Molecular Optomechanics Approach to Surface-Enhanced Raman Scattering

Conspectus Molecular vibrations constitute one of the smallest mechanical oscillators available for micro-/nanoengineering. The energy and strength of molecular oscillations depend delicately on the attached specific functional groups as well as on the chemical and physical environments. By exploiting the inelastic interaction of molecules with optical photons, Raman scattering can access the information contained in molecular vibrations. However, the low efficiency of the Raman process typically allows only for characterizing large numbers of molecules. To circumvent this limitation, plasmonic resonances supported by metallic nanostructures and nanocavities can be used because they localize and enhance light at optical frequencies, enabling surface-enhanced Raman scattering (SERS), where the Raman signal is increased by many orders of magnitude. This enhancement enables few- or even single-molecule characterization. The coupling between a single molecular vibration and a plasmonic mode constitutes an example of an optomechanical interaction, analogous to that existing between cavity photons and mechanical vibrations. Optomechanical systems have been intensely studied because of their fundamental interest as well as their application in practical implementations of quantum technology and sensing. In this context, SERS brings cavity optomechanics down to the molecular scale and gives access to larger vibrational frequencies associated with molecular motion, offering new possibilities for novel optomechanical nanodevices. The molecular optomechanics description of SERS is recent, and its implications have only started to be explored. In this Account, we describe the current understanding and progress of this new description of SERS, focusing on our own contributions to the field. We first show that the quantum description of molecular optomechanics is fully consistent with standard classical and semiclassical models often used to describe SERS. Furthermore, we note that the molecular optomechanics framework naturally accounts for a rich variety of nonlinear effects in the SERS signal with increasing laser intensity. Furthermore, the molecular optomechanics framework provides a tool particularly suited to addressing novel effects of fundamental and practical interest in SERS, such as the emergence of collective phenomena involving many molecules or the modification of the effective losses and energy of the molecular vibrations due to the plasmon–vibration interaction. As compared to standard optomechanics, the plasmonic resonance often differs from a single Lorentzian mode and thus requires a more detailed description of its optical response. This quantum description of SERS also allows us to address the statistics of the Raman photons emitted, enabling the interpretation of two-color correlations of the emerging photons, with potential use in the generation of nonclassical states of light. Current SERS experimental implementations in organic molecules and two-dimensional layers suggest the interest in further exploring intense pulsed illumination, situations of strong coupling, resonant-SERS, and atomic-scale field confinement.

■ KEY REFERENCES Addressing molecular optomechanical effects in nanocavity-enhanced Raman scattering beyond the single plasmonic mode. Nanoscale 2021, 13, 1938−1954. 3 Consideration of the f ull plasmonic response to correctly address the nanoscale optomechanical interaction which induces broadening and a spectral shif t of the SERS signal. The resulting inelastic emission of Stokes and anti-Stokes photons at slightly smaller ℏ(ω las − ω vib ) or larger ℏ(ω las + ω vib ) energies, respectively, leads to a characteristic fingerprint of peaks in the emission spectra. This fingerprint is mostly determined by the chemical bonds within the functional groups but is also sensitive to the temperature, the molecular surroundings, and the isotopic composition of the molecules, among other influences. The weak Raman scattering cross section of individual molecules limits the performance of this spectroscopy technique. However, the signal is hugely boosted in surfaceenhanced Raman scattering (SERS), 5,6 where molecules are placed near metallic nanostructures acting as nanoresonators (Figure 1a). This makes it possible to characterize very small numbers of molecules or even a single molecule. 7,8 The enhancing mechanism of SERS has been traditionally assigned to two main sources: first, a chemical enhancement 9 produced by the bonding of the molecule to the metal, inducing repolarization and/or charge transfer, and second, an electromagnetic enhancement, usually the largest contribution, related to the intense plasmonic fields excited in metallic nanostructures, which very efficiently couple to molecular vibrations.
