Observation of a Localization Transition in Quasiperiodic Photonic Lattices

Lahini, Yoav; Pugatch, Rami; Pozzi, F.; Sorel, Marc; Morandotti, Roberto; Davidson, Nir; Silberberg, Yaron

doi:10.1103/physrevlett.103.013901

Cited by 401 publications

(328 citation statements)

References 39 publications

(20 reference statements)

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“…The effects of interaction have been recently the subject of several theoretical investigations in the case of localization in purely random potentials [7,8,9,10,11,12] and quasi-periodic potentials [13,14,15], but some results are still controversial. It is worth mentioning that the Aubry-Andrè model has been recently implemented also in experiments with diffusion of light in photonic lattices [16].…”

Section: Introductionmentioning

confidence: 99%

Effects of interaction on the diffusion of atomic matter waves in one-dimensional quasiperiodic potentials

2009

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We study the behaviour of an ultracold atomic gas of bosons in a bichromatic lattice, where the weaker lattice is used as a source of disorder. We numerically solve a discretized mean-field equation, which generalizes the one-dimensional Aubry-Andrè model for particles in a quasi-periodic potential by including the interaction between atoms. We compare the results for commensurate and incommensurate lattices. We investigate the role of the initial shape of the wavepacket as well as the interplay between two competing effects of the interaction, namely self-trapping and delocalization. Our calculations show that, if the condensate initially occupies a single lattice site, the dynamics of the interacting gas is dominated by self-trapping in a wide range of parameters, even for weak interaction. Conversely, if the diffusion starts from a Gaussian wavepacket, self-trapping is significantly suppressed and the destruction of localization by interaction is more easily observable.

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Section: Introductionmentioning

confidence: 99%

Effects of interaction on the diffusion of atomic matter waves in one-dimensional quasiperiodic potentials

2009

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“…Fascinating questions related to entropy generation in the field, the potential impact of nonlinearities induced in the lattice at high fluence levels, the effect of timevarying potentials, and the evolution of non-classical light such as spatially entangled biphoton and Fock states in activated chiral lattices can now be pursued. The question of the existence of disorder-immune symmetries and the associated thermalization gap in quasicrystals 5 and incommensurate Aubry-André lattice models 32,33 is intriguing. Finally, although we have couched our results in an optical setting, they may be readily mapped onto other physical systems by virtue of the generic tight-binding model we have adopted.…”

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confidence: 99%

A photonic thermalization gap in disordered lattices

2015

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The formation of gaps -forbidden ranges in the values of a physical parameter -is a ubiquitous feature of a variety of physical systems: from energy bandgaps of electrons in periodic lattices 1 and their analogs in photonic 2 , phononic 3 , and plasmonic 4 systems to pseudo energy gaps in aperiodic quasicrystals. 5 Here, we report on a 'thermalization' gap for light propagating in finite disordered structures characterized by disorder-immune chiral symmetry 6 -the appearance of the eigenvalues and eigenvectors in skew-symmetric pairs. In this class of systems, the span of subthermal photon statistics is inaccessible to input coherent light, which -once the steady state is reached -always emerges with super-thermal statistics no matter how small the disorder level. We formulate an independent constraint that must be satisfied by the input field for the chiral symmetry to be 'activated' and the gap to be observed. This unique feature enables a new form of photon-statistics interferometry: the deterministic tuning of photon statistics -from sub-thermal to super-thermal -in a compact device, without changing the disorder level, via controlled excitation-symmetry-breaking realized by sculpting the amplitude or phase of the input coherent field.

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“…As an important paradigm, the Aubry-André (AA) model 14 can undergo a transition from the extended state to the localized state as the amplitude of the incommensurate potential increases. The nature of the AA model has been well understood with extensive researches [15][16][17][18][19][20] . It is well known that at the phase transition point the spectrum of the AA model is a Cantor set and all wave-functions are critical, i.e., neither extended nor localized.…”

Section: Anderson Localizationmentioning

confidence: 99%

Localization and mobility edges in the off-diagonal quasiperiodic model with slowly varying potentials

Liu¹,

Xianlong²,

Chen³

et al. 2017

Physics Letters A

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We study a one-dimensional system that includes both a commensurate off-diagonal modulation of the hopping amplitude and an incommensurate, slowly varying diagonal on-site modulation. By using asymptotic heuristic arguments, we identify four closed form expressions for the mobility edges. We further study numerically the inverse participation ratio, the density of states and the Lyapunov exponent. The numerical results are in exact agreement with our theoretical predictions. Besides a metal-insulator transition driven by the strength of the slowly varying potential, another four insulator-metal transitions are found in this model as the energy is increased in magnitude from the band center (E = 0) to the mobility edges (±Ec2, ±Ec1).

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Observation of a Localization Transition in Quasiperiodic Photonic Lattices

Cited by 401 publications

References 39 publications

Effects of interaction on the diffusion of atomic matter waves in one-dimensional quasiperiodic potentials

Effects of interaction on the diffusion of atomic matter waves in one-dimensional quasiperiodic potentials

A photonic thermalization gap in disordered lattices

Localization and mobility edges in the off-diagonal quasiperiodic model with slowly varying potentials

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