Ultrafast optical gating in a nonlinear lithium niobate microcavity.

Ultrafast optical gating in a nonlinear lithium niobate microcavity - PMC Skip to main content An official website of the United States government Here's how you know Here's how you know Official websites use .gov A .gov website belongs to an official government organization in the United States. Secure .gov websites use HTTPS A lock ( Lock Locked padlock icon ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites. Search Log in Dashboard Publications Account settings Log out Search… Search NCBI Primary site navigation Search Logged in as: Dashboard Publications Account settings Log in Search PMC Full-Text Archive Search in PMC Journal List User Guide PERMALINK Copy As a library, NLM provides access to scientific literature. Inclusion in an NLM database does not imply endorsement of, or agreement with, the contents by NLM or the National Institutes of Health. Learn more: PMC Disclaimer | PMC Copyright Notice Sci Adv . 2026 Apr 17;12(16):eaed3664. doi: 10.1126/sciadv.aed3664 Search in PMC Search in PubMed View in NLM Catalog Add to search Ultrafast optical gating in a nonlinear lithium niobate microcavity Ouri Karni Ouri Karni 1 Physics & Informatics Laboratories, NTT Research Inc., 940 Stewart Dr, Sunnyvale, CA 94085, USA. Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing - original draft, Writing - review & editing Find articles by Ouri Karni 1, * , Chirag Vaswani Chirag Vaswani 1 Physics & Informatics Laboratories, NTT Research Inc., 940 Stewart Dr, Sunnyvale, CA 94085, USA. Investigation, Methodology, Resources, Software, Validation, Writing - review & editing Find articles by Chirag Vaswani 1 , Thibault Chervy Thibault Chervy 1 Physics & Informatics Laboratories, NTT Research Inc., 940 Stewart Dr, Sunnyvale, CA 94085, USA. Conceptualization, Data curation, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing Find articles by Thibault Chervy 1, * Author information Article notes Copyright and License information 1 Physics & Informatics Laboratories, NTT Research Inc., 940 Stewart Dr, Sunnyvale, CA 94085, USA. * Corresponding author. Email: [email protected] (O.K.); * Corresponding author. Email: [email protected] (T.C.) Roles Ouri Karni : Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing - original draft, Writing - review & editing Chirag Vaswani : Investigation, Methodology, Resources, Software, Validation, Writing - review & editing Thibault Chervy : Conceptualization, Data curation, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing Received 2025 Oct 24; Accepted 2026 Mar 17; Collection date 2026 Apr 17. Copyright © 2026 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC). This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license , which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited. PMC Copyright notice PMCID: PMC13089332  PMID: 41996514 Abstract Advances in optical simulation and computation have renewed interest in high-finesse optical cavities for enhancing light-matter interactions, engineering complex photonic band structures, and storing quantum information. However, the extended interaction times in these cavities dictate slow optical readout and limited control over system transients. Addressing this challenge, we demonstrate an ultrafast intracavity optical gating scheme in high-finesse, second-order nonlinear microcavities incorporating thin films of lithium niobate. A femtosecond optical gate pulse, tuned to the transparency region of the cavity’s dielectric mirrors, instantaneously upconverts the intracavity field via sum-frequency generation. The upconverted pulse promptly exits the cavity, providing space- and time-resolved information on the intracavity field. We validate this approach by tracking the dynamics of multiple resonant modes excited in a plano-concave microcavity, comparing well with analytical models. In addition, we demonstrate that intracavity difference-frequency generation can efficiently instantiate the cavity fields. Fully compatible with low-temperature microcavity experiments, this gating scheme enables future real-time control of light-matter interactions or quantum-optical state manipulations. Ultrafast optical nonlinearity in a high-finesse microcavity