In this Account, we describe the recently developed quantum optomechanical description of (nonresonant) SERS that goes beyond this simple picture and explicitly considers the inelastic interaction between cavity plasmons and molecular vibrations at the origin of SERS (Figure 1a). This new approach establishes a connection between SERS configurations and standard optomechanical systems, where a mechanical oscillation of a cavity is coupled to one of its electromagnetic modes ( Figure  1b). 1,10,11

CLASSICAL DESCRIPTION OF SERS
The electromagnetic field that interacts with the molecules in SERS configurations arises from the excitation of localized surface plasmon polaritons. Plasmonic resonances in metallic nanoresonators can strongly enhance the electromagnetic field at visible and near-infrared wavelengths λ and confine it to extremely small volumes, 12,13 far below the ∼(λ/2) 3 diffraction limit of free photons, leading to a huge increase in the SERS signal, as typically explained through the following classical picture. 5,14 The local electric field exciting the molecule E(ω las ) is enhanced by a factor K(ω las ) = E(ω las )/E 0 , with E 0 being the amplitude of the incident illumination (local intensity increased by |K(ω las )| 2 ). This enhanced field induces a Raman dipole whose (frequency-shifted) emission rate is also strongly enhanced by the large local density of states (LDOS) of the plasmonic resonance. 13,15 When the optical reciprocity theorem is applied, this increase in the emission rate can be related to the square of the field enhancement at the Raman emission frequency, |K(ω las ± ω vib )| 2 . (See refs 14 and 16 for details.) The classical electromagnetic enhancement of the emitted SERS intensity EM class SERS can thus be expressed as The total enhancement factor in eq 1 is often simplified to |K(ω las )| 4 , which is useful in estimating the order of magnitude of enhancement at the expense of accuracy: the energy of typical vibrations ℏω vib can be comparable to the line width of plasmonic resonances, so K(ω vib ) and K(ω las ± ω vib ) can be rather different. We note that the SERS signal scales with the fourth power of the field enhancement, i.e., the square of the intensity enhancement, but in this classical framework, it remains linear with the intensity of the excitation laser. Equation 1 emphasizes that a key to maximizing SERS is to increase the field enhancement as much as possible. Plasmonic structures composed of two (or more) nanoparticles separated by nanometer gaps have proved to be particularly well suited for this purpose. 17,18 A related configuration that has the advantage Figure 1. Comparison between molecular and conventional optomechanics. Sketch of (a) a SERS configuration consisting of a molecular vibration coupled to a plasmonic mode and (b) a canonical optomechanical system consisting of a Fabry−Peŕot cavity where the motion of one of the mirrors induced by a vibrational mode varies the cavity length. of being precise and relatively straightforward to integrate with molecular self-assembled monolayers (SAMs) or with 2D materials is the nanoparticle-on-mirror (NPoM) configuration, where a metallic nanoparticle is deposited on a metallic substrate with the SAM acting as a separator between them. 19 Another important configuration which naturally produces a controllable gap is the junction between a tip and a substrate sandwiching molecules in-between, as in scanning probe microscopy such as tip-enhanced Raman spectroscopy (TERS). 20 The simple enhancement estimate in eq 1 has proved to be very useful for the interpretation of many results in SERS, but it also shows limitations in the description of nonlinear effects or correlations, for instance. These limitations can be overcome with an optomechanical description, as described in this Account.

Vibrational Population Dynamics
