Transport in Sawtooth photonic lattices

Weimann, Steffen; Morales‐Inostroza, Luis; Real, Bastián; Cantillano, Camilo; Szameit, Alexander; Vicencio, Rodrigo A.

doi:10.1364/ol.41.002414

Cited by 89 publications

(93 citation statements)

References 34 publications

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“…Localization would occur close to the FB condition V F B sp , while transport would manifest away this value. This behavior is quite similar to the one found for Sawtooth lattices [16], where a FB is formed only for a very specific condition between coupling constants. Therefore, our simple 1D binary model could show an insulator transition when coupling interaction V sp /V s is varied along the experiment.…”

Section: Linear Spectrumsupporting

confidence: 86%

“…However, by numerically diagonalizing a finite lattice system, we find that an edge with a vertically oriented waveguide generates an exponentially decaying eigenmode, while a horizontal edge waveguide does not. In order to investigate this edge state, we consider a vertical waveguide at site n = 1 and assume the following ansatz [1,2,16] {u n , v n , x n , w n }(z) = {A, B, C, D} n−1 e iβez , for n 1, with | | < 1 (which implies an exponentially decaying state). A, B and D correspond to the amplitudes of this mode to be determined by solving a set of coupled equations.…”

Section: Edge Statesmentioning

confidence: 99%

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Perfect localization on flat-band binary one-dimensional photonic lattices

Cáceres-Aravena

Vicencio

2019

Phys. Rev. A

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The existence of flat bands is generally thought to be physically possible only for dimensions larger than one. However, by exciting a system with different orthogonal states this condition can be reformulated. In this work, we demonstrate that a one-dimensional binary lattice supports always a trivial flat band, which is formed by isolated single-site vertical dipolar states. These flat band modes correspond to the highest localized modes for any discrete system, without the need of any aditional mechanism like, e.g., disorder or nonlinearity. By fulfilling a specific relation between lattice parameters, an extra flat band can be excited as well, with modes composed by fundamental and dipolar states that occupy only three lattice sites. Additionally, by inspecting the lattice edges, we are able to construct analytical Shockley surface modes, which can be compact or present staggered or unstaggered tails. We believe that our proposed model could be a good candidate for observing transport and localization phenomena on a simple one-dimensional linear photonic lattice.

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Section: Linear Spectrumsupporting

confidence: 86%

Section: Edge Statesmentioning

confidence: 99%

Perfect localization on flat-band binary one-dimensional photonic lattices

Cáceres-Aravena

Vicencio

2019

Phys. Rev. A

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“…4(c), where the unitary cell of four sites is denoted by an enclosed area. However, due to the Sawtooth symmetry the four sites can be reduced to just two sites [18]. We solve the eigenvalue problem (2) with this geometry and find two linear bands: −2V 2 , 4V 2 cos 2 (k x ); i.e., a Flat Band emerges for this particular ratio between coupling coefficients.…”

Section: B Sawtooth Latticementioning

confidence: 99%

“…In these quasi-1D or 2D systems, a complete band (not only a section of it) is completely flat, implying zero dispersion and not diffraction at all for the states belonging to this band. Diamond [15], Stub [16], Sawtooth [17,18], Kagome [19,20] or Lieb [21][22][23] lattices are some examples of recent explored FB systems, in diverse physical contexts. These examples show the diversity of fabrication techniques and impressive possibilities for creating, in principle, any wished lattice.…”

Section: Introductionmentioning

confidence: 99%

Simple method to construct flat-band lattices

2016

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We develop a simple and general method to construct arbitrary Flat Band lattices. We identify the basic ingredients behind zero-dispersion bands and develop a method to construct extended lattices based on a consecutive repetition of a given mini-array. The number of degenerated localized states is defined by the number of connected mini-arrays times the number of modes preserving the symmetry at a given connector site. In this way, we create one or more (depending on the lattice geometry) complete degenerated Flat Bands for quasi-one and two-dimensional systems. We probe our method by studying several examples, and discuss the effect of additional interactions like anisotropy or nonlinearity. At the end, we test our method by studying numerically a ribbon lattice using a continuous description.

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“…With regard to the significant in real experimental materials, we would like mention that using photonic lattices and optical lattices [43][44][45][46] can be constructed a double sawtooth spin ladder with special model in the real world. For instance, authors in Ref.…”

Section: Introductionmentioning

confidence: 99%

Phase transitions and thermal entanglement of the distorted Ising–Heisenberg spin chain: topology of multiple-spin exchange interactions in spin ladders

Zad

Ananikian²

2017

J. Phys.: Condens. Matter

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Abstract. We consider a symmetric spin-1/2 Ising-XXZ double sawtooth spin ladder obtained from distorting a spin chain, with the XXZ interaction between the interstitial Heisenberg dimers (which are connected to the spins based on the legs via an Ising-type interaction), the Ising coupling between nearest-neighbor spins of the legs and rungs spins, respectively, and additional cyclic four-spin exchange (ring exchange) in square plaquette of each block. The presented analysis supplemented by results of the exact solution of the model with infinite periodic boundary implies a rich ground state phase diagram. As well as the quantum phase transitions, the characteristics of some of the thermodynamic parameters such as heat capacity, magnetization and magnetic susceptibility are investigated. We here prove that among the considered thermodynamic and thermal parameters, solely the heat capacity is sensitive versus the changes of the cyclic four-spin exchange interaction. By using the heat capacity function, we obtain a singularity relation between the cyclic four-spin exchange interaction and the exchange coupling between pair spins on each rung of the spin ladder. All thermal and thermodynamic quantities under consideration should investigate by regarding those points which satisfy the singularity relation. The thermal entanglement within the Heisenberg spin dimers is investigated by using the concurrence, which is calculated from a relevant reduced density operator in the thermodynamic limit.

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Transport in Sawtooth photonic lattices

Cited by 89 publications

References 34 publications

Perfect localization on flat-band binary one-dimensional photonic lattices

Perfect localization on flat-band binary one-dimensional photonic lattices

Simple method to construct flat-band lattices

Phase transitions and thermal entanglement of the distorted Ising–Heisenberg spin chain: topology of multiple-spin exchange interactions in spin ladders

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