enables the seeding and retrieval of spatiotemporal field dynamics. INTRODUCTION Optical cavities play a central role in the development of experimental quantum optics. Confining light to a finite volume of space forces photons to occupy discrete sets of resonant modes, defined by their wavelengths, polarization, and spatial field profiles. These modes circulate in the cavity for extended durations, thus prolonging the light-matter interaction time and enabling applications in acute sensing and spectroscopy ( 1 , 2 ) and efficient nonlinear ( 3 , 4 ) and quantum optics ( 5 ). In this context, Fabry-Pérot microcavities have emerged as versatile platforms for the simulation of solid-state Hamiltonians ( 6 – 10 ) and many-body systems ( 11 – 13 ), all-optical information processing ( 14 – 16 ), and storage ( 17 – 19 ) and are instrumental in the advancement of polaritonic chemistry ( 20 – 22 ). In these systems, the resonant light bouncing between the cavity mirrors dynamically evolves as it interacts with the host material, forming, for example, exciton-polariton states. This evolution occurs over multiple timescales spanning from the fast round-trips between the mirrors and across the transverse plane, through any material-related dynamics, to the slow leakage of light out of the cavity. Hence, the time-dependent state of light resonating in the cavity is carrying key information, for instance, on the converging results of a quantum simulator ( 23 ) or on the formation of complex many-body excitations ( 24 ), constantly motivating the development of techniques to instantiate, control, and measure these field transients. Thus far, most of the techniques developed for this purpose have relied on the slow decay of the intracavity field through the microcavity mirrors and its characterization by, e.g., time-resolved photon-counting ( 25 ), upconversion spectroscopy ( 26 – 28 ), spectral interferometry ( 26 ), or on collecting indirect observables such as transient absorption signals ( 29 , 30 ). However, to fully exploit the potential of microcavity systems, it is necessary to implement dynamical control schemes where the coupling between the intracavity field and its environment can be tuned over timescales much shorter than cavity mode lifetime. Such dynamical control schemes are particularly important in the context of storage and retrieval of quantum optical information, where the coherent extraction of the intracavity state into a single output temporal mode could facilitate quantum state tomography and enable cascaded operations in a well-defined mode basis ( 31 – 35 ). Despite its great potential, dynamic control of high-quality photonic structures remains largely unexplored and have not been demonstrated in standard Fabry-Pérot microcavities. In this work, we introduce a platform for ultrafast dynamical control of light by integrating thin-film lithium niobate (TFLN) with a high-finesse, tunable, zero-dimensional (0D) microcavity tightly confining resonant light in all spatial directions. To demonstrate the platform’s capabilities, we show that the intracavity field can be extracted on femtosecond timescales through second-order nonlinear optical gating by an external control pulse. This technique enables coherent mapping of the cavity field’s spatiotemporal dynamics with femtosecond temporal and micrometer spatial resolution. In addition, we demonstrate nonlinear excitation of the cavity field via stimulated intracavity difference-frequency generation (DFG), enabling ultrafast and efficient instantiation of optical modes in a high-finesse resonator. The platform is fully compatible with low-temperature operation, as demonstrated in a closed-loop cryostat at 4 K, making it suitable for integration with quantum optical and cryogenic photonics experiments. The device at the basis of our experiment is shown schematically in Fig. 1A . It consists of a plano-concave dielectric Bragg reflector (DBR) microcavity, embedding a thin film of X-cut MgO:LiNbO 3 (TFLN). The 10-μm-thick TFLN layer is wafer bonded to the flat DBR substrate, and a curved microstructured DBR mirror (30-μm radius of curvature) is held at a controlled distance (around 2 μm) above by piezoactuators, forming a high-finesse tunable microcavity [see