The emission of Raman photons at slightly decreased (S(ω las − ω vib ), Stokes line) or increased (S(ω las +ω vib ), anti-Stokes line) energy is associated with an inelastic process that creates or annihilates molecular vibrations, respectively. S(ω las − ω vib ) and S(ω las + ω vib ) arise from the (incoherent) population of vibrations, n b , at ω vib , and the incident laser intensity, I las , as Representative Raman spectra as a function of emission frequency for a single vibrational mode in the presence of a plasmonic resonator are sketched in Figure 2(a) for both the Stokes and the anti-Stokes lines (two incident intensities considered as discussed below). Under weak illumination intensity, the vibrational populations follow a thermal distribution, n b = n b th = [e (ℏω vib /k B T) − 1] −1 , where k B is the Boltzmann constant and T is the temperature. In this regime, the ratio S(ω las + ω vib )/S(ω las -ω vib ) allows an estimation of the temperature of a medium, after correcting for the frequencydependent response of the plasmonic resonator. 21 By contrast, under large incident illumination intensity, the coupling of the molecular vibration and the cavity plasmon can optically pump the molecule, modifying n b . A corrected vibrational population can be obtained in the framework of cavity optomechanics when an appropriate plasmon-vibration coupling term (or optomechanical coupling) is included in the Hamiltonian describing the Raman process. 1,10,22 The evolution of the vibrational population can then be obtained by solving the Langevin equations 10 or the master equation 1 for the corresponding density matrix, including incoherent optomechanically induced decay and pumping, in addition to the thermal pumping and the intrinsic vibrational losses γ vib . This approach is typically equivalent to solving a semiclassical rate equation of vibration creation and annihilation under the influence of optomechanical pumping and decay rates: 22,23 Here, Γ + and Γ − are the incoherent optomechanical pumping and decay rates, respectively, which are introduced by considering the plasmonic resonator to be a reservoir affecting the vibrational dynamics. The optomechanical interaction destroys vibrations at a rate of Γ_n b and creates them at rate of Γ + (1 + n b ), with Γ + and Γ + n b corresponding to spontaneous and stimulated processes. 1 For a single Lorentzian plasmonic mode of frequency ω res , 22 where κ is the plasmonic decay rate, α is the amplitude of the plasmonic mode under laser illumination (|α| 2 ∝ I las /[(ω res − ω las ) 2 + κ 2 /4] for small and moderate laser intensity, I las ), and g 0 is the single-photon optomechanical coupling rate. This g 0 is the key magnitude that determines the optomechanical interaction in SERS (section 3.2). Equations 4−6 are obtained under the assumption of optomechanical weak coupling, g 0 ≪ κ, the typical situation in optomechanics, considering harmonic vibrations and neglecting an optomechanically induced shift of the plasmonic resonance. Γ ± contains both the enhanced excitation of the molecule and its enhanced emission, analogous to the classical SERS enhancement (eq 1). The steady-state solution of the vibrational population is where the optomechanical damping rate Γ opt = Γ − − Γ + is defined. According to eqs 5 and 6, the optomechanical rates Γ + and Γ − depend on the optical response at the Stokes, ω las − ω res , and anti-Stokes, ω las + ω res , frequencies, respectively. Depending on the detuning between the illumination and the plasmonic mode, both Γ + > Γ − and Γ + < Γ − are possible. This can be observed in Figure 2(b), which shows the explicit frequency dependence of Γ + (green curve), Γ − (blue curve), and the total optomechanical damping rate Γ opt (gray curve) in the presence of a single plasmonic mode at frequency ω res . These three rates are proportional to the intensity of the incident laser I las (eqs 5 and 6). Γ opt is negative when the illumination frequency is bluedetuned from the mode (ω las >ω res ) and positive when reddetuned.
The vibrational population also depends on the incident light intensity and frequency through Γ + and Γ − (eq 7), as observed in Figure 2(c). Moreover, the optomechanical pumping and annihilation of vibrations modify the line width of the Raman lines for sufficiently intense illumination, which can be understood as a change in the effective rate of molecular losses from γ vib to γ vib + Γ opt . The sign of Γ opt becomes particularly important for large intensites where |Γ opt | ≈ γ vib . A narrowing of the line width (under blue-detuned illumination) with increasing intensity is illustrated in Figure 2(a), where the Stokes and anti-Stokes peaks in the Raman spectra are shown for moderate and strong laser intensities. The shift of the Raman line, also apparent in the figure, is discussed below.

