Quantum Mechanical Description of Raman Scattering from Molecules in Plasmonic Cavities

Abstract

Plasmon-enhanced Raman scattering can push single-molecule vibrational spectroscopy beyond a regime addressable by classical electrodynamics. We employ a quantum electrodynamics (QED) description of the coherent interaction of plasmons and molecular vibrations that reveal the emergence of nonlinearities in the inelastic response of the system. For realistic situations, we predict the onset of phonon-stimulated Raman scattering and a counterintuitive dependence of the anti-Stokes emission on the frequency of excitation. We further show that this QED framework opens a venue to analyze the correlations of photons emitted from a plasmonic cavity.Surface Enhanced Raman Scattering (SERS) is a spectroscopic technique in which the inelastic scattering from a molecule is increased by placing it in a hotspot of a plasmonic cavity, where the electric fields associated with the incident and the scattered photons are strongly enhanced (see the schematic in Fig. 1(a)). 1 The difference between the energy of those two photons provides a fingerprint of the molecule, i.e., detailed chemical information about its vibrational structure. Since the initial observation of Raman scattering from single molecules, 2,3 the use of a variety of plasmonic structures that act as effective optical nanoantennas over the last decades has allowed a tremendous advance of this molecular spectroscopy 4 . Metallic particles such as nanoshells 5,6 , nanorings 7 , nanorods 8 , nanowires 9 , or nano stars 10 , as well as plasmonic nanogap structures formed in particle dimers [11][12][13] , nanoparticle-on-a-mirror morphologies [14][15][16][17] , or nanoclusters 18 , are among the variety of structures that offer huge and controllable enhancements of the field intensity in their hotspots, boosting the inherently weak Raman scattering intensity, 1,19 and ultimately enabling the chemical identification and imaging of particular vibrational modes of a molecule with subnanometer resolution. 20 These results suggest that some experiments might have reached the regime where the quantum-mechanical nature of both the molecular vibrations and the plasmonic cavity emerges, 21 and call for an adequate theoretical description that goes beyond the classical treatment of the electric fields produced in plasmonic cavities. 1,22,23 In this work we address the underlying quantummechanical nature of Raman scattering processes by quantizing as bosonic excitations both the vibrations of the molecule and the electromagnetic field of a plasmonic cavity. The description of the vibrations through bosonic operators can be justified by considering the harmonic approximation to the energy landscape of the molecule along a generalized atomic coordinate ( Fig. 1(b)), such as the length of a molecular bond, e.g., C=O. 21,22 These vibrations interact with the cavity photons through a nonlinear Hamiltonian, reminiscent of that found in optomechanical systems. 24 In this description, the large enhancement of the Raman scattering from a molecule in the plasmonic cavity occurs thanks to ...

Pulsed Molecular Optomechanics in Plasmonic Nanocavities: From Nonlinear Vibrational Instabilities to Bond-Breaking

“…Analogous optomechanical systems use macroscopic vibrational modes such as cantilevers [9,10], beams [11], or pillars [12][13][14][15] coupled to highfinesse optical cavities in order to demonstrate a variety of effects such as cooling to the quantum vibrational ground state [16], parametric oscillation [17], and supercontinuum comb generation [18]. Recent theory [19,20] and experiments [8,21] have shown that this same optomechanical Hamiltonian describes vibrating molecular bonds in nanocavities, but with single-photon coupling coefficients ℏg 0 ∼ 10-100 meV, a millionfold larger than for macroscopic resonators. Here, we explore how this coupling can be used to elicit stimulated phonon scattering within vibrating bonds, leading toward phonon lasing or "phasing," observed previously in microfabricated mechanical oscillators [22][23][24], and we suggest how such mechanical resonances can lead to chemical reactions [ Fig.…”

“…Using an optomechanical model, it is possible to extract the photon-phonon coupling [8,20]. When the nanocavities are formed by ultrathin gaps between plasmonic metal nanostructures that trap the optical field, this strongly amplified process is termed surface-enhanced Raman spectroscopy (SERS) of the molecules in the gap.…”

Impact of the Crosslinker’s Molecular Structure on the Aggregation of Gold Nanoparticles

“…a molecule. Such plasmonic cavities are as well of experimental [6][7][8] as of theoretical interest [9].…”

Single-molecule optomechanics in “picocavities”

“…This process is dramatically amplified by the extreme confinement of the incident light in the plasmonic gap. As a result, the population of excited vibrational states (at frequencies ) is boosted above that provided by thermal excitations from the environment at temperature , , by an additional contribution due to the optomechanical coupling of the plasmonic cavity with the molecular vibration (9). We first model the interaction of quantized plasmons with phonons in the classical limit of weak coupling between the vibrations and cavity plasmons (with for cavity decay rate ), through the optomechanical Hamiltonian described in (7,9).…”

“…As a result, the population of excited vibrational states (at frequencies ) is boosted above that provided by thermal excitations from the environment at temperature , , by an additional contribution due to the optomechanical coupling of the plasmonic cavity with the molecular vibration (9). We first model the interaction of quantized plasmons with phonons in the classical limit of weak coupling between the vibrations and cavity plasmons (with for cavity decay rate ), through the optomechanical Hamiltonian described in (7,9). This gives (1) with volume-dependent optomechanical amplification rate dependent on optomechanical coupling strength and laser power , with phonon decay rate (full expressions in (7), Section S1 and (9)).…”