Compact flat band states in optically induced flatland photonic lattices

Travkin, Evgenij; Diebel, Falko; Denz, Cornélia

doi:10.1063/1.4990998

Cited by 41 publications

(32 citation statements)

References 48 publications

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“…The physics of flat band (FB) systems has drawn a lot of research attention in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. One of the main reasons why such dispersionless flat bands are of great interest to the physics community is that, they give rise to highly degenerate manifold of single-particle states, which can act as a good platform to study rich, strongly correlated phenomena.…”

Section: Introductionmentioning

confidence: 99%

Nontrivial topological flat bands in a diamond-octagon lattice geometry

Pal

2018

Phys. Rev. B

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We present the appearance of nearly flat band states with nonzero Chern numbers in a twodimensional "diamond-octagon" lattice model comprising two kinds of elementary plaquette geometries, diamond and octagon, respectively. We show that the origin of such nontrivial topological nearly flat bands can be described by a short-ranged tight-binding Hamiltonian. By considering an additional diagonal hopping parameter in the diamond plaquettes along with an externally finetuned magnetic flux, it leads to the emergence of such nearly flat band states with nonzero Chern numbers for our simple lattice model. Such topologically nontrivial nearly flat bands can be very useful to realize the fractional topological phenomena in lattice models when the interaction is taken into consideration. In addition, we also show that perfect band flattening for certain energy bands, leading to compact localized states can be accomplished by fine-tuning the parameters of the Hamiltonian of the system. We compute the density of states and the wavefunction amplitude distribution at different lattice sites to corroborate the formation of such perfectly flat band states in the energy spectrum. Considering the structural homology between a diamond-octagon lattice and a kagome lattice, we strongly believe that one can experimentally realize a diamond-octagon lattice using ultracold quantum gases in an optical lattice setting. A possible application of our lattice model could be to design a photonic lattice using single-mode laser-induced photonic waveguides and study the corresponding photonic flat bands.

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Section: Introductionmentioning

confidence: 99%

Nontrivial topological flat bands in a diamond-octagon lattice geometry

Pal

2018

Phys. Rev. B

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“…Due to their completely opposite characteristics, flatband and Dirac dispersion are usually attributed to different bands of the photonic structures (2D tight-binding lattices [5,6,8,9], accidental degeneracy in 2D photonic crystal [15][16][17][18]). Other configurations exhibit the sole presence of flatband states (1D tight-binding lattices [7,10], dispersion engineering with hybrid micro cavities [11,13]). …”

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Symmetry Breaking in Photonic Crystals: On-Demand Dispersion from Flatband to Dirac Cones

et al. 2018

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We demonstrate that symmetry breaking opens a new degree of freedom to tailor the energymomentum dispersion in photonic crystals. Using a general theoretical framework in two illustrative practical structures, we show that breaking symmetry enables an on-demand tuning of the local density of states of a same photonic band from zero (Dirac cone dispersion) to infinity (flatband dispersion), as well as any constant density over an adjustable spectral range. As a proof-of-concept, we experimentally demonstrate the transformation of a very same photonic band from conventional quadratic shape to Dirac dispersion, flatband dispersion and multivaley one, by finely tuning the vertical symmetry breaking. Our results provide an unprecedented degree of freedom for optical dispersion engineering in planar integrated photonic devices.Engineering the energy-momentum dispersion of photonic structures is at the heart of contemporary optics research. This fundamental feature molds the light propagation [1], dictates the coupling with free space [2], and tailors light-matter interactions [3]. Such a dispersion engineering is generally achieved through a designed periodic arrangement of materials with different permittivities in photonic crystals, metamaterials and metasurfaces. Recently, two particular types of dispersions have been intensively studied: flatband dispersion [4][5][6][7][8][9][10][11][12][13] and Dirac dispersion [15][16][17][18][19][20][21][22][23][24][25][26][27][28]. The first one provides slow light of zero group velocity with high density of states for a broad range of the Brillouin zone, thus greatly enhances light-matter interaction and nonlinear behaviors for low-threshold micro-lasers and information processing applications [30,31]. Moreover, flatband gives rise to localized stationary eigenstates which are extremely sensitive to disorder effects due to an infinite effective mass [7,14]. This suggests new regime of light localization [8,9] other than conventional concepts such as Anderson localization [32,33] and optical bound states in continuum [34,35]. Being an opposite extreme to flat dispersion, Dirac dispersion (double Dirac cones with no bandgap) corresponds to massless photonic states. By analogy with the propagation of electrons in graphene, Dirac photons propagation could lead to phenomena such as Klein tunneling [19] and Zitterbewegung [20] for photons. Moreover, photonic Dirac dispersion opens the way to realize large-area single mode lasers [21,22]; and enables many exotic physical features such as zero-refractive index materials for transformation optics applications [15,17,18] and photonic topological insulator [23][24][25][26][27][28]. Due to their completely opposite characteristics, flatband and Dirac dispersion are usually attributed to different bands of the photonic structures (2D tight-binding lattices [5,6,8,9], accidental degeneracy in 2D photonic crystal [15][16][17][18]). Other configurations exhibit the sole presence of flatband states (1D tight-binding lattices [7,10], dispersio...

