Anderson localization in synthetic photonic lattices

Vatnik, Ilya D.; Tikan, Alexey; Onishchukov, G.; Churkin, Dmitry V.; Sukhorukov, Andrey A.

doi:10.1038/s41598-017-04059-z

Cited by 58 publications

(32 citation statements)

References 20 publications

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“…Even within 1D, there have been proposals to realize unique photon transport phenomena using dynamically modulated cavities, which could be implemented in a reconfigurable fashion in our platform [24,55]. Longer fiber ring resonators in the pulsed regime have been previously used for realizing parity-time symmetry [56] and optical Ising machines [57] and soliton interactions [58], in a synthetic temporal dimension [59,60] that is complementary to our cw-pumped synthetic frequency dimension. Lastly, the advent of on-chip silicon [61,62] and lithium niobate ring resonators [63] with modulation bandwidths higher than the FSR of on-chip ring resonators can enable synthetic dimensions and topological photonics in a monolithically integrated platform.…”

Section: Discussionmentioning

confidence: 99%

Experimental Band Structure Spectroscopy along the Synthetic Dimension

Dutt¹,

Minkov²,

Lin³

et al. 2019

Conference on Lasers and Electro-Optics

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In recent years there has been significant interest in the concepts of synthetic dimensions, where one couples the internal degrees of freedom of a particle to form higher-dimensional lattices in lower-dimensional physical structures. For these systems the concept of band structure along the synthetic dimension plays a central role in their theoretical description. Here we provide the first direct experimental measurement of the band structure along the synthetic dimension. By dynamically modulating a ring resonator at frequencies commensurate with its mode spacing, we realize a periodically driven system with a synthetic frequency dimension lattice. The strength and range of the couplings along the lattice can be dynamically reconfigured by changing the amplitude and frequency of modulation. We show theoretically and demonstrate experimentally that time-resolved transmission measurements of this system result in a direct "read out" of its band structure. We also show how long-range coupling, photonic gauge potentials and nonreciprocal bands can be realized in the system by simply incorporating additional frequency drives, enabling great flexibility in engineering the band structure.The concept of band structure for periodic systems plays a central role in understanding the electronic properties of solid-state systems as well as the photonic properties of photonic crystals and metamaterials [1]. Recently, there has been significant interest in creating analogous periodic systems not in real space but in synthetic space, allowing one to explore higher-dimensional physics with a structure of fewer physical dimensions [2][3][4][5][6][7][8][9][10][11][12]. Synthetic dimensions are internal degrees of freedom of a system that can be configured into a lattice, for example the hyperfine spin states in cold atoms [4][5][6][13][14][15][16][17], the orbital angular momentum of photons [7,[18][19][20], or the modes at different frequencies of optical ring resonators [8,9]. These systems are again characterized by a band structure in synthetic space, but an experimental demonstration of directly measuring this band structure is lacking.In this work we provide the first direct experimental demonstration of a band structure in the synthetic dimension. For this purpose, we consider a particular construction of a synthetic space -the equidistant frequency modes of a ring resonator. This synthetic frequency dimension enables one to study fundamental physics such as the effective gauge field and magnetic field for photons, 2D topological photonics in a 1D array, and 3D topological photonics in planar structures [8,9,[21][22][23][24][25][26]. Moreover, the concept is interesting for applications such as unidirectional frequency translation, quantum information processing, nonreciprocal photon transport and spectral shaping of light [27][28][29][30][31][32][33][34][35][36][37]. While the frequency dimension has been theoretically investigated in great detail, mostly using the band structure in synthetic space, there is a dearth of e...

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Section: Discussionmentioning

confidence: 99%

Experimental Band Structure Spectroscopy along the Synthetic Dimension

Dutt¹,

Minkov²,

Lin³

et al. 2019

Conference on Lasers and Electro-Optics

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“…1b and supplementary note 1) consisting of two mutually coupled, but slightly dissimilar fibre loops. In similar experimental realizations of time multiplexed synthetic lattices Anderson localization was studied 22 , 23 as well as Boson sampling 24 . The system is widely tuneable in terms of amplitude and phase modulation and capable of depicting linear and nonlinear light evolution 25 .…”

Section: Methodsmentioning

confidence: 99%

Observation of Time Reversed Light Propagation by an Exchange of Eigenstates

Wimmer¹,

Peschel

2018

Sci Rep

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As time flow dictates all evolution, its effective reversal is a topic of active research in a broad range of disciplines, including acoustics, hydrodynamics and optics. This multifarious set of environments is reflected by a great diversity of approaches to observe various echoes of wave functions. Here, we experimentally demonstrate time reversal of a pulse sequence propagating through a photonic mesh lattice realized by two coupled loops of telecommunication fibres. Our system features a symmetric band structure, which allows for almost perfect reversal of its evolution by exchanging the population between two opposing bands. The protocol applied is based on a non-adiabatic and instantaneous exchange of eigenstates resulting in highly efficient time reversal of a pulse chain.

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“…We consider discrete-time quantum walk of optical pulses in synthetic photonic mesh lattices [84][85][86][87][88][89][90][91], realized in coupled fiber rings with unbalanced path-lengths. Such synthetic lattices have been experimentally used to demonstrated a wealth of phenomena, such as Bloch oscillations [86], parity-time symmetric phase transitions [87,88], Anderson localization [85,89,90], and the non-Hermitian skin effect [91]. By proper combination of amplitude and phase modulators in the fiber loops [87,90,91], they can engineer rather arbitrary non-Hermitian potentials.…”

Section: Proposal Of Experimental Implementationmentioning

confidence: 99%

“…At each transit in the main loop, a pulse entering into the interferometer is split at the output port into three pulses with time delays − t, 0, and t, where t = L/c is the time delay introduced by the unbalanced arms in the interferometer. The successive pulse splitting emulates a discrete-time quantum walk, where the complex amplitude a (m) n of pulse occupying the nth time slot (discrete space distance) at the mth round trip evolves according a linear map [84][85][86][87][88][89][90][91]. The symmetric 3 × 3 fiber couplers between the three-arm interferometer and the main fiber loop is described by the scattering matrix [92] S (3)…”

Section: Appendix D: Photonic Implementation Of Model IImentioning

confidence: 99%

Generalized Aubry-André self-duality and mobility edges in non-Hermitian quasiperiodic lattices

et al. 2020

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We demonstrate the existence of generalized Aubry-André self-duality in a class of non-Hermitian quasiperiodic lattices with complex potentials. From the self-duality relations, the analytical expression of mobility edges is derived. Compared to Hermitian systems, mobility edges in non-Hermitian ones not only separate localized from extended states but also indicate the coexistence of complex and real eigenenergies, making possible a topological characterization of mobility edges. An experimental scheme, based on optical pulse propagation in synthetic photonic mesh lattices, is suggested to implement a non-Hermitian quasicrystal displaying mobility edges.

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Anderson localization in synthetic photonic lattices

Cited by 58 publications

References 20 publications

Experimental Band Structure Spectroscopy along the Synthetic Dimension

Experimental Band Structure Spectroscopy along the Synthetic Dimension

Observation of Time Reversed Light Propagation by an Exchange of Eigenstates

Generalized Aubry-André self-duality and mobility edges in non-Hermitian quasiperiodic lattices

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