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In this work we study the role of the plasmonic equivalent of a quantum dynamical phase transition on different systems consisting of metallic nanoparticles (NPs) interacting through their surface plasmons. The system is modeled as a set of coupled dipoles with interactions in a near field approximation, which is justified when NPs are sufficiently small compared with excitation wavelengths and if the separation between NPs is not too small compared with their radii [1]. Under these conditions the physics of the system is equivalent to that of an array of damped harmonic oscillators [2] and similar to some quantum mechanical models [3,4]. We focus on two plasmonic systems: one consists of a one dimensional semi-infinite linear array of small NPs where we study the plasmonic energy transfer from a locally excited NP at the end of the array, to its interior [3]. In this case, we analyze the role of virtual states and localized-delocalized transition on the injection and transport of excitations [3,5]. The other system corresponds to two NPs interacting indirectly through a semi-infinite linear array of Nps, where we study the synchronization conditions. In both cases, the dynamical matrix of the system results in the plasmonic equivalent of non-Hermitian Hamiltonians [6]. Among the questions to be addressed are: "why a non-physical pole of the response function, such as a virtual state, becomes high relevant in this case", and "how to use the extreme sensitivity of dynamical phase transitions to the system's parameters in different plasmonic applications". Bibliography: [1] M. L. Brongersma, J. W. Hartman, and H. A. Atwater, Phys. Rev. B \textbf, R16356 (2000). [2] L. A. Sweatlock, S. A. Maier, H. A. Atwater, Proceedings - Electronic Components and Technology Conference, 1648 (2003); H.L. Calvo, E. P. Danieli, H. M. Pastawski, Phys. B \textbf, 317 (2007); L. Guti\'rrez \textit{et al.}, Phys. Rev. Lett. \textbf, 114301 (2006). [3] R. A. Bustos-Mar\'n, E. A. Coronado, and H. M. Pastawski., Phys. Rev. B \textbf, 035434 (2010). [4] D. M. Newns, Phys. Rev. \textbf, 1123 (1969); E. Santos, M.T.M. Koper and W. Schmickler, Chem. Phys. Lett. \textbf, 421(2006). [5] A. D. Dente, R.A. Bustos-Mar\'n, and H.M. Pastawski, Phys. Rev. A \textbf, 062116 (2008). 6] Ingrid Rotter, J. Opt. \textbf, 065701 (2010) |
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