Quantum frequency combs from chip-scale integrated sources are promising candidates for scalable and robust quantum information processing (QIP). However, to use these quantum combs for frequency domain QIP, demonstration of entanglement in the frequency basis, showing that the entangled photons are in a coherent superposition of multiple frequency bins, is required. We present a verification of qubit and qutrit frequency-bin entanglement using an on-chip quantum frequency comb with 40 mode pairs, through a two-photon interference measurement that is based on electro-optic phase modulation. Our demonstrations provide an important contribution in establishing integrated optical microresonators as a source for high-dimensional frequency-bin encoded quantum computing, as well as dense quantum key distribution.

Simultaneous Kerr comb formation and second-harmonic generation with on-chip microresonators can greatly facilitate comb self-referencing for optical clocks and frequency metrology. Moreover, the presence of both second- and third-order nonlinearities results in complex cavity dynamics that is of high scientific interest but is still far from being well-understood. Here, we demonstrate that the interaction between the fundamental and the second-harmonic waves can provide an entirely new way of phase matching for four-wave mixing in optical microresonators, enabling the generation of optical frequency combs in the normal dispersion regime under conditions where comb creation is ordinarily prohibited. We derive new coupled time-domain mean-field equations and obtain simulation results showing good qualitative agreement with our experimental observations. Our findings provide a novel way of overcoming the dispersion limit for simultaneous Kerr comb formation and second-harmonic generation, which might prove to be especially important in the near-visible to visible range where several atomic transitions commonly used for the stabilization of optical clocks are located and where the large normal material dispersion is likely to dominate.

Optical resonators with high quality factors (Qs) are promising for a variety of applications due to the enhanced nonlinearity and increased photonic density of states at resonances. In particular, frequency combs (FCs) can be generated through four-wave mixing in high-Q microresonators made from Kerr nonlinear materials such as silica, silicon nitride, magnesium fluoride, and calcium fluoride. These devices have potential for on-chip frequency metrology and high-resolution spectroscopy, high-bandwidth radiofrequency information processing, and high-data-rate telecommunications. Silicon nitride microresonators are attractive due to their compatibility with integrated circuit manufacturing; they can be cladded with silica for long-term stable yet tunable operation, and allow multiple resonators to be coupled together to achieve novel functionalities. Despite previous demonstrations of high-Q silicon nitride resonators, FC generation using silicon nitride microresonator chips still requires pump power significantly higher than those in whispering gallery mode resonators made from silica, magnesium, and calcium fluorides, which all have shown resonator Qs between 0.1 and 100 billion. Here, we report on a fabrication procedure that leads to the demonstration of "finger-shaped" Si 3 N 4 microresonators with intrinsic Qs up to 17 million at a free spectrum range (FSR) of 24.7 GHz that are suitable for telecommunication and microwave photonics applications. The frequency comb onset power can be as low as 2.36 mW and broad, single FSR combs can be generated at a low pump power of 24 mW, both within reach of on-chip semiconductor lasers. Our demonstration is an important step toward a fully integrated on-chip FC source. Kerr comb generation in microresonators starts when an external continuous-wave (CW) laser is tuned into a cavity resonance; this causes intracavