Continuous-time quantum walk on an extended star graph: Trapping and superradiance transition

Yalouz, Saad; Pouthier, Vincent

doi:10.1103/physreve.97.022304

Cited by 13 publications

(10 citation statements)

References 51 publications

(55 reference statements)

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“…Indeed, whatever the strength of the disorder, an exciton starting on a peripheral site of a disordered graph is always fully trapped at the core site. This is a feature that clearly contrasts with the incomplete trapping process observed in an ordered graph 57 .…”

Section: Discussionmentioning

confidence: 61%

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Continuous-time quantum walk on an extended star graph: Disorder-enhanced trapping process

Yalouz

Pouthier

2020

Phys. Rev. E

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Using a tight binding model, we investigate the dynamics of an exciton on a disordered extended star graph whose central site acts as an energetic trap. Our results highlight the beneficial role of the disorder to improve the excitonic absorption at the core of the graph. In this context, we evidence the existence of an optimal disorder allowing to strongly minimize the absorption time. Numerical proofs are given to demonstrate that this enhancement originates from a disorder-induced restructuring process that positively affects the system eigenstates. In a complementary way, we also evidence the existence of an optimal value of absorption rate allowing to reduce even more the aborption time when the disorder is optimal. The resulting super optimized trapping process is interpreted as the positive interplay between the action of the disorder and the arising of the so-called superradiance transition.

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Section: Discussionmentioning

confidence: 61%

“…Following our previous work 57 , the aim of the present study is to characterize the excitonic absorption process at the core of a disordered extended star graph assuming that an exciton is initially located on a peripheral site ( 0 = 1, s 0 = 1).…”

Section: B Quantum Dynamicsmentioning

confidence: 99%

Continuous-time quantum walk on an extended star graph: Disorder-enhanced trapping process

Yalouz

Pouthier

2020

Phys. Rev. E

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“…They exists if and only if N is the sum of two squares. Examples include the Paley graphs (see parametrization (27)). Type II graphs, for which (µ − λ) 2 + 4(k − µ) is a perfect square d 2 , where d divides (N − 1)(µ − λ) − 2k, and the quotient is congruent to N − 1 (mod 2).…”

Section: Measures Of Connectivitymentioning

confidence: 99%

“…Quantum transport has been investigated with this approach on restricted geometries [19], semi-regular spidernet graphs [20], Sierpinski fractals [21], and on large-scale sparse regular networks [22]. CTQWs have been used to model transport of nonclassical light in coupled waveguides [23], coherent exciton transport on hierarchical systems [24], small-world networks [25], Apollonian networks [26], and on an extended star graph [27], coherent transport on complex networks [28], and exciton transfer with trapping [29,30]. It is worth noting that CTQWs do not necessarily perform better than their classical counterparts, since the transport properties strongly depend on the graph, the initial state, and on the propagation direction under investigation [31].…”

Section: Introductionmentioning

confidence: 99%

Transport efficiency of continuous-time quantum walks on graphs

Razzoli,

Paris,

Bordone

2020

Preprint

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Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting systems. In particular, the transport properties strongly depend on the initial state and on the specific features of the graph under investigation. In this paper, we address the role of graph topology, and investigate the transport properties of graphs with different regularity, symmetry, and connectivity. We neglect disorder and decoherence, and assume a single trap vertex accountable for the loss processes. In particular, for each graph, we analytically determine the subspace of states having maximum transport efficiency. Our results provide a set of benchmarks for environment-assisted quantum transport, and suggest that connectivity is a poor indicator for transport efficiency. Indeed, we observe some specific correlations between transport efficiency and connectivity for certain graphs, but in general they are uncorrelated.

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“…Up to present, the SR phase transition has been predicted and observed with atomic ensembles [30][31][32], exciton polaritons in semiconductor microstructures [33], superconductor circuits [34,35], solids [36], and extended star graphs [37]. The evidence of the SR state in such experiments is usually achieved by means of cavity exploiting that enables to enhance a photon lifetime [7,38,39].…”

Section: Introductionmentioning

confidence: 99%

Superradiant phase transition in complex networks

Bazhenov,

Tsarev,

Alodjants

2020

Preprint

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In this work we consider a superradiant phase transition problem for the Dicke-Ising model, which generalizes the Dicke and Ising models for annealed complex networks presuming spin-spin interaction. The model accounts the interaction between a spin (two-level) system and external classical (magnetic) and quantized (transverse) fields. We examine regular, random, and scale-free network structures characterized by the delta-function, random (Poisson), and power-law exponent (p(k) ∝ k −γ ) degree distributions, respectively. To describe paramagnetic (PM) -ferromagrenic (FM) and superradiant (SR) phase transitions we introduce two order parameters: the total weighted spin z-component and the normalized transverse field amplitude, which correspond to the spontaneous magnetization in z and x directions, respectively. Due to the interplay between the spin interaction and the finite size effects in the networks we first elucidate novel features of the SR state in the presence of the PM-FM phase transition. In particular, we show that the critical temperature essentially depends on parameter ζ = k 2 / k , which characterizes statistical properties of the network structure. Moreover, we reveal that the critical temperature of the SR phase transition grows monotonically from some certain value that corresponds to the critical number of nodes. For the scale-free networks we find that this critical temperature rises with the degree exponent increase accompanied both by establishing spontaneous magnetization in a quantum transverse field and vanishing of the collective spin component in z direction. In addition, we establish the conditions for the network parameters to obtain a quantum phase transition in the spin system when the critical temperature approaches zero. The fundamental features, which involve critical values of the classical and quantum field parameters, are discussed for the occurrence of the superradiance phase in this limit.

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Continuous-time quantum walk on an extended star graph: Trapping and superradiance transition

Cited by 13 publications

References 51 publications

Continuous-time quantum walk on an extended star graph: Disorder-enhanced trapping process

Continuous-time quantum walk on an extended star graph: Disorder-enhanced trapping process

Transport efficiency of continuous-time quantum walks on graphs

Superradiant phase transition in complex networks

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