Non-equilibrium quantum plasmonics in nanoparticle-on-mirror nanocavities

Abstract

We develop a novel approach to ultrafast optical modulation of quantum-mechanical phenomena at the interface of plasmonic metals. Focusing on efficient and versatile nanoparticle-on-mirror plasmonic nanocavities, we discuss indirect control of plasmonic properties through laser-induced ballistic hot electron injection. Overcoming the limitations precluding the observations of laser-driven mesoscopic phenomena in the time domain with state-of-the-art amplified sources, our proposed experimental approach can be readily realized without irreversible optical damage and holds immense potential for the future development of ultrafast electrodynamics in nanogaps, applications in photochemistry and nanoscale control of quantum emitters. Agreeing with the results of numerical simulations, an intuitive microscopic model for the proposed time-dependent mesoscopic electrodynamics facilitates the analysis of the temperature-induced modulation of quantum plasmonic properties in a broad parameter space. Our work expands the realm of quantum nanophotonics onto non-equilibrium electronic systems and facilitates the development of ultrafast methods in active plasmonics.

Figures (12)

• Figure 1: Electron temperature-dependent nonlocal surface response. (a) Computed Feibelman parameter $d_{\perp}$ at a gold-vacuum interface at 300 K and 2000 K. (b) Comparison of TD-LDA results (solid) with the specular reflection model (SRM, dotted). The red-shaded area indicates the region where interband transitions dominate. (c) Zoomed-in view of (a, blue-shaded area) around $\hbar\omega=1.5$ eV. The shaded areas in (c) indicate contributions from static (orange) and dynamic (green) screening to the total change of $d_{\perp}(\omega, T_e)$ upon heating from 300 K (solid line) to 2000 K (dashed line). The damping contribution (red) is invisible at the current scale. (d) Dependence of d$_{\perp}$($\hbar\omega=1.5$ eV) on the electron temperature.
• Figure 2: Proposed experimental configuration. An ultrashort pump pulse is absorbed in the Fe layer, inducing hot electron injection from Fe into Au and their subsequent ballistic transport across the Au layerMelnikov2011. The delayed probe pulse monitors transient variations of the plasmonic (glowing red hotspot) spectral response of a NPoM nanocavity. The latter is formed by a spherical Au nanoparticle resting on a dielectric layer with a thickness $h$ and dielectric function $\varepsilon_g$. The blue dashed line indicates the region simulated numerically using the Finite Elements Method (FEM) with the help of Comsol Multiphysics.
• Figure 3: Role of nonlocality and gap size in gold NPoM: (a) Scattering cross-sections of NPoMs with varied gap width in local theory (dashed lines) and nonlocal theory with d$_{\perp}$ taken from Ref. RodriguezEcharri2021 (solid lines); (b-c) Relative variations in peak position $\Delta\lambda/\lambda$ (b) and scattering amplitude at the maximum $\Delta\sigma/\sigma$ (c) between the local and nonlocal theories.
• Figure 4: Interplay of nonlocality and substrate heating in Au NPoMs with the gap width $h=1$ nm. (a-b) Scattering cross-section spectra of NPoMs with: (a) varied mirror temperatures and $d_{\perp}=d_{\perp0}$, and (b) cold mirror at 300 K and varied $d_{\perp}$. (c-d) Extracted scattering peak positions at various mirror temperatures and $d_{\perp}/d_{\perp 0}=1$ (c), and non-locality $d_{\perp}$ in the mirror at $T_e=300$ K and $2000$ K (d). Because $d_{\perp 0}<0$, the horizontal axis in (d) points in the direction of further decrease of $d_{\perp}$, i.e. stronger spill-in.
• Figure 5: Variations of the calculated resonant wavelengths with the Feibelman parameter $d_{\perp}$ for different gap widths (a) and temperatures of the gold mirror (b) with the analytic circuit model. The dashed and solid lines represent the expected scaling of the gap capacitance with $d_{\perp}$ with and without the correction factor $\alpha = 2.1$, respectively. The inset in the bottom-left corner shows a schematic circuit of a nanoparticle dimer with non-locality. The red-colored $C_{\rm g}$ is modified through the Feibelman non-locality $d_{\perp}$ which can be described by the effective gap width renormalization (Eq. \ref{['eq:circuit:capac']}, red-shaded spheres). (c) Calculated resonance shifts with temperature: the impact of bulk $\varepsilon$ (orange) and Feibelman non-locality $d_{\perp}$ (green) with temperature, and the total shift (blue). The solid and dashed lines indicate the results of numerical simulations and the circuit model, respectively.