Exciton localization-delocalization transition in an extended dendrimer

Abstract

Exciton-mediated quantum state transfer between the periphery and the core of an extended dendrimer is investigated numerically. By mapping the dynamics onto that of a linear chain, it is shown that a localization-delocalization transition arises for a critical value of the generation number G(c) ≈ 5. This transition originates in the quantum interferences experienced by the excitonic wave due to the multiple scatterings that arise each time the wave tunnels from one generation to another. These results suggest that only small-size dendrimers could be used for designing an efficient quantum communication protocol.

Disorder-enhanced exciton delocalization in an extended dendrimer

“…Note that the population of the central core remains very small during the simulation (not drawn), its limiting value being approximately equal to 0.48%. This result contrasts with previous calculations which revealed that 84% of the exciton population can reach the central core when the initial wave function is uniformly distributed over the periphery of the dendrimer 32 .…”

“…1). Note that the case of an initial wave function uniformly distributed over all the surface site has been investigated recently 32 . The exciton dynamics is described by the evolution operator U (t) whose behavior is governed by the Schrödinger equation, as…”

“…In an extended dendrimer, when the initial wave function is either uniformly distributed over the periphery or localized on the central core, quantum interferences arise because multiple scatterings occur each time the exciton tunnels from one generation to another. As a result, the exciton localizes when the generation number exceeds a critical value indicating that only small-size dendrimers allow an efficient communication between the core and the surface 32 . By contrast, in a compact dendrimer, the exciton delocalizes coherently between the periphery and the core, its dynamics being mapped onto that of a linear chain 33 .…”

Exciton-mediated quantum search on a star graph

“…Such an approach is not the result of chance since recent investigations have revealed that exciton-mediated quantum state transfer could be a promising way for quantum information processing in nanowires [22,23], tree-like molecules [24][25][26][27] and star graphs [28]. The protocol we propose differs from previous search algorithms for at least three main reasons.…”

The excitonic qubit coupled with a phonon bath on a star graph: anomalous decoherence and coherence revivals

“…Different lattices were considered, such as unmodulated spin chains and complex networks [31], spin chains with preengineered interactions [32,33], and parallel spin chains [34]. However, other excitations can be used for performing QST and many alternatives to spin excitons were proposed such as electronic excitons in extended dendrimers [35,36], phonons in crystals with reduced dimensionality [37][38][39] and vibrons in molecular chains (vibrons define high-frequency vibrational excitons associated with the delocalization of intramolecular vibrations in molecular lattices) [40].…”