Optomechanical Coupling at the Nanoscale
The optomechanical pumping and annihilation rates introduced in the previous section (eqs 5 and 6) depend on the optomechanical coupling, g 0 , which together with the losses and the frequency and intensity of the incident light determines the nonlinear regimes of SERS. The coupling g 0 can be obtained by quantizing the plasmonic field and the molecular vibrations, following the standard procedure. The electric field operator Eô f a single plasmonic mode is mostly determined by the effective volume V eff describing the localization of the electromagnetic field, 22,25 a E u r a u r ( ( ) ( ) ) and b̂ † and b̂as the creation and annihilation operators associated with the generalized coordinate Q k . Q k parametrizes the vibration (assumed to be perfectly harmonic) and depends on the properties of the molecule, including its mass. 6 In the following text, we consider just a single vibrational mode and Hence we express the induced Raman , whose interaction with the plasmonic mode leads to the optomechanical interaction Hamiltonian where g 0 is the (single-photon) optomechanical coupling strength, given by The additional Hamiltonian terms describing the plasmonic and vibrational excitations as well as the laser excitation of the system follow the standard form. The prefactor 1/2 is included in eq 8 because pr is an induced dipole moment operator. 13 A detailed discussion of this framework can be found in ref 22 .  Equation 8 has been derived to model SERS but is formally identical to the interaction Hamiltonian that describes traditional optomechanical systems 24 such as a Fabry−Peŕot optical cavity where one of the mirrors supports mechanical vibrational modes. The connection between these two previously unrelated disciplines is further emphasized by an alternative interpretation of the interaction Hamiltonian ĤI. 10,11 By adding ĤI to the Hamiltonian Ĥr es = ℏω res â †âdescribing the cavity mode at energy ℏω res , we obtain ĤI + Ĥr es = ℏ(ω res -g 0 (b̂+ b̂ †))â †a. Thus, the excitation of the vibrational modes induces a shift, g 0 (⟨b⟩ + ⟨b̂ †⟩), of the cavity mode frequency (⟨ ⟩ indicates the expectation value). For example, in a Fabry−Peŕot configuration, the mechanical oscillation of a macroscopic mirror changes the length of the optical cavity, modifying the resonant energy of the optical mode 24 (Figure 1(b)). A similar mechanism arises in SERS (Figure 1(a)): the microscopic vibration of the atoms modifies the polarizability of the molecule , which shifts the energy of the plasmonic mode. (In a simple picture, this shift is due to the electromagnetic coupling of two strongly detuned dipoles, with one representing the plasmonic mode and the other representing the molecular excitation.) Although their interaction Hamiltonians are analogous, SERS and traditional optomechanical systems explore a different set of energies, losses, and coupling rates. Plasmonic modes exhibit very large losses (small quality factors), but the vibrational frequencies ω vib and the optomechanical coupling strengths g 0 are very large. The large ω vib gives very low vibrational populations at room temperature, as desired for quantum applications. The huge value of g 0 is a direct consequence of the plasmonic nanocavity confinement of electromagnetic fields to extremely small regions (very small V eff ). 19,26,27 As an example, Figure 2

NONLINEARITIES IN SERS
We analyze in this section the consequences of optomechanical coupling in the evolution of the SERS signal as a function of incident illumination intensity, I las . Optomechanical pumping and decay can lead to three different regimes of SERS as I las increases: • Weak illumination (thermal regime): In most experiments, the laser intensity is sufficiently weak so that Γ + and Γ − are small and the vibrational population n b is given by the thermal pumping n b = n b th . The Stokes S(ω las − ω vib ) and anti-Stokes S(ω las + ω vib ) scattering rates are then proportional to the laser intensity (eqs 2 and 3 and Figure 3(a), white-shaded area). In this regime, the molecular optomechanics treatment is equivalent to the classical description, 22 recovering the classical dependence in eq 1.
• Intermediate illumination intensity (vibrational pumping regime): For larger laser intensity, the system enters the vibrational pumping regime, where vibrations are predominantly created by the Stokes processes induced by pumping (Γ + ) rather than by thermal processes so that the vibrational population n b in eq 7 becomes proportional to the laser intensity n b ∝ I las (in this regime, Γ + ≳ γ vib n b th and Γ opt ≪ γ vib ). Importantly, the emission of an anti-Stokes photon requires the destruction of a vibration, so the anti-Stokes scattering is proportional to both I las and n b (eq 3) and thus scales quadratically with laser intensity (brown-shaded area, Figure 3a). The Stokes signal also acquires a quadratic contribution due to vibrationally stimulated Raman scattering 1 (eq 2), but experimental observation of this effect is demanding because it requires a large vibrational population (n b ≳ 1). These results are fully consistent with semiclassical models of vibrational pumping 22, 28 and have also been discussed in studies of Stokes−antiStokes correlations. 29 An analysis of the quadratic anti-Stokes signal depend-ence allows an estimation of the optomechanical coupling strength g 0 , as has been demonstrated for the NPoM constructs 2 [ Figure 3(b)]. Combining the ultranarrow gap between the gold particle and substrate together with atomic-scale protrusions (picocavities) formed by the induced movement of gold atoms strongly localizes the field, which can address vibrations of individual molecules efficiently. Estimated values of g 0 reached tens of meV, much larger than for any conventional cavity optomechanical system. Attempts to probe into the nonlinear regime of the Stokes signal use pulsed illumination, 30,31 which better mitigates the damage to molecules while allowing large vibrational populations before bond breaking.
