Optical frequency combs, which emit pulses of light at discrete, equally spaced frequencies, are cornerstones of modern-day frequency metrology, precision spectroscopy, astronomical observations, ultrafast optics and quantum information. Chip-scale frequency combs, based on the Kerr and Raman nonlinearities in monolithic microresonators with ultrahigh quality factors, have recently led to progress in optical clockwork and observations of temporal cavity solitons. But the chromatic dispersion within a laser cavity, which determines the comb formation, is usually difficult to tune with an electric field, whether in microcavities or fibre cavities. Such electrically dynamic control could bridge optical frequency combs and optoelectronics, enabling diverse comb outputs in one resonator with fast and convenient tunability. Arising from its exceptional Fermi-Dirac tunability and ultrafast carrier mobility, graphene has a complex optical dispersion determined by its optical conductivity, which can be tuned through a gate voltage. This has brought about optoelectronic advances such as modulators, photodetectors and controllable plasmonics. Here we demonstrate the gated intracavity tunability of graphene-based optical frequency combs, by coupling the gate-tunable optical conductivity to a silicon nitride photonic microresonator, thus modulating its second- and higher-order chromatic dispersions by altering the Fermi level. Preserving cavity quality factors up to 10 in the graphene-based comb, we implement a dual-layer ion-gel-gated transistor to tune the Fermi level of graphene across the range 0.45-0.65 electronvolts, under single-volt-level control. We use this to produce charge-tunable primary comb lines from 2.3 terahertz to 7.2 terahertz, coherent Kerr frequency combs, controllable Cherenkov radiation and controllable soliton states, all in a single microcavity. We further demonstrate voltage-tunable transitions from periodic soliton crystals to crystals with defects, mapped by our ultrafast second-harmonic optical autocorrelation. This heterogeneous graphene microcavity, which combines single-atomic-layer nanoscience and ultrafast optoelectronics, will help to improve our understanding of dynamical frequency combs and ultrafast optics.

Vertically stacked van der Waals heterostructures constitute a promising platform for providing tailored band alignment with enhanced excitonic systems. Here we report the first observations of neutral and charged interlayer excitons in trilayer WSe2-MoSe2-WSe2 van der Waals heterostructures and their dynamics. The addition of a WSe2 layer in the trilayer leads to significantly higher photoluminescence quantum yields and tunable spectral resonance compared to its bilayer heterostructures at cryogenic temperatures. The observed enhancement in the photoluminescence quantum yield is due to significantly larger electronhole overlap and higher light absorbance in the trilayer heterostructure, supported via firstprinciple pseudopotential calculations based on spin-polarized density functional theory. We further uncover the temperature-and power-dependence, as well as time-resolved photoluminescence of the trilayer heterostructure interlayer neutral excitons and trions. Our study elucidates the prospects of manipulating light emission from interlayer excitons and designing atomic heterostructures from first-principles for optoelectronics. In two-dimensional (2D) materials, Coulomb-induced electronic states of excitons have been examined as a platform to understand many-body carrier-carrier interactions. These excitonic interactions dominate in layered materials due to quantum confinement and reduced dielectric screening. 2D atomic crystals of transition metal dichalcogenides (TMDs) have provided new opportunities in the studies of single-exciton single-photon interactions, spin-orbit coupling, ultrafast dynamics, and nanoelectronic devices [1-22]. Layer-by-layer stacking of TMDs-based van der Waals (vdWs) heterostructures has recently captured the attention of the scientific community where the tailored band alignment with diverse 2D materials can be achieved via advanced 2D growth and transfer techniques [23-28]. This has allowed the extension of indirect excitons with spatially separated electrons and holes from, for example, coupled quantum wells in GaAs/AlGaAs [29,30] to TMD vdW heterostructure bilayers, where they are referred to as interlayer excitons. These interlayer excitons exhibit rich physics in TMDs-based vdWs heterostructures due to the novel atomic granularity control through layer-by-layer stacking and the chiral properties of quantum electronic states [8,31,32]. Recently several studies observed that heterostructure interlayer excitons feature long lifetimes, spin-valley polarization by circularlypolarized pumping, near-unity valley polarization via large magnetic splitting, and charge transfer at the heterogeneous interfaces [32-45].Here we demonstrate TMDs-based vdWs heterostructures composed of a three-layer WSe2-MoSe2-WSe2 stack to achieve unique band alignment that promotes efficient interlayer radiative recombination. We first design the heterostructure through pseudopotential calculations based on Supplementary Information Enhanced interlayer neutral excitons and trions in trilayer van der Waals ...

Qudit entanglement is an indispensable resource for quantum information processing since increasing dimensionality provides a pathway to higher capacity and increased noise resilience in quantum communications, and cluster-state quantum computations. In continuous-variable time–frequency entanglement, encoding multiple qubits per photon is only limited by the frequency correlation bandwidth and detection timing jitter. Here, we focus on the discrete-variable time–frequency entanglement in a biphoton frequency comb (BFC), generating by filtering the signal and idler outputs with a fiber Fabry–Pérot cavity with 45.32 GHz free-spectral range (FSR) and 1.56 GHz full-width-at-half-maximum (FWHM) from a continuous-wave (cw)-pumped type-II spontaneous parametric downconverter (SPDC). We generate a BFC whose time-binned/frequency-binned Hilbert space dimensionality is at least 324, based on the assumption of a pure state. Such BFC’s dimensionality doubles up to 648, after combining with its post-selected polarization entanglement, indicating a potential 6.28 bits/photon classical-information capacity. The BFC exhibits recurring Hong–Ou–Mandel (HOM) dips over 61 time bins with a maximum visibility of 98.4% without correction for accidental coincidences. In a post-selected measurement, it violates the Clauser–Horne–Shimony–Holt (CHSH) inequality for polarization entanglement by up to 18.5 standard deviations with an S-parameter of up to 2.771. It has Franson interference recurrences in 16 time bins with a maximum visibility of 96.1% without correction for accidental coincidences. From the zeroth- to the third-order Franson interference, we infer an entanglement of formation (Eof) up to 1.89 ± 0.03 ebits—where 2 ebits is the maximal entanglement for a 4 × 4 dimensional biphoton—as a lower bound on the 61 time-bin BFC’s high-dimensional entanglement. To further characterize time-binned/frequency-binned BFCs we obtain Schmidt mode decompositions of BFCs generated using cavities with 45.32, 15.15, and 5.03 GHz FSRs. These decompositions confirm the time–frequency scaling from Fourier-transform duality. Moreover, we present the theory of conjugate Franson interferometry—because it is characterized by the state’s joint-temporal intensity (JTI)—which can further help to distinguish between pure-state BFC and mixed state entangled frequency pairs, although the experimental implementation is challenging and not yet available. In summary, our BFC serves as a platform for high-dimensional quantum information processing and high-dimensional quantum key distribution (QKD).