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“…Flat band networks have been proposed in one, two, and three dimensions and various flat band generators were identified [3][4][5][6]. Experimental observations of flat bands and CLS are reported in photonic waveguide networks [7][8][9][10][11][12][13][14][15], exciton-polariton condensates [16][17][18], and ultracold atomic condensates [19,20]. The tight binding network equations correspond to an eigenvalue problem EΨ l = − m t lm Ψ m .…”

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confidence: 99%

Topological flat Wannier-Stark bands

2018

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We analyze the spectrum and eigenstates of a quantum particle in a bipartite two-dimensional tight-binding dice network with short range hopping under the action of a dc bias. We find that the energy spectrum consists of a periodic repetition of one-dimensional energy band multiplets, with one member in the multiplet being strictly flat. The corresponding macroscopic degeneracy invokes eigenstates localized exponentially perpendicular to the dc field direction, and super-exponentially along the dc field direction. We also show that the band multiplet is characterized by a topological winding number (Zak phase), which changes abruptly if we vary the dc field strength. These changes are induced by gap closings between the flat and dispersive bands, and reflect the number of these closings.Recently much attention has been paid to flat bands in one-, two-and three-dimensional lattices with short range hoppings and non-trivial geometry [1]. Flat bands with finite range hoppings exist due to destructive interference leading to a macroscopic number of degenerate compact localized eigenstates (CLS) which have strictly zero amplitudes outside a finite region of the lattice [2]. Flat band networks have been proposed in one, two, and three dimensions and various flat band generators were identified [3][4][5][6]. Experimental observations of flat bands and CLS are reported in photonic waveguide networks [7][8][9][10][11][12][13][14][15], exciton-polariton condensates [16][17][18], and ultracold atomic condensates [19,20]. The tight binding network equations correspond to an eigenvalue problem EΨ l = − m t lm Ψ m . For bipartite lattices, the existence of flat bands and CLS is ensured through a proper usage of the protecting chiral symmetry [6]. For example, for the dice lattice shown in Fig. 1(a) and t lm = 1 the CLS consists of an empty C site which is surrounded by six excited A and B sites with alternating amplitudes ±1/ √ 6.When a dc field is added, quantum particles start to experience well studied Bloch oscillations (see e.g. [21,22]). Our results are therefore applicable for ultracold atoms in optical lattices where the electric field is substituted by a tilt of the lattice in the gravitational field [23] or accelerating the whole lattice [24]. The same type of perturbations can be arranged in optical waveguide arrays where the electric field is modeled by a curved geometry of the waveguides [25].In the present letter we report on a new family of flat bands which exist in dc biased bipartite lattices and which are not supported by CLS, despite of the short range hopping. We consider the dice lattice in the presence of a dc field oriented along the y-direction (Fig.1(a)). The absence of CLS indicates nontrivial topology. We compute winding numbers (Zak phase) which indeed show abrupt changes through conical intersection point degeneracies upon variations of the dc field strength. We also generalize to different orientations of the field F and other lattice geometries.

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Compact flat band states in optically induced flatland photonic lattices

Cited by 41 publications

References 48 publications

Nontrivial topological flat bands in a diamond-octagon lattice geometry

Nontrivial topological flat bands in a diamond-octagon lattice geometry

Symmetry Breaking in Photonic Crystals: On-Demand Dispersion from Flatband to Dirac Cones

Topological flat Wannier-Stark bands

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