High-Q microresonators unveil quantum rare events

TL;DR

Classical linear optics fails to describe rare quantum vacuum–mediated events in $high-$Q$ microresonators coupled to dielectrics, where vacuum fluctuations enable Stokes and constrained anti-Stokes Raman processes to imprint molecular fingerprints onto linear transmission without changing the linear susceptibility $\chi^{(1)}(\omega)$. The authors develop a theoretical framework using an input-output formalism and a Dyson expansion of the photon Green's function up to fourth order in the light-matter coupling $g$, and they decompose cavity modes into symmetric and antisymmetric combinations to isolate vacuum-mediated pathways. For a single molecule, this yields new absorption features near the cavity resonance $\omega_c$ that reflect the molecular Raman spectrum via $R_{\text{vib}}(\omega)$; for ensembles of molecules, collective coupling $g\sqrt{N}$ amplifies the signal, producing detectable Raman peaks in the tails of the Lorentzian with strengths up to $\sim 10^8$ photons. The findings open routes to quantum-vacuum-enabled sensing and spectroscopy with potential THz Raman capabilities in mid-IR to UV microresonators, while avoiding fluorescence backgrounds and enabling novel interference-based enhancements.

Abstract

Classical linear optics posits that at sufficiently low intensities, light propagation in dielectric media is governed solely by their linear susceptibilities. Here, we demonstrate a departure from this paradigm in high-Q microresonators, where prolonged photon confinement enables rare quantum electrodynamical (QED) events, mediated by the quantum vacuum, to embed distinctive Raman signatures of the coupled analyte into the resonator's linear transmission spectrum despite their absence from the linear susceptibility. We further show that increasing the amount of adsorbed analyte amplifies these Raman fingerprints well above typical noise floors, rendering them experimentally accessible with state-of-the-art photonic architectures and detection schemes. This novel weak-coupling cavity-QED effect offers unique routes to harness extended photon lifetimes and constrained geometries for leveraging vacuum fluctuations in next-generation photonic technologies for chemical and biological sensing and high-precision optical spectroscopy.

Figures (4)

