Entangled two-plasmon generation in carbon nanotubes and graphene-coated wires

Y. Muniz, P. P. Abrantes, L. Martín-Moreno, F. A. Pinheiro, C. Farina, and W. J. M. Kort-Kamp

Phys. Rev. B 105, 165412 – Published 11 April 2022

Abstract

We investigate the two-plasmon spontaneous decay of a quantum emitter near single-walled carbon nanotubes (SWCNTs) and graphene-coated wires (GCWs). We demonstrate efficient, enhanced generation of two-plasmon entangled states in SWCNTs due to the strong coupling between tunable guided plasmons and the quantum emitter. We predict two-plasmon emission rates more than twelve orders of magnitude higher than in free space, with average lifetimes of a few dozen nanoseconds. Given their low dimensionality, these systems could be more efficient for generating and detecting entangled plasmons in comparison to extended graphene. Indeed, we achieve a tunable spectrum of emission in GCWs, where sharp resonances occur precisely at the plasmons' minimum excitation frequencies. We show that by changing the material properties of the GCW's dielectric core, one could tailor the dominant modes and frequencies of the emitted entangled plasmons while keeping the decay rate ten orders of magnitude higher than in free space. By unveiling the unique properties of two-plasmon spontaneous emission processes in the presence of low-dimensional carbon-based nanomaterials, our findings set the basis for a novel material platform with applications to on-chip quantum information technologies.

Received 21 December 2021
Accepted 29 March 2022

DOI:https://doi.org/10.1103/PhysRevB.105.165412

Physics Subject Headings (PhySH)

Nonlinear optics Plasmonics Plasmons Second order nonlinear optical processes Spontaneous emission Surface plasmon polariton

Graphene Nanotubes Nanowires

Dipole approximation Perturbative methods

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Y. Muniz ^1,*, P. P. Abrantes ^1,†, L. Martín-Moreno ^2,‡, F. A. Pinheiro^1,§, C. Farina^1,∥, and W. J. M. Kort-Kamp ^3,¶

¹Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro 21941-972, Rio de Janeiro, Brazil
²Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, E-50009 Zaragoza, Spain
³Theoretical Division, Los Alamos National Laboratory, MS B262, Los Alamos, New Mexico 87545, USA

^*yurimuniz@pos.if.ufrj.br
^†ppabrantes91@gmail.com
^‡lmm@unizar.es
^§fpinheiro@if.ufrj.br
^∥farina@if.ufrj.br
^¶kortkamp@lanl.gov

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Vol. 105, Iss. 16 — 15 April 2022

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Images

Figure 1
(a) Schematics of the system under study. A quantum emitter separated by a distance $d$ from a SWCNT of radius $R$ . (b) Real part of the plasmon's wave vector $k_{p}$ for the fundamental mode ( $n = 0$ ) normalized by the free-space wave vector $k = ω / c$ as a function of the light oscillation frequency for different values of the Fermi energy. (c) The ratio between the real and imaginary parts of $k_{p}$ of the fundamental plasmonic mode versus the free-space frequency for different values of the Fermi energy.
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Figure 2
(a) Normalized TPSE rate for the $6 s \to 5 s$ transition in hydrogen ( $ℏ ω_{t} \approx 166$ meV) as a function of the distance between the emitter and the surface of the SWCNT. Upper right inset: Normalized TPSE spectral density as a function of distance for three frequencies of emission. In this inset, the Fermi energy is given by $E_{F} = 1$ eV. Lower left inset: Normalized TPSE spectral density at $d = 10$ nm. Since only the fundamental plasmonic mode is present, we observe a broadband spectrum of emission. The divergences at $ω = 0$ and $ω = ω_{t}$ are solely due to the normalization by the free-space spectral density, which goes to zero at the boundaries of the spectrum. (b) Quantum efficiency given by Eq. (15) of TPSE for the $6 s \to 5 s$ transition in hydrogen as a function of distance. In both plots, $E_{F} = {0.25, 0.5, 0.75, 1}$ eV (dotted blue, dash-dotted purple, dashed green, and solid red lines, respectively).
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Figure 3
(a) Schematics of the system: A quantum emitter separated by a distance $d$ of a dielectric cylinder of relative electric permittivity $ɛ$ and radius $R$ , coated with graphene. (b) Dispersion relation for all the plasmonic modes supported with free-space oscillating light of frequency $ℏ ω < 200$ meV. Each color is associated with a GCW of a different radius, while the line style characterizes the order of the mode. (c) The ratio between the real and imaginary parts of $k_{p}$ for each plasmonic mode as a function of frequency. In both plots we choose silicon as the dielectric medium, which has permittivity $ɛ = 11.68$ in the frequency range considered. Also, $R = {20, 30, 42}$ nm (blue, purple, and green lines, respectively), and the Fermi energy is $E_{F} = 1$ eV.
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Figure 4
(a) TPSE spectral density near a silicon ( $ɛ = 11.68$ ) nanowire covered with graphene as a function of the wire radius. The transition frequency considered is $ℏ ω_{t} \approx 166$ meV. (b) TPSE spectral density for various dielectric coated nanowires of radius $R = 100$ nm. For $ɛ = 7.33$ ( $ɛ = 15.66$ ), the minimum excitation frequency of the mode $m = 1$ ( $m = 2$ ) is precisely at $ω_{t} / 2$ , which results in a huge resonance in the middle of the spectrum. In both plots the Fermi energy is $E_{F} = 1$ eV.
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Figure 5
(a) Normalized TPSE rate for the $6 s \to 5 s$ transition in hydrogen as a function of the inner dielectric cylinder permittivity. We choose a nanowire of radius 25 nm and Fermi energies of 0.5 eV (blue solid curve) and 1 eV (red dashed curve). Inset: Plasmon dispersion relations for $ɛ = 3.11$ (left) and $ɛ = 5.15$ (right). (b) TPSE rate for the same hydrogen transition as a function of distance. The Fermi energy is equal to 1 eV. Inset: Quantum efficiency [Eq. (15)] as a function of distance for the same parameters of the main plot.
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