Quantum transport in fractal networks

Xu, Xiao-Yun; Wang, Xiaowei; Chen, Dan-Yang; Smith, C. Morais; Jin, Xian

doi:10.1038/s41566-021-00845-4

Cited by 79 publications

(64 citation statements)

References 55 publications

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“…These connections bring a simple understanding of the origin of steady-state localization in the drivendissipative scenario [35], as well as the discovery of other phenomena such as directional steady-states or the antilocalization of light. These results opens new avenues in the active control of light, and can pave the way for further experimental works in setups where such structured energy dispersions can be implemented, e.g., photoniccrystal waveguides [30][31][32], photonic lattices based on coupled microwave resonators [33,34], semiconductor microcavities [35,36], or coupled waveguide arrays [41][42][43].…”

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confidence: 93%

Connecting steady-states of driven-dissipative photonic lattices with spontaneous collective emission phenomena

González-Tudela

2021

Preprint

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Recent experimental advances enable the fabrication of photonic lattices in which the light propagates with non-trivial energy dispersions. When interfaced with quantum emitters, such systems yield strong collective spontaneous emission phenomena, such as perfect sub-radiance, in which the decay into the bath is completely suppressed, forming bound-states-in-the-continuum. Since such photonic lattices are generally lossy, an alternative way of probing them consists in coherently driving them to an steady-state from which photoluminescence can be extracted. Here, we formalize connections between these two seemingly different situations and use that intuition to predict the formation of non-trivial photonic steady-states in one and two dimensions. In particular, we show that subradiant emitter configurations are linked to the emergence of steady-state light-localization in the driven-dissipative setting, in which the light features the same form than the spontaneously formed bound-states-in-the-continuum. Besides, we also find configurations which leads to the opposite behaviour, an anti-localization of light, that is, it distributes over all the system except for the region defined between the driving lasers. These results shed light on the recently reported optically-defined cavities in polaritonic lattices, and can guide further experimental studies.

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confidence: 93%

Connecting steady-states of driven-dissipative photonic lattices with spontaneous collective emission phenomena

González-Tudela

2021

Preprint

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“…In [9], the authors suggested a fractal Kronig-Penney model describing the quantum behavior of a particle in a one-dimensional fractal lattice. In [10], the properties of plasmon transport in fractal Sierpinski carpets were experimentally examined. The observed mean squared displacements and the Polia numbers provided evidence for anomalous diffusion of plasmons in considered carpets.…”

Section: Introductionmentioning

confidence: 99%

“…The observed mean squared displacements and the Polia numbers provided evidence for anomalous diffusion of plasmons in considered carpets. The authors of [10] related the critical point of transition from normal to anomalous transport with fractal geometry parameters.…”

Section: Introductionmentioning

confidence: 99%

Modelling of Electron and Thermal Transport in Quasi-Fractal Carbon Nitride Nanoribbons

et al. 2022

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In this work, using calculations based on the density functional theory, molecular dynamics, non-equilibrium Green functions method, and Monte Carlo simulation, we study electronic and phonon transport in a device based on quasi-fractal carbon nitride nanoribbons with Sierpinski triangle blocks. Modifications of electronic and thermal conductance with increase in generation g of quasi-fractal segments are estimated. Introducing energetic disorder, we study hopping electron transport in the quasi-fractal nanoribbons by Monte Carlo simulation of a biased random walk with generalized Miller–Abrahams transfer rates. Calculated time dependencies of the mean square displacement bear evidence of transient anomalous diffusion. Variations of anomalous drift-diffusion parameters with localization radius, temperature, electric field intensity, and energy disorder level are estimated. The hopping in quasi-fractal nanoribbons can serve as an explicit physical implementation of the generalized comb model.

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“…This difference conjures up novelty in quantum emergent phenomena. Recently, fractal quantum systems have been realized in experiments of quantum materials and optical systems with fractalitydependent behavior observed [1][2][3][4][5]. These inspiring advancements have motivated exploration of novel quantum phases of matter in fractal geometry, and more generally of fractional dimension [6][7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…The basic consideration is that fixed points with zero (infinite) correlation length possess the "cleanest" entanglement patterns to represent quantum order (critical points) since the short-range part of entanglement is washed out as much as possible in the renormalization flow [26,27]. We consider qudits on the Sierpiński lattice (which has attracted most attention in experiments [1][2][3][4][5]). Fixed points are represented in tensor network as solutions to a scale-invariance equation.…”

Section: Introductionmentioning

confidence: 99%

A new realization of the long-range entanglement: fractality replacing the topological order

Wang¹

2022

Preprint

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Quantum matter with fractal geometry has been recently observed and studied in experiments. The fractal self-similarity and the fractional nature of the spatial dimension in such systems suggest exotic quantum order lying beyond paradigms developed in integer dimension. However, the existence of such uncomprehended novelty is still to be established in terms of quantum states with nontrivial many-body entanglement. To lay a foundation for exploring such states and to provide example that demonstrates such novelty, we study many-body entanglement patterns in entanglement-renormalization fixed points of qudit systems with Sierpiński lattice geometry, and introduce corresponding toy models. We show that the interplay between entanglement and selfsimilarity can be realized in fixed-point states with well-defined self-similar entanglement patterns. These fixed-point states exhibit distinct orders and are all given by single tensors as solutions to a scale invariance equation. In particular, we prove that an example of fixed-point state possesses long-range entanglement, i.e., it is short-range correlated but cannot be completely disentangled through constant-depth local quantum circuit. While the existence of long-range entanglement implies topological order in 2D and is disproved in 1D, our example proves the coexistence between long-range entanglement and fractality, a paradigm in fractional dimension. We show that such long-range entanglement pattern cannot be read as an extension of topological order, but rather exhibits novel quantum ordering inherent in fractional dimension, an evidence of new paradigm describing long-range entanglement.

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Quantum transport in fractal networks

Cited by 79 publications

References 55 publications

Connecting steady-states of driven-dissipative photonic lattices with spontaneous collective emission phenomena

Connecting steady-states of driven-dissipative photonic lattices with spontaneous collective emission phenomena

Modelling of Electron and Thermal Transport in Quasi-Fractal Carbon Nitride Nanoribbons

A new realization of the long-range entanglement: fractality replacing the topological order

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