• Figure 1: Schematic illustration of vacuum-mediated Raman processes in the linear optics of a microresonator system, highlighting the Stokes and anti-Stokes components.a, A high-$Q$ microtoroid resonator at frequency $\omega_c$ is evanescently coupled to a single molecule and probed with an incident laser at frequency $\omega$, introduced via an optical fiber through evanescent coupling. The key phenomenon we reveal is that contrary to classical linear optics predictions, a molecule’s Raman vibrational fingerprints directly manifest in linear transmission, $T(\omega)$, of the microtoroid, provided the cavity lifetime is sufficiently long. The adjacent ladder and double-sided Feynman diagrams (DSFDs) illustrate a cavity Raman process, where Stokes scattering populates the cavity vacuum with a field that subsequently drives the anti-Stokes transition. Notably, this mechanism solely involves quantum coherences, unlike the Purcell effect. Moreover, distinct from conventional Raman, it neither induces vibrational heating or cooling nor results in the up- or downconversion of photons. Instead, the process operates within the linear regime, introducing additional absorption channels at new frequencies. This vacuum-mediated process cannot occur outside the single-mode cavity, as the Stokes field becomes irreversibly dispersed among the numerous modes of the free-field electromagnetic continuum. In contrast, b, (c,) denote a conventional anti-Stokes (Stokes) Raman process that occurs when an incident laser photon at frequency $\omega_L$ inelastically scatters to $\omega_{AS}$ ($\omega_S$) by extracting (leaving behind) vibrational energy from the molecule. This leads to vibrational cooling (heating) as the population is transferred to the vibrational ground (excited) state. Being an inherently nonlinear process, this upconvert (downconvert) the laser photon, unlike in the linear regime of the microtoroid resonator. The corresponding DSFD MukamelBook and ladder diagrams tokmakoff_nonlinear_notes illustrate the underlying mechanism. Solid and dotted lines in the ladder diagrams indicate the ket- and bra-side interactions in the DSFDs.
• Figure 2: Cavity vacuum-mediated Raman processes in isoprene encode the information of the bare Raman spectrum.a, Raman spectrum of bare isoprene, where the $y$-axis represents the normalized scattered intensity, and the $x$-axis corresponds to the Raman shift, defined as the frequency difference between incident and scattered light. b, Frequency-resolved absorption spectrum of a microresonator coupled to a single isoprene molecule. The exact calculation of the spectra is plotted in violet. The blue inset highlights the lifting of degeneracy in the microresonator modes, leading to symmetric and anti-symmetric combinations. The red inset reveals additional peaks attributed to cavity vacuum-mediated Raman processes near the cavity resonance at $\omega=0$, as depicted in Fig. \ref{['fig: schematic_raman_process']}. The $0^{\text{th}}$ order term (magenta) in Eq. \ref{['eqn:pert_4_one_isoprene']} reproduces the bare cavity spectrum. The fourth-order term in the Dyson expansion is split into two parts. The first part (black) includes only Rayleigh features, encoding only the linear susceptibility, $\chi^{(1)}(\omega)$, of the molecule and fall in the paradigm of classical linear optics. In contrast, the second part of the fourth-order(green) term unveils new, subtle peaks around the cavity resonance—signatures of quantum vacuum-mediated Stokes-anti Stokes Raman processes that introduce additional absorption channels at frequencies detuned from the cavity resonance by the Raman shifts. These peaks do not exist in the absorption spectra outside the cavity and are signatures of the cavity vacuum-mediated weak coupling effect presented in this work.
• Figure 3: Proposed experimental protocol for enhanced Raman peak detection in the linear transmission spectra. a, Schematic of the experimental protocol for Raman peak enhancement, where an ensemble of isoprene molecules are evanescently coupled to a microtoroid resonator (highlighted by the magnifying glass). An optical fiber delivers the laser, which couples evanescently to the resonator, thereby imprinting the molecular Raman signatures onto the absorption spectrum in the linear regime. Corresponding ladder diagram illustrating the energy-level transitions, $\Omega$ assuming the role that $\omega_c$ took in the single-molecule case. b, The main plot presents the logarithm (base 10) of the number of absorbed photons, $\log_{10} n_{\text{abs}}$, as a function of $\omega - \omega_{\text{LP}}$, where $\omega_{\text{LP}}$ corresponds to the lower peak of the absorption spectrum. The system parameters are set as $\Delta = 0$, $g = 1.63 \times 10^{-4}$ eV, $N = 3\times10^6$, $\kappa_{\text{ex}} =\gamma = 3 \times 10^{-5}$ eV, and $\gamma_{\text{vib}} = 5 \times 10^{-4}$ eV (considering $\omega_c=\omega_{0-0}$, this corresponds to $Q=2\times10^5$perin2022highMin2006UltrahighQLiu18ultravioletrichter2018microtoroid). The inset highlights the second-order correction to the absorption, revealing distinct Raman signatures. Both the fundamental Raman band and its higher-order overtones emerge, suggesting that vacuum-mediated effects play a role in the observed vibrational features. Notably, the photon absorption remains well above the noise equivalent power (NEP, $10^5$), with $n_{\text{abs}} > 10^7$.
• Figure 4: Dependence of absolute Raman peak height and its ratio to the Rayleigh background on key experimental parameters. Contour plots of a, the absolute Raman peak height as a function of $\Delta=\omega_c-\omega_{0-0}$ and $\log_{10}(\kappa/\text{1 eV})$, b, the ratio of Raman peak height to the Rayleigh background over the same parameter space with $g = 1.63 \times 10^{-4}$ eV, $N = 3\times10^6$, $\gamma = 3 \times 10^{-5}$ eV, and $\gamma_{\text{vib}} = 5 \times 10^{-4}$ eV for this simulation. c, the absolute Raman peak height as a function of $\log_{10}(g/\text{1 eV})$ and $\log_{10}(N)$, and d, the ratio of Raman peak height to the Rayleigh background over the same parameter space with $\kappa_{\text{ex}} = \gamma = 3 \times 10^{-5}$ eV and $\gamma_{\text{vib}} = 5 \times 10^{-4}$ eV for this simulation, These simulations focus on the dominant Raman feature from the vibrational mode with frequency ($\omega_v=0.202$ eV) and Huang-Rhys factor ($S=1.57$). Figs. a. and b. indicate that $Q$ factors in the range of $2\times10^4$ to $2\times10^6$ are optimal for maximizing both the signal strength and the Raman/background ratio.