Materials and Methods for fabrication details]. A representative transmission spectrum of the microcavity, polarized along the extraordinary axis of LiNbO 3 , is shown in Fig. 1B for a fixed cavity length, displaying a series of Ince-Gaussian modes ( 36 ) (see fig. S1 for a comparison to analytically calculated Ince-Gaussian profiles). Note that these modes only constitute a subset of the full modal manifold, which also includes additional transverse and longitudinal mode orders. In addition, the in-plane crystal anisotropy of X-cut TFLN splits the manifold of cavity modes into two orthogonally polarized series. In the following, we fix the polarization of all beams along the crystal extraordinary axis, corresponding to the largest χ ( 2 ) coefficient of TFLN. Fig. 1. Nonlinear microcavity and optical gating scheme. Open in a new tab ( A ) Schematic of the nonlinear microcavity structure. A 10-μm-thick Mg:LiNbO 3 slab (TFLN) is wafer bonded to the flat bottom DBR mirror (bottom inset: micrograph of the diced chip). The curved top mirror is held at a controllable distance above, defining the cavity length and transverse mode confinement (top inset: phase-contrast micrograph, featuring several curved micromirrors with varied radii of curvature, fabricated on an elevated SiO 2 mesa. All color contrasts are a result of the phase-contrast imaging mode of the microscope). A radius of curvature of 30 μm was used in our experiments. ( B ) Transmission spectrum of a ~12-μm-long cavity, illuminated by a broadband source polarized along the extraordinary axis of the TFLN slab, showing successive transverse resonances (measured mode images raised by a 0.5 power to enhance the visibility of low-intensity details are shown in the insets). ( C ) Illustration of the optical gating procedure. Cavity modes are resonantly populated by a 150-fs pump pulse. The copropagating gating pulse (angled here for clarity) arrives at a controlled delay time τ, generating the SFG signal. ( D ) Spectral arrangement of the experiment. The resonant cavity mode near 750 nm (red) is within the DBR stop-band. The gate pulse (1040 nm) and SFG signal (436 nm) are located in the transparency regions of the DBR. The gating procedure is schematically presented in Fig. 1C . Resonant modes of the cavity are first excited by a short optical pulse (150 fs) centered at around 750-nm wavelength, within the DBR stop-band. After an adjustable delay τ, the gating pulse (150 fs, ~30 μm spot diameter) is launched at the cavity. This pulse is centered around 1040-nm wavelength, outside the DBR stop-band, and thus passes only once through the cavity, retaining both its short-pulse and wide-spot characters. While traversing the TFLN layer, the gating pulse upconverts the instantaneous and local intracavity field into a sum-frequency generated (SFG) signal around 436 nm. As depicted in Fig. 1D , the SFG spectrum is well outside the DBR stop-band and therefore quickly escapes the cavity as a pulse as well. The SFG signal thus extracts instantaneous and local information about the intracavity field, which we then measure in two complementary modalities: time-resolved SFG images, I SFG ( x , y , τ ) , and time-resolved SFG spectrograms S SFG ( ω , τ ) [see Materials and Methods ]. The results we show below, alongside an analytical model of the gating procedure, serve to explore the capabilities of this technique. RESULTS Evolution of individual modes We begin by considering two simple-to-interpret scenarios: when the cavity is excited in only a single resonant mode and then when a pair of modes is excited. Each is achieved by spectrally filtering the excitation pulse around the desired mode. The identity of the selected mode is confirmed in each experiment by its spectral position in the ladder of transverse modes as well as by its time-integrated transmission image, as shown in Fig. 2 (A and E) . Fig. 2. Individual mode dynamics. Open in a new tab ( A and E ) Transmission spectra of the cavity (red) when excited with a filtered pulse (gray) centered on the (A) fundamental and (E) IG 11 e and IG 11 o cavity modes. Insets: Time-integrated images of the transmitted resonant light. a.u., arbitrary units. Scale bar, 10 μm. ( B and F ) Snapshots of the transmitted SFG images at specific