• Strong illumination (population saturation and parametric instability): For very large intensities (red-shaded area in Figure 3a), the modification of the total vibrational loss from γ vib to γ vib + Γ − − Γ + = γ vib + Γ opt (e.g., the denominator in eq 7) is critical. If Γ opt is negative, then the effective losses become zero for a sufficiently intense laser, leading to the narrowing of the Raman line (Figure 2(a), red spectra) and to a divergence known as the parametric instability. In the context of SERS, these instabilities were first predicted using rate equations. 22,23 In contrast, for Γ opt > 0 the effective losses γ vib + Γ opt are increased, the Raman line broadens, the vibrational population eventually saturates (similarly to cooling in conventional optomechanical systems 24 ), and the scaling of the anti-Stokes signal with laser intensity turns out to be linear again. 32 For a situation with a single plasmonic mode, the optomechanical instability and line-width narrowing occur when the laser energy is larger than the energy of the plasmonic resonance (blue detuning), whereas reddetuned illumination leads to vibrational saturation and broadening 24 (red-dashed line, Figure 3a). We discuss in section 6 how this simple criterion is no longer appropriate for complex plasmonic systems. Nevertheless, We discuss in the Outlook the challenge of distinguishing optomechanical effects from other additional effects that can be present in SERS experiments. We also discuss the convenience of using pulsed illumination to obtain information on the excitations of the system in the time domain and to attain the large laser intensities required for inducing the system into a regime of substantial optomechanical coupling, without damaging the samples.

COLLECTIVE EFFECTS
In the last few decades, various SERS experiments have shown the ability to measure Raman scattering from single molecules, 7,8 but very often target samples are constituted by molecular assemblies. In NPoM configurations, for instance, hundreds to thousands of self-assembled molecules can be placed in each NPoM gap. 19 In typical theoretical calculations, these molecules are considered separately, adding the Raman scattering from each molecule as if they did not interact. This simple approach is valid under weak illumination conditions (thermal regime), but an extension of the optomechanical model 10,32 to consider multiple molecules reveals that the singlemolecule description fails at large laser intensity I las . In such a situation, the molecule−molecule correlations established via their mutual Raman interaction through the plasmonic resonator become large enough to modify the emitted Raman signal, revealing the collective nature of the response 33 of the full molecular assembly.
An increase in the number of molecules leads to a reduction of laser intensity thresholds needed to observe the nonlinear optomechanical effects at intermediate and strong illumination (section 4). For instance, the scaling of the anti-Stokes emission with I las 2 induced by vibrational pumping (brown-shaded area in Figure 4a), the parametric instability (red-shaded area in Figure  4a), and the changes in the Raman line width all occur at lower intensities with more coupled molecules.
An analysis of the anti-Stokes signal as a function of the number of molecules N (Figure 4b) indicates a quadratic N 2 scaling in the vibrational pumping regime (blue line), resembling superradiance. 34 This superradiant-like scaling can be observed for weaker incident intensity if the temperature is reduced, making experimental observation easier. A more pronounced scaling with N is also attainable at large I las (at a suitable laser frequency), i.e., when the system approaches the parametric instability (black line in Figure 4b).
The superradiant-like scaling and the change in the intensity thresholds can be understood by invoking the excitation of a collective vibrational bright mode that couples efficiently with the plasmon, 10 similar to collective excitonic bright modes. 34,35 For a simple situation with identical molecules, the optomechanical coupling strength associated with this bright mode scales with the square root of the number of molecules. Alternatively, these collective effects can also be understood as emerging from the correlations established between the different molecules, which synchronize their response. 32 The collective response is often ignored in the interpretation of SERS, but it may be at the origin of unexpectedly large experimental signals. 36 Recent work on the analysis of nonlinearities in the Stokes signal 30 could reconcile the measurements and the predictions from molecular optomechanics only when the excitation of a collective bright mode involving ∼200 molecules was considered.

