Coherent Electron-Vibron Interactions in Surface-Enhanced Raman Scattering (SERS)

Miguel Á. Martínez-García and Diego Martín-Cano

Phys. Rev. Lett. 132, 093601 – Published 26 February 2024

Abstract

In this Letter we identify coherent electron-vibron interactions between near-resonant and nonresonant electronic levels that contribute beyond standard optomechanical models for off-resonant or resonance surface-enhanced Raman scattering (SERS). By developing an open-system quantum model using first molecular interaction principles, we show how the Raman interference of both resonant and nonresonant contributions can provide several orders of magnitude modifications of the SERS peaks with respect to former optomechanical models and over the fluorescence backgrounds. This cooperative optomechanical mechanism allows for generating an enhancement of nonclassical photon pair correlations between Stokes and anti-Stokes photons, which can be detected by photon-counting measurements. Our results demonstrate Raman enhancements and suppressions of coherent nature that significantly impact the standard estimations of the optomechanical contribution from SERS spectra and their quantum mechanical observable effects.

Received 31 July 2023
Accepted 18 January 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.093601

Physics Subject Headings (PhySH)

Atoms, ions, & molecules in cavities Optomechanics Plasmonics Quantum optics

Atomic, Molecular & Optical

Authors & Affiliations

Miguel Á. Martínez-García and Diego Martín-Cano ^*

Departamento de Físíca Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E28049 Madrid, Spain

^*diego.martin.cano@uam.es

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Vol. 132, Iss. 9 — 1 March 2024

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Images

Figure 1
(a) Sketch of the SERS system. (b) Energy level diagram for the displaced oscillator model for several electronic transitions (left) and the cavity optomechanical model as a result of an adiabatic elimination of the electronic degrees of freedom (right). (c) Emission spectra for the adiabatic elimination Hamiltonian (blue line), the collective oscillator approximation $H_{B}$ (magenta dashed), full spectral analytical solution of a linearized cavity optomechanical Hamiltonian [26] (black dotted), and simplified analytical formula without fluctuations [27] (yellow dash-dot). We consider a molecule with a strong Raman polarizability with $N = 1000$ , $g_{om} = 0.1 THz$ , and $ω_{i} / 2 π = 673.0 THz$ . The rest of the parameters are fixed to $ω_{c} / 2 π = 270 THz$ , $ω_{v} / 2 π = 30 THz$ , $Ω / 2 π = 4 THz$ , $g / 2 π = 2.5 THz$ , $g_{0} / 2 π = 3 THz$ , $ω_{L} / 2 π = 240$ THz, $κ / 2 π = 33 THz$ , $κ_{v} / 2 π = 60 GHz$ , and $γ / 2 π = 50 MHz$ .
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Figure 2
Emission spectra $S (ω)$ for the optomechanical Hamiltonian $H_{om}$ [8] (solid blue), the resonant SERS Hamiltonian $H_{res}$ [13] (dashdot olive green), and the total Hamiltonian $H_{om + res}$ containing both contributions (dashed magenta). (a) An enhancement scenario of the anti-Stokes peak with the resonant transition at $ω_{r} / 2 π = 270 THz$ . (b) A case of suppression with the ZPL at $ω_{r} / 2 π = 262 THz$ . The plasmon detuning is set at $Δ_{c}^{'} / 2 π = 15 THz$ , whereas $g_{om} / 2 π = 0.1 THz$ , $g_{0, r} / 2 π = 3 THz$ , $g_{r} / 2 π = 2.5 THz$ , and $N = 1000$ . The rest of the parameters coincide with Fig. 1.
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Figure 3
(a),(b) Semianalytical anti-Stokes spectral ratio of the total model $S_{R} (ω_{L} + ω_{v})$ , using formula (5), compared to the standard optomechanical model, $\log [S_{R, aS}^{theo} / S_{R, aS}^{om, theo}]$ (a), and compared to the bare resonant one, $\log [S_{R, aS}^{theo} / S_{R, aS}^{res, theo}]$ (b). (c),(d) Analogous full-computational anti-Stokes Raman ratios, $\log [S_{aS} / S_{aS}^{om}]$ (c), and $\log [S_{aS} / S_{aS}^{res}]$ (d), respectively. (e) Vibron population ratio comparing the total model with the optomechanical one, $\log [⟨ v^{†} v ⟩ / ⟨ v^{†} v ⟩_{om}]$ , and (f) compared to the bare resonant model, $\log [⟨ v^{†} v ⟩ / ⟨ v^{†} v ⟩_{res}]$ . The rest of the parameters coincide with Fig. 2.
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Figure 4
Map of the Cauchy-Schwarz inequality parameter $R_{Γ} (ω_{S}, ω_{aS})$ in logarithmic scale, for the optomechanical Hamiltonian $H_{om}$ [8] (b), the resonant SERS Hamiltonian $H_{res}$ [13] (c), and the total Hamiltonian $H_{om + res}$ containing both contributions (a). The filter linewidth is $Γ = κ_{v}$ . The parameters coincide with those in Fig. 3.
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