Compact discrete breathers on flat-band networks

Danieli, Carlo; Maluckov, Aleksandra; Flach, Sergej

doi:10.1063/1.5041434

Cited by 32 publications

(36 citation statements)

References 46 publications

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“…Such dissipative CLS may also become dissipative compact solutions of the nonlinear regime -in agreement with Ref. [21] -as well as their time behavior (exponential growth, decay or being constant) can be controlled by tuning the dissipation parameters, in analogy with what we herewith reported. Moreover, following [6,7], we ob-serve that the absorption conditions in Eq.…”

supporting

confidence: 84%

“…Indeed, as discussed in Ref. [21], Kerr nonlinearity preserves destructive interference, and the dissipative CLS at n = 0 with amplitude A…”

mentioning

confidence: 85%

“…This still holds in the nonlinear regime g = 0 of Eq. (10) since the linear CLS locate at the unitcell n = 0 can be continued as compact breather with frequency Ω = h + gA 2 − iγ(1 − δ)/2 [21]. This yields a precise control of the time behavior of the breather density S 0 , namely S 0 decays exponentially for δ < 1, grows exponentially for δ > 1 and stay constant for δ = 1 -as shown in the inset of Fig.6(d).…”

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confidence: 99%

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Casting dissipative compact states in coherent perfect absorbers

Danieli

Mithun

2020

Phys. Rev. Research

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Coherent perfect absorption (CPA), also known as time-reversed laser, is a wave phenomenon resulting from the reciprocity of destructive interference of transmitted and reflected waves. In this work we consider quasi one-dimensional lattice networks which posses at least one flat band, and show that CPA and lasing can be induced in both linear and nonlinear regimes of this lattice by fine-tuning non-Hermitian defects (dissipative terms localized within one unit-cell). We show that local dissipations that yield CPA simultaneously yield novel dissipative compact solutions of the lattice, whose growth or decay in time can be fine-tuned via the dissipation parameter. The scheme used to numerically visualize the theoretical findings offers a novel platform for the experimental implementation of these phenomena in optical devices.

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supporting

confidence: 84%

“…Indeed, as discussed in Ref. [21], Kerr nonlinearity preserves destructive interference, and the dissipative CLS at n = 0 with amplitude A…”

mentioning

confidence: 85%

mentioning

confidence: 99%

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Casting dissipative compact states in coherent perfect absorbers

Danieli

Mithun

2020

Phys. Rev. Research

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“…As far as we are aware, the corresponding nonlinear compact modes have not been investigated in any earlier work. By contrast, there are several works studying nonlinear compactons in a 'sawtooth' lattice [22,23] which would result if an additional next-nearest neighbour (horizontal) coupling was added to either the upper or the lower sub-chain (but not both) in figure 1. In this case, compactons may appear without presence of spin-orbit coupling, instead due to balance between nearerst and next-nearest neighbor couplings.…”

Section: Flat Band and Compact Modesmentioning

confidence: 98%

Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains

et al. 2019

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We consider a system of generalized coupled Discrete Nonlinear Schrödinger (DNLS) equations, derived as a tight-binding model from the Gross-Pitaevskii-type equations describing a zigzag chain of weakly coupled condensates of exciton-polaritons with spin-orbit (TE-TM) coupling. We focus on the simplest case when the angles for the links in the zigzag chain are ±π/4 with respect to the chain axis, and the basis (Wannier) functions are cylindrically symmetric (zero orbital angular momenta). We analyze the properties of the fundamental nonlinear localized solutions, with particular interest in the discrete gap solitons appearing due to the simultaneous presence of spin-orbit coupling and zigzag geometry, opening a gap in the linear dispersion relation. In particular, their linear stability is analyzed. We also find that the linear dispersion relation becomes exactly flat at particular parameter values, and obtain corresponding compact solutions localized on two neighboring sites, with spin-up and spindown parts π/2 out of phase at each site. The continuation of these compact modes into exponentially decaying gap modes for generic parameter values is studied numerically, and regions of stability are found to exist in the lower or upper half of the gap, depending on the type of gap modes. , integrating over x and y, using the orthogonality of Wannier functions and neglecting all overlaps beyond nearest neighbors, we obtain from (4) a 1D lattice equation of the following form for the site amplitudes of the spin-up component:

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“…Flatband geometries [1][2][3][4][5][6][7][8][9][10][11][12] have attracted great interest in recent years due to the existence of at least one completely dispersionless band in their energy spectrum which bring new perspectives to the study of various fascinating phenomena, including fractional quantum Hall effect [13][14][15][16] , inverse Anderson localization [17][18][19][20][21][22] , conservative PT-symmetric compact solutions [23][24][25][26][27][28] , and nonlinear compact breathers [29][30][31][32] . Destructive interference is the essence of a flatband existence, and the associated eigenmodes are compact in real space -hence dubbed compact localized states (CLSs).…”

Section: Introductionmentioning

confidence: 99%

Observation of quincunx-shaped and dipole-like flatband states in photonic rhombic lattices without band-touching

et al. 2020

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We demonstrate experimentally the existence of compact localized states (CLSs) in a quasi-one-dimensional photonic rhombic lattice in presence of two distinct refractive-index gradients (i.e., a driven lattice ribbon) acting as external direct current (dc) electric fields. Such a lattice is composed of an array of periodically arranged evanescently coupled waveguides, which hosts a perfect flatband that touches both remaining dispersive bands when it is not driven. The external driving is realized by modulating the relative writing beam intensity of adjacent waveguides. We find that a y-gradient set perpendicularly to the ribbon preserves the flatband while removing the band-touching. The undriven CLS -which occupies two lattices sites over one unit cell -turns into a quincunx-shaped CLS spanned over two unit cells. Instead, an x-gradient acting parallel to the ribbon yields a Stark ladder of CLS whose spatial profile is unchanged with respect to the undriven case. We notably find that their superposition leads to Bloch-like oscillations in momentum space.

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Compact discrete breathers on flat-band networks

Cited by 32 publications

References 46 publications

Casting dissipative compact states in coherent perfect absorbers

Casting dissipative compact states in coherent perfect absorbers

Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains

Observation of quincunx-shaped and dipole-like flatband states in photonic rhombic lattices without band-touching

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