COMPLEXITY OF THE PLASMONIC RESONATOR
Typical models in traditional cavity optomechanics consider the optical response of a cavity dominated by a single Lorentzian mode, a questionable approximation for a complex plasmonic nanocavity where several overlapping modes emerge. A more general description of the linearized optomechanical interaction was now developed that incorporates the full plasmonic response of an arbitrary nanosystem using a continuum-field formalism. 37 The plasmonic response is described in such case via the field enhancement and dyadic Green's function G ⃡ of the plasmonic resonator. The application of this continuum-field model to a NPoM nanocavity 3 that exhibits a complex optical response (Figure 5a) clearly emphasizes the limitations of the single-cavity-mode approximation. Contributions from highenergy plasmonic modes (often described as a pseudomode 38 ) that are fully included in the continuum-field description can

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Article invalidate the single-mode approximation, particularly because these high-energy modes strongly influence the dyadic Green's function that describes the self-interaction of the molecule (Figure 5a). In Figure 5b, the spectral dependence of the optomechanical damping rate, Γ opt , for a single mode (dashed blue line) is compared with that obtained for the full plasmonic response (red curve), showing substantial differences. Contrary to the single-cavity-mode approximation (section 4), the continuum-field model indicates that the laser detuning (from the main mode) is not the only parameter determining the sign of Γ opt and thus whether the Raman peaks narrow or broaden for large illumination intensities as well as the specific scaling of these peaks with laser intensity. Furthermore, the specifics of the optomechanical interaction also depend on the energy of the molecular vibration. The optomechanical interaction can also strongly modify the energy ℏω vib of the molecular vibrations, leading to a frequency shift of the Raman emission lines. This so-called optical spring shift 24 is proportional to the laser intensity and is already present for a single plasmonic mode. However, including the full plasmonic response indicates that the excitation of mirror charges in the metallic surfaces can enhance this shift by 2 orders of magnitude, compared to considering a single mode 3,39 [ Figure 5(c)]. This facilitates the practical implementation of large vibrational energy shifts in molecules at reasonable laser intensities, thus opening a new avenue for optical control of chemical reactivity.
The optomechanical response can be particularly rich when a nanostructure with a complex plasmonic response interacts with many molecules (section 5). In this situation, different collective modes contribute to the scattered signal, with each mode experiencing a different spring shift and broadening (or narrowing) of the Raman line. Recent experiments 39 with intense pulsed illumination have obtained unexpected scaling of the Raman signal with laser intensity I las , an effect attributed to the redistribution of the intensity of the emitted light between these collective modes. The emergence of a strongly shifted and strongly broadened bright collective mode can effectively saturate the intensity of the sharp Raman lines and can provide anomalous increases in the "background" signal. The complex plasmonic response and collective effects can thus have large impacts on practical implementations of molecular optomechanics at the nanoscale.

STATISTICS OF SERS EMISSION
Typical SERS experiments obtain spectral information from the intensity of the scattered radiation. However, the emitted light also contains information on the photon statistics, which can be accessed, for instance, by measuring the second-order correlation between photons arriving at two detectors in a Hanbury Brown-Twiss configuration. Furthermore, interest in spectrally filtering the light before detection (Figure 6a) has recently been emphasized to extract the correlations of pairs of photons of different colors. 40 For example, in Raman spectroscopy 29,41,42 and more generally in molecular optomechanics, 1 the correlations of Stokes and anti-Stokes photons can reveal very large photon bunching. Indeed, each anti-Stokes photon gains energy from a quantum of molecular vibration that (at zero temperature) has been created by the emission of a Stokes photon so that the possibility of these two photons arriving at the detector at the same time is typically much larger than the product of the individual probabilities.
