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Photonic integrated circuits with second-order (χ⁽²⁾) nonlinearities are rapidly scaling to remarkably low powers. At this time, state-of-the-art devices achieve saturated nonlinear interactions with thousands of photons when driven by continuous-wave lasers, and further reductions in these energy requirements enabled by the use of ultrafast pulses may soon push nonlinear optics into the realm of single-photon nonlinearities. This tutorial reviews these recent developments in ultrafast nonlinear photonics, discusses design strategies for realizing few-photon nonlinear interactions, and presents a unified treatment of ultrafast quantum nonlinear optics using a framework that smoothly interpolates from classical behaviors to the few-photon scale. These emerging platforms for quantum optics fundamentally differ from typical realizations in cavity quantum electrodynamics due to the large number of coupled optical modes. Classically, multimode behaviors have been well studied in nonlinear optics, with famous examples including soliton formation and supercontinuum generation. In contrast, multimode quantum systems exhibit a far greater variety of behaviors, and yet closed-form solutions are even sparser than their classical counterparts. In developing a framework for ultrafast quantum optics, we identify what behaviors carry over from classical to quantum devices, what intuition must be abandoned, and what new opportunities exist at the intersection of ultrafast and quantum nonlinear optics. Although this article focuses on establishing connections between the classical and quantum behaviors of devices withχ⁽²⁾nonlinearities, the frameworks developed here are general and are readily extended to the description of dynamical processes based on third-orderχ⁽³⁾nonlinearities. 

The sensitivity of gravitational-wave detectors is limited by the mechanical loss associated with the amorphous coatings of the detectors’ mirrors. Amorphous silicon has higher refraction index and lower mechanical loss than current high-index coatings, but its optical absorption at the wavelength used for the detectors is at present large. The addition of hydrogen to the amorphous silicon network reduces both optical absorption and mechanical loss for films prepared under a range of conditions at all measured wavelengths and temperatures, with a particularly large effect on films grown at room temperature. The uptake of hydrogen is greatest in the films grown at room temperature, but still below 1.5 at.% H, which show an ultralow optical absorption (below 10 ppm) measured at 2000 nm for 500-nm-thick films. These results show that hydrogenation is a promising strategy to reduce both optical absorption and mechanical loss in amorphous silicon, and may enable fabrication of mirror coatings for gravitational-wave detectors with improved sensitivity. 

Abstract This article reviews recent progress in quasi-phasematched ${\chi }^{\left(2\right)}$nonlinear nanophotonics, with a particular focus on dispersion-engineered nonlinear interactions. Throughout this article, we establish design rules for the bandwidth and interaction lengths of various nonlinear processes, and provide examples for how these processes can be engineered in nanophotonic devices. In particular, we apply these rules towards the design of sources of non-classical light and show that dispersion-engineered devices can outperform their conventional counterparts. Examples include ultra-broadband optical parametric amplification as a resource for measurement-based quantum computation, dispersion-engineered spontaneous parametric downconversion as a source of separable biphotons, and synchronously pumped nonlinear resonators as a potential route towards single-photon nonlinearities. 

We establish a model for supercontinuum generation in dispersion-engineered χ(2) nanowaveguides based on saturated second-harmonic generation, and show that this process exhibits favorable scaling laws when compared to approaches based on χ(3) nonlinearities. 

Abstract We report on the development and extensive characterization of co-sputtered tantala–zirconia (Ta 2 O 5 -ZrO 2 ) thin films, with the goal to decrease coating Brownian noise in present and future gravitational-wave detectors. We tested a variety of sputtering processes of different energies and deposition rates, and we considered the effect of different values of cation ratio η = Zr/(Zr + Ta) and of post-deposition heat treatment temperature T a on the optical and mechanical properties of the films. Co-sputtered zirconia proved to be an efficient way to frustrate crystallization in tantala thin films, allowing for a substantial increase of the maximum annealing temperature and hence for a decrease of coating mechanical loss φ c . The lowest average coating loss was observed for an ion-beam sputtered sample with η = 0.485 ± 0.004 annealed at 800 °C, yielding φ ¯ c = 1.8 × 1 0 − 4 rad. All coating samples showed cracks after annealing. Although in principle our measurements are sensitive to such defects, we found no evidence that our results were affected. The issue could be solved, at least for ion-beam sputtered coatings, by decreasing heating and cooling rates down to 7 °C h −1 . While we observed as little optical absorption as in the coatings of current gravitational-wave interferometers (0.5 parts per million), further development will be needed to decrease light scattering and avoid the formation of defects upon annealing. 

Abstract The Gravitational-Wave Transient Catalog (GWTC) is a collection of short-duration (transient) gravitational-wave signals identified by the LIGO–Virgo–KAGRA Collaboration in gravitational-wave data produced by the eponymous detectors. The catalog provides information about the identified candidates, such as the arrival time and amplitude of the signal and properties of the signal’s source as inferred from the observational data. GWTC is the data release of this dataset, and version 4.0 extends the catalog to include observations made during the first part of the fourth LIGO–Virgo–KAGRA observing run up until 2024 January 31. This Letter marks an introduction to a collection of articles related to this version of the catalog, GWTC-4.0. The collection of articles accompanying the catalog provides documentation of the methods used to analyze the data, summaries of the catalog of events, observational measurements drawn from the population, and detailed discussions of selected candidates. 

Abstract We report the observation of gravitational waves from two binary black hole coalescences during the fourth observing run of the LIGO–Virgo–KAGRA detector network, GW241011 and GW241110. The sources of these two signals are characterized by rapid and precisely measured primary spins, nonnegligible spin–orbit misalignment, and unequal mass ratios between their constituent black holes. These properties are characteristic of binaries in which the more massive object was itself formed from a previous binary black hole merger and suggest that the sources of GW241011 and GW241110 may have formed in dense stellar environments in which repeated mergers can take place. As the third-loudest gravitational-wave event published to date, with a median network signal-to-noise ratio of 36.0, GW241011 furthermore yields stringent constraints on the Kerr nature of black holes, the multipolar structure of gravitational-wave generation, and the existence of ultralight bosons within the mass range 10⁻¹³–10⁻¹²eV. 

Abstract On 2023 November 23, the two LIGO observatories both detected GW231123, a gravitational-wave signal consistent with the merger of two black holes with masses $137_{-18}^{+23}{M}_{\odot }$and $101_{-50}^{+22}{M}_{\odot }$(90% credible intervals), at a luminosity distance of 0.7–4.1 Gpc, a redshift of $0.40_{-0.25}^{+0.27}$, and with a network signal-to-noise ratio of ∼20.7. Both black holes exhibit high spins— $0.90_{-0.19}^{+0.10}$and $0.80_{-0.52}^{+0.20}$, respectively. A massive black hole remnant is supported by an independent ringdown analysis. Some properties of GW231123 are subject to large systematic uncertainties, as indicated by differences in the inferred parameters between signal models. The primary black hole lies within or above the theorized mass gap where black holes between 60–130M_⊙should be rare, due to pair-instability mechanisms, while the secondary spans the gap. The observation of GW231123 therefore suggests the formation of black holes from channels beyond standard stellar collapse and that intermediate-mass black holes of mass ∼200M_⊙form through gravitational-wave-driven mergers.