ranging from artificial graphene 3,4 and quantum walks 5-8 to mode-locking of lasers 9 and quantum state preparation 10,11 . These systems are usually based on coupling between nearest neighbours. Coupling between more distant sites can often be neglected, due to an exponential decay of the waveguide modes 12 . Yet, there are configurations for which precise knowledge and control of such couplings become crucial. For instance, some one-dimensional arrays are designed towards an effective cancellation of nearest-neighbour coupling after certain distances, such that coupling between next-nearest-neighbours (henceforth termed 'second-order coupling') can become the dominant mechanism of transverse transport [13][14][15][16] . Evidently, the distance between next-nearest neighbours in two-dimensional lattices does not need to be much larger than the one between nearest neighbours 4,7 . Therefore, second-order coupling is often quite relevant in such systems. Moreover, second-order coupling has been shown to have considerable impact in nonlinear optics, where it determines the existence of a power treshold for discrete solitons 17 , as well as on two-particle interference conditions in the quantum regime 18 .In order to obtain systematic knowledge of how and with which strength second-order coupling arises in the configurations of interest it would be desirable to measure it directly. However, its subtle influence on the propagation dynamics is often masked by the much stronger firstorder coupling (or the unknown fidelity of its cancelling mechanism), such that it is quite hard to unambiguously extract the second-order coupling from light propagation experiments. It seems more promising to use the impact of second-order coupling on the eigenmodes of the system for experimental access. Indeed, second-and even third-order coupling in square and honeycomb lattices of microwave resonators have been unambiguously identia) Electronic mail: robert.keil@uibk.ac.at fied from their frequency spectra 19 . In optics, however, a direct measurement of waveguide eigenmodes is more challenging and requires interferometric techniques. In this work, we present such a method and apply it to measure second-order coupling in the most fundamental system where it can occur -an array of three waveguides. In particular, we investigate whethe...

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“…Shaken optical lattices [13] and photonic crystals with extended helical wave guides in the third spatial dimension (that simulates a circular in-plane vector potential [19]) constitute concrete physical systems with a high level of control, in which the different phases discussed here can be achieved. Microwave honeycomb crystals have also been demonstrated to be correctly described by a tight-binding model [27]. The recent realization of a Floquet microwave crystal exhibiting sidebands features [28] provides an additional promising direction for the achievement of the different regimes we describe here (the hopping parameter being of the order of a few MHz [27] whereas the driving frequency of the cavity can vary up to the GHz [28]).…”

mentioning

confidence: 99%

“…Microwave honeycomb crystals have also been demonstrated to be correctly described by a tight-binding model [27]. The recent realization of a Floquet microwave crystal exhibiting sidebands features [28] provides an additional promising direction for the achievement of the different regimes we describe here (the hopping parameter being of the order of a few MHz [27] whereas the driving frequency of the cavity can vary up to the GHz [28]). In graphene, the possibility to induce phases with higher Chern numbers would correspond to electromagnetic frequencies ω/2π above the THz, from the mid-infrared to visible light.…”

mentioning

confidence: 99%

Engineering anomalous quantum Hall plateaus and antichiral states with ac fields

2014

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We investigate the ac electric field induced quantum anomalous Hall effect in honeycomb lattices and derive the full phase diagram for arbitrary field amplitude and phase polarization. We show how to induce antichiral edge modes as well as topological phases characterized by a Chern number larger than 1 by means of suitable drivings. In particular, we find that the Chern number develops plateaus as a function of the frequency, providing a time-dependent analog to the ones in the quantum Hall effect. Introduction. The realization of different topological states of matter is one of the major challenges for both fundamental reasons and technological perspectives. Several of these states have been originally predicted in the honeycomb lattice, whose Dirac-like band structure brings the system at a critical point of a topological phase transition. There, the development of gaps by different mechanisms results in a variety of topological phases [1,2]. In this line, the quantum spin Hall phase was first obtained in HgTe quantum wells [3,4], where the topological phase transition was controlled by the thickness of the quantum well. Likewise, the quantum anomalous Hall effect (QAHE)-for which time-reversal symmetry (TRS) is broken in the absence of a magnetic field-was originally proposed by Haldane in the honeycomb lattice [1]. However, despite the success of the theoretical model, it has been very difficult to achieve experimentally, until very recently in doped topological insulators [5].Simultaneously, different techniques have been proposed to externally control the topological properties of a system. One of the most promising consists in periodically driving the system in order to achieve a topological phase transition [6][7][8][9][10][11]. Proposals with a time periodic driving in semiconductors [6,12], optical lattices [13], or graphene [7,[14][15][16][17][18] have been suggested to achieve various dynamical generalizations of static topological phases, called Floquet topological phases [12], and have been recently observed in photonic crystals [19]. Importantly for our purposes, the previous studies for the honeycomb lattice were restricted either to numerical calculations in finite-size systems, where the physical mechanism driving the topological phase transitions was not clear, or to very high frequencies and low-energy approximations, where most of the phase diagram remained unknown.In the present work, we derive the full phase diagram of periodically driven honeycomb lattices in the QAHE regime, by explicitly calculating the Chern number of the Floquet bands. Our model is valid for arbitrary field frequency, amplitude, and polarization and therefore goes beyond the single Dirac cone description and the rotating wave approximation. Surprisingly, we find that a clockwise driving may also lead to counterclockwise (or antichiral) edge states, and demonstrate that their appearance is linked to two distinct band inversion mechanisms. Moreover, we show how to induce topological phases with Chern numbers larger tha...

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Tight-binding couplings in microwave artificial graphene

Cited by 114 publications

References 35 publications

Conical intersections for light and matter waves

Conical intersections for light and matter waves

Direct measurement of second-order coupling in a waveguide lattice

Engineering anomalous quantum Hall plateaus and antichiral states with ac fields

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