The generalization of these results to the analysis of the second-order correlations between all pair of frequencies 4 leads to two-dimensional correlations maps (Figure 6b) that reflect the complexity of the underlying emission processes. In addition to the Stokes/anti-Stokes bunching, the maps exhibit additional features associated with the intrinsic nonlinearity of the molecular optomechanics Hamiltonian, with two-photon leapfrog processes involving emission via a virtual state and with interference effects between Raman and elastically scattered photons. Information about the dynamics of these processes can be obtained by measuring the correlations as a function of the time delay between the two photons. Finally, the Cauchy− Schwarz inequality reveals that nonclassical states of light can be obtained. 41 Thus, the measurement of photon correlations  Other alternatives include exploiting DNA origami to place individual molecules at well-defined positions in nanocavities 48,49 or implementing nanolenses to increase the detected signal as well as the coupling to incoming lasers. 50 Alternative approaches rely on the design of hybrid dielectric− plasmonic structures, which exhibit modes characterized by much smaller losses than in plasmonic resonances. 51,52 In addition to the engineering of the optical response, an improvement of the chemical enhancement due to the binding of the molecules to metallic surfaces 9 can also increase the optomechanical interaction. The use of some of these strategies to optimize the optomechanical coupling strength could lead to values comparable to plasmonic losses and thus to accessing interesting interaction regimes such as single-photon optomechanical strong coupling, 24,52 g 0 ≈ κ. Molecular optomechanics also allows for exploring complex situations beyond standard optomechanics involving the rich multiresonant response of plasmonic cavities as well as simultaneous coupling with many molecules.
The physical (and chemical) mechanisms unearthed in SERS signals are challenging to interpret because the complexity of organic molecule−metal interactions and the rich dynamics governing plasmonic and molecular decay can affect the emitted signal in many different ways. Nonlinear scaling of SERS signals and broadenings of Raman lines with laser intensity can have other origins besides optomechanical interactions, such as structural molecular changes during irradiation, heating, decay from excitonic states, or the decay of plasmons into hot carriers. 28,53−55 However, careful modeling of each experiment, together with suitable control measurements, can reveal the role of molecular optomechanics. 30,39 For this purpose, it is also useful to repeatedly cycle the laser intensity to ensure that the sample is not damaged, 39 to measure the transient Raman signal at very short time scales to characterize the system dynamics, 2,47 and to calibrate the input and output energy carefully to obtain absolute values of Raman cross sections. Future possibilities to identify unambiguous optomechanical molecular dynamics might examine the correlations of emitted photons or, alternatively, access specific optomechanical signatures such as optomechanically induced transparency 24 or a strong dependence on laser detuning. 1,22,32 Coupling the plasmon with phonons in solids or van der Waals materials 31,56 opens an alternative path to exploiting optomechanical interactions at the nanoscale.
In this context, the use of ultrafast pulsed illumination 30,54,57 is particularly promising because it allows for stronger (peak) laser intensities without harming samples and for directly accessing the dynamics of vibrations by controlling the delay between pulses. Pulsed illumination can also be useful to study the influence of intramolecular vibrational redistribution (IVR) 54, 58 (the interchange of energy between different vibrations) and environment effects on molecular vibrational states and thus on Raman signals. Such studies use picosecond pulses or twodimensional femtosecond spectroscopies. 59,60 Moreover, timeresolved measurements of molecular dynamics can help to identify if the width of the Raman lines is due to either pure dephasing or to other decay processes.
Additionally, the optomechanical framework can be further generalized in the future to other situations of interest in SERS. For example, the emission of Raman photons from systems where vibrations are strongly coupled with infrared cavity modes 61−63 is still poorly understood, and the optomechanical framework introduced here can address this situation. Furthermore, plasmonic structures can create regions of strong fields (hot spots) smaller than ∼1 nm 3 via atomically sharp

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pubs.acs.org/accounts Article features that form picocavities. 26,64 These atomic-scale hot spots enable us to address individual molecular vibrations, 2 including those that are inaccessible to standard Raman spectroscopy, and even map them with submolecular resolution. 20,65,66 A combined classical and quantum treatment can explain many of the results observed in these picocavities, 66,67 but a full description of the optomechanical interaction in such a situation requires further elaboration. Moreover, the study of nonresonant SERS, as described in this Account, can be completed with the inclusion of electronically resonant SERS processes, driving a new variety of nonlinear effects. 68−70 Advances in molecular optomechanics can also be useful in the design of new devices. It has recently been proposed that the sensitivity of the Raman signal to the molecular vibrational state can be exploited to fabricate terahertz detectors 71 using a similar principle as in surface-enhanced sum frequency generation (SE-SFG 57 ). These devices can exhibit a fast response and a low level of noise as compared to current technologies. The first experimental demonstrations of IR detection have recently been achieved. 72,73 In conclusion, molecular optomechanics brings the field of optomechanics into the realm of the nanoscale with organic molecules and solid-state phonons, introducing a new plethora of physical and chemical effects in SERS and thus opening a new technological avenue for molecular nanotechnologies.