time delays. ( C and G ) SFG spectrograms. For clarity, the normalized intensity is corrected by a power of 0.5. ( D and H ) Integral of the SFG spectrograms over the wavelength coordinates (black curve) and fitted decay dynamics (D) A 1 ( τ ) and (H) A 2 ( τ ) (orange dashes). Upon selectively exciting a fundamental IG 00 e mode, the time-resolved SFG images present a steady spot profile that resembles the IG 00 e distribution, with negligible changes over time, as shown in Fig. 2B (see also movie S1 in the Supplementary Materials). The SFG spectrogram, recorded over 500 ps in Fig. 2C , shows a smooth amplitude decay across the entire SFG spectrum, in accord with the expected dynamics of a single eigenmode excited in the cavity. The spectral bandwidth of the SFG spectrum matches that of the gating pulse, translated to the sum-frequency domain. The dynamics become more elaborate when a pair of modes is excited. We specifically choose the pair of IG 11 e and IG 11 o modes, with a single node in their spatial shape and a 20-GHz spectral gap between them due to residual astigmatism in the parabolic microcavity mirror ( Fig. 2E ). The SFG images now display periodic transitions between two rotated copies of the original Ince-Gaussian mode profiles, as shown in the selected snapshots in Fig. 2F (full video in movie S2 of the Supplementary Materials). These correspond to the symmetric and antisymmetric superpositions of the IG 11 e and IG 11 o eigenmodes. The periodicity of these transients is about 50 ps, in agreement with the inverse of the spectral gap between the modes. The SFG spectrogram ( Fig. 2G ) features corresponding temporal beatings with the same periodicity, which show up uniformly across the SFG spectrum. A quantitative understanding of these results can be obtained by comparing the data to an analytical derivation of the transient SFG fields, based on a well-known nonlinear optics formalism ( 37 ) (a full derivation is provided in Supplementary Text). Assuming that the gating spot is much larger than the mode profiles yields the following expression for the time-resolved SFG images I SFG ( x , y , τ ) ∝ ∫ ∣ G ( t − τ ) ∣ 2 ∑ ν F ν ( x , y ) R ν ( t ) e j ω ν t 2 dt (1) where F ν ( x , y ) are the spatial profiles of the excited modes ν, with slowly decaying amplitudes R ν ( t ) and frequencies ω ν . G ( t − τ ) is the delayed envelope of the gating pulse. This approximation is justified in fig. S3, showing less than 5% deviation between the gated mode profiles and the original Ince-Gaussian profiles. Because the spectral distribution of excited cavity modes is much narrower than the pulse bandwidth, we can approximate that G ( t − τ ) ∼ δ ( t − τ ) I SFG ( x , y , τ ) ∝ ∑ ν F ν ( x , y ) R ν ( τ ) e j ω ν τ 2 (2) The SFG spectrograms are obtained by collecting the SFG signal through the slit of a spectrometer. Assuming that the cavity resonances are much narrower than the gate pulse bandwidth yields S SFG ( ω , τ ) ∝ ∫ ∑ ν F ν ( 0 , y ) R ν ( τ ) e j ω ν τ g ( ω − ω G − ω ν ) 2 dy (3) where g ( ω − ω G − ω ν ) is the gating pulse spectrum shifted to the sum-frequency domain for each cavity mode ν, ω G is the carrier frequency of the gating pulse, and the integral over the y coordinate accounts for full vertical binning in the imaging spectrometer. On the basis of this model, the spectral features observed, for instance, in Fig. 2C , stem from the specific gating pulse spectrum at that measurement. Then, integrating the single-mode spectrogram ( Fig. 2C ) along the wavelength coordinate results in the decay trace of the excited mode. As seen in Fig. 2D , the integration (black curve) fits well with an exponential decay curve (orange dashes): A 1 ( τ ) = Θ ( τ ) Ae − τ / τ 0 , with Θ ( τ ) being the Heaviside function. The fitted lifetime τ 0 is 156 ± 5 ps ( Q -factor of 62,000). This translates to a 26-μeV (12 pm) linewidth of the resonant mode, well below our spectrometer spectral resolution. Similarly, the integration of the two-mode spectrogram ( Fig. 2G ) yields the temporal beating trace shown in black in Fig. 2H . Fitting it with a two-mode beating model A 2 ( τ ) = Θ ( τ ) ∣ R 11 e + R 11 o e j ( Δ ϕ + Δ ω τ ) ∣ 2 e − τ / τ 11 (orange dashes) allows to reconstruct the complete dynamics of the two modes: They decay with a lifetime of τ 11 = 203 ± 0.7 ps ( Q -factor of 80,000), a phase offset Δ ϕ = 0.1 ± 0.003 π rad, and an amplitude ratio R 11 o R 11 e = 0.13 ± 0.008 . Once again, the extracted lifetimes translate to modal linewidths below the spectrometer resolution. The longer lifetime of these modes as compared to the fundamental mode can be explained by possible scattering defects at the center of the cavity that affect the fundamental mode more severely than the IG 11 modes, as well as potential slow mechanical drifts affecting the excitation efficiency over the course of the experiment. Ultrafast multimodal dynamics Having confirmed that intracavity optical gating can provide both qualitative and quantitative information about the dynamics of individual resonant modes, we now explore the cavity dynamics when a full manifold of modes is excited ( Fig. 3A ). The time-resolved SFG images now display complex multimode dynamics in the transverse field distribution, as shown in Fig. 3B (see movie S3 in the Supplementary Materials). This is a result of coherently superimposing together many modes of various transverse and longitudinal orders. The corresponding SFG spectrogram is shown in Fig. 3C , featuring fast oscillations along the temporal axis, with noticeable variations across the SFG spectrum. Fig. 3. Multimodal dynamics. Open in a new tab ( A ) Transmission spectrum of the cavity (red) when excited with a broadband resonant pulse (gray). Multiple longitudinal and transverse modes are excited. The more intense modes are labeled with their Ince-Gaussian identifiers. The weaker ones are remnants of the modes polarized along the ordinary axis of LiNbO 3 . ( B ) Snapshots of the transmitted SFG images at specific time delays. ( C ) SFG spectrogram. ( D ) Fourier transform of (C) along the time delay coordinate. For clarity, the normalized intensities in (C) and (D) are corrected by a power of 0.5. This is further highlighted by taking the Fourier transform of the spectrogram along the temporal coordinate, as shown in Fig. 3D . Several notable features are observed: First, two spectral domains are lit up around 434 and 437 nm, corresponding to two different excited longitudinal cavity modes, separated by 5 THz. Second, the fundamental beating periodicity, corresponding to the heterodyning of nearest-neighboring transverse modes with one another, changes sensibly across the spectrum, from 0.42 THz around 438 nm to 0.69 THz at 436 nm. These changes reveal an anharmonic distribution of the transverse cavity modes and are rooted in residual deviations of the curved micromirror from a perfect parabola. Third, harmonics of these frequencies are visible up to a few terahertz, indicating heterodyning between second-nearest (or higher-order) neighboring modes. These observations emphasizes another virtue of the spectrogram, allowing to capture signal bandwidths that are larger than the gating pulse bandwidth thanks to time-frequency redundancy ( 38 ). Note that a full characterization of the complex intracavity field can be obtained by recording SFG spectrograms from each point of the ( x , y ) plane and applying established phase retrieval ( 38 – 40 ) or machine learning algorithms ( 41 ). Such data-intensive analysis, although important for the characterization of more complex optical resonators, is beyond the scope of the present work. To further demonstrate the capabilities of this approach, we report in fig. S5 and movie S4, the time-resolved dynamics of a nominally flat monolithic TFLN microcavity (fig. S4), featuring in-plane propagation and wave packet dynamics. There, the sample boundaries and residual mirror curvature lead to periodic refocusing of the excited wave packet on a picosecond timescale. These results open avenues for exploring complex and topological photonic band structures, where intracavity optical gating offers a powerful tool for probing ultrafast wave packet dynamics. Nonlinear initialization of cavity modes Although the results presented thus far highlight optical gating for the on-demand extraction of multimode intracavity dynamics, we now introduce a complementary approach that enables the on-demand injection of optical fields into the cavity. In this scheme, depicted in Fig. 4A , the microcavity is simultaneously excited by a pump and a gate pulse, both located outside of the DBR stop-band (150-fs durations and 436 and 1040 nm carrier frequencies, respectively). As the two pulses traverse the microcavity, the gate stimulates DFG from the pump, generating photons in the cavity resonance wavelength range. Crucially, as this process occurs within the structured electromagnetic vacuum field of a 0D, high-finesse, microcavity, the excess energy can only be carried away through the generation of photons at the discrete cavity mode frequencies ( Fig. 4B ). Fig. 4. Excitation of cavity resonances through frequency downconversion. Open in a new tab ( A ) Illustration of the stimulated intracavity DFG generation process. The copropagating pump and gate pulses (angled here for clarity) reach the cavity with a controlled delay time τ . Cavity modes are populated by stimulated intracavity DFG when the pump and gate signals overlap in space and time within the cavity. ( B ) Spectral arrangement for intracavity DFG. The gate pulse (1040 nm) stimulates the DFG of resonant cavity photons near 750 nm. ( C ) Time-integrated emission spectrum of the cavity, as a function of delay between the pump and gate pulses. Top and side panels show linecuts along the gray dashed lines, corresponding to τ = 0 ps and λ = 749.8 nm, respectively. This scheme is experimentally validated in Fig. 4C , showing the spectrum emitted from the cavity around its resonant wavelengths, as a function of the time delay between the pump and gate pulses. The attached cross-sectional insets clearly demonstrate the instantaneous excitation of a series of transverse cavity modes (~0.6-nm mode spacing), when both the pump and gate pulses are simultaneously present in the microcavity. The span of modes excited through this process is determined by the spectral overlap between the cavity mode spectrum and the convolved pump and gate spectra, as well as by modal overlap between the cavity modes and the pulses. In the present case, the gating and pump beams were tightly focused, resulting in higher overlap with the fundamental (lowest energy) transverse mode of the excited manifold, making it sensibly stronger than the other modes in the emission spectrum. Spectral selectivity can thus be improved by narrowing the bandwidths of the pump and gate pulses, at the expense of an increased uncertainty over the instantiation time of the cavity modes. Alternatively, temporal and spatial pulse shaping may be used to improve overlap with certain target intracavity state ( 33 ). This technique provides an efficient pathway for all-optical, ultrafast control of cavity excitation dynamics, fully compatible with ultrahigh-finesse DBR resonators. DISCUSSION We have demonstrated a platform for ultrafast nonlinear optics in high-finesse Fabry-Pérot microcavities, enabled by the integration of TFLN with a tunable 0D DBR resonator. This architecture combines long-lived optical resonances with femtosecond dynamical control via instantaneous second-order nonlinear processes. Using this platform, we achieve ultrafast optical gating—both injection and extraction—of cavity fields, offering coherent access to complex intracavity dynamics. A key advantage of this approach is its ability to extract and instantiate the intracavity field with control over its spatiotemporal profile, enabling selective excitation and readout of optical modes. This makes the technique broadly applicable to the study of complex photonic structures, such as coupled cavity arrays ( 7 , 42 , 43 ), with direct relevance to polaritonics ( 14 ), photon Bose-Einstein condensates (BECs) ( 44 ), optical thermodynamics ( 45 ), as well as for atom-cavity quantum electrodynamics ( 46 ). The open architecture of our nonlinear microcavity allows for straightforward integration of diverse material systems, including epitaxial thin films via wafer bonding, 2D materials through van der Waals assembly, molecular dyes via spin-coating, or cold atoms and ions. This flexibility paves the way toward hybrid χ ( 2 ) - χ ( 3 ) nonlinear photonic systems. We further strengthen this point by demonstrating, in figs. S6 and S7, ultrafast optical gating in a high-finesse tunable microcavity, assembled within a close-loop cryostat operating at 4 K. Another important aspect of the demonstrated technique is the efficiency of the nonlinear interactions. Although the present scheme allows for ultrafast spatially resolved measurement of arbitrary intracavity field dynamics, it does not implement efficient nonlinear conversion of a specific cavity mode. This is primarily due to the deliberate choice of a small wavefunction overlap between the long-lived confined cavity modes and the spatially extended, short gating pulses. In this configuration, a large number of intracavity photons (~10 6 ) only yields a few SFG photons per pulse with our available gate power, as further discussed in the Supplementary Text. Although improvements can be made to the device in terms of phase matching of the interacting waves (see fig. S8) or by using different nonlinear materials with quasi-phase-matched stacking ( 47 ), more marked gain in efficiency require selective mode matching through spatial and temporal pulse shaping ( 33 ). This regime of efficient depletion of a specific cavity mode using tailored gate pulses is particularly appealing in the context of photonic and polaritonic lattices, where it could offer precise control over the non-Hermitian evolution of intracavity states, enabling studies of position- and time-dependent quenches in driven-dissipative photonic systems. Last, in the limit of deterministic quantum state extraction, intracavity optical gating could enable manipulation and study of quantum optical states in a well-defined temporal mode basis—an essential requirement for various all-optical quantum information protocols ( 31 ). Such schemes, however, require vastly different configurations, both in terms of device architecture and gating scheme, as discussed above. Notably, the second-order correlation function g ( 2 ) ( τ ) of the intracavity field is faithfully upconverted through the local and instantaneous SFG process ( 28 ), even at finite conversion efficiencies, and should be directly measurable with the current device architecture (see derivation in Supplementary Text). This platform thus constitutes a powerful tool for the advancing ultrafast quantum optics in integrated photonics systems. MATERIALS AND METHODS Device fabrication The main device presented in the text was fabricated in two parts. The flat DBR mirror (quarter-wave stack of Ta 2 O 5 and SiO 2 ) was sputter-coated onto a silica wafer by FiveNine Optics Inc. (USA). A slab of LiNbO 3 (NGK, Japan) was then wafer bonded onto the DBR and then polished to a thickness of 10 μm. The bonded wafer was then diced into 7 mm–by–7 mm chips. The curved DBR was sputtered onto an ablated SiO 2 mesa chip (Qlibri GmbH, Germany), realizing a curved DBR with a radius of curvature of about 30 μm. The two DBRs where brought into proximity using micromanipulators and piezoactuators. The device used in the cryogenic setup was based on a similar flat TFLN layer bonded to a DBR chip. For this experiment, the curved mirror was sputtered onto the ablated facet of a single-mode optical fiber (Qlibri GmbH, Germany). The monolithic cavity device, shown in Supplementary Data, was fabricated from a 7-μm-thick TFLN flake, chipped off a commercially available LiNbO 3 wafer (NanoLN Ltd., China), and attached to a flat DBR (FiveNine Optics Inc., USA) using a 150-nm-thick layer of poly(methyl methacrylate) (PMMA). Subsequent sputtering of the top DBR (FiveNine Optics Inc., USA) completed the cavity. Stress transfer during the top mirror deposition resulted in slight buckling of the flake, yielding a nominally flat Fabry-Pérot microcavity, with a mirror radius of curvature of the order of millimeters. Time-integrated spectroscopy and imaging For the time-integrated spectra and images, we illuminate the cavity with the broadband pulses (750 nm, 10-nm full width at half maximum bandwidth, and 500-mW average power impinging at the input of the cavity) sourced from the tunable output of a Chameleon Discovery NX laser (Coherent Inc., USA). Most of the power is reflected back by the DBRs, and only light resonant with the cavity is transmitted. The transmission spectrum is collected with an imaging spectrometer (SpectraPro HRS-750, Princeton Instruments Inc., USA) equipped with a charge-coupled device (CCD) camera (ProEM-HS, Princeton Instruments Inc., USA). To resolve the spectrum and the spatial distributions of the modes in the same measurement, we use the horizontal coordinate of the CCD for the spectrum and the vertical coordinate of the CCD for the spatial y coordinate and sweep the horizontal position of the tube lens at the spectrometer input to scan the x coordinate. Thus, we acquire a 3D dataset. The spatial coordinates were calibrated against microscopically measured dimensions. The transmission spectra recorded in the cryogenic setup used a superluminescent light-emitting diode (Exalos AG, Switzerland) as a broadband spectroscopic light source. Time-resolved spectroscopy and imaging To generate the time-resolved data, we tune the delay between two pulses generated by the same pulsed laser (Chameleon Discovery NX). Its tunable output is used to seed the cavity with the resonant modes (pump pulse), and the fixed wavelength output at 1040 nm is used as the gating pulse. To produce the clear signals shown in the text, we used an ~500-mW average power over the full bandwidth of the tunable pump as well as for the gating pulse average power. The gating pulse fluence was 0.2 mJ/cm 2 . Our derivation of the upconversion efficiency (Supplementary Text) shows that such signal intensities can generate a few SFG photons per interaction, yielding detectable SFG signals after accumulation times in the order of seconds (~10 8 interactions at an 80-MHz repetition rate). Both pulses were polarized along the extraordinary axis of the LiNbO 3 crystal. For the stimulated loading of the cavity by DFG, we doubled the tunable output of the laser (tuned to 872 nm) using a beta-barium borate (BBO) crystal to generate a 436-nm pulse. The pump signal average power was 150 mW, whereas the gating fluence was enhanced by focusing to 0.6 mJ/cm 2 . Both pulses were polarized along the extraordinary axis of the LiNbO 3 crystal. Collecting the SFG light is done in two modalities: Imaging: The spectrometer slit is wide open, the grating is tuned to zeroth-order scattering, and the CCD array is used as a camera. Spectroscopy: The spectrometer slit is closed, and the CCD is fully vertically binned to generate a spectrum at each time delay between the pump and the gating pulses. Cryogenic setup To work at cryogenic temperatures, the cavity setup was built into a cryostat (AttoDRY800, Attocube GmbH, Germany) equipped with free-space and fiber optical ports. The flat DBR mirror of the cavity was held static, whereas the fiber DBR was actuated. To control this motion, we used a cryocompatible piezoelectric stage [CPSHR1, JPE, The Netherlands; see ref. ( 48 )] that also passively damped the vibrations in the setup. The pump pulse average power was set to 13 mW, whereas the gate pulse average power was reduced to 50 mW, with a fluence of 20 μJ/cm 2 . Acknowledgments We acknowledge insightful discussions with P. Murthy and E. Ng and thank E. Lorchat, J. Wouda, Y. Bakkouch, and L. Seidt for contributions to the experimental setup. Funding: We thank NTT Research Inc. for financing this work. Author contributions: O.K. and T.C. conceptualized the work. O.K., C.V., and T.C. fabricated the samples and assembled the experimental apparatus. O.K., C.V., and T.C. performed the measurements. O.K., C.V., and T.C. analyzed the results. O.K. derived the theoretical model. O.K. and T.C. wrote the manuscript. T.C. supervised the project. Competing interests: The authors declare that they have no competing interests. Data, code, and materials availability: All data and code needed to evaluate and reproduce the results in the paper are present in the paper and/or the Supplementary Materials. This study did not generate new materials. Supplementary Materials The PDF file includes: Supplementary Text Figs. 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S1 to S8 Table S1 Legends for movies S1 to S4 References sciadv.aed3664_sm.pdf (17MB, pdf) Movies S1 to S4 sciadv.aed3664_movies_s1_to_s4.zip (3.9MB, zip) Data Availability Statement All data and code needed to evaluate and reproduce the results in the paper are present in the paper and/or the Supplementary Materials. This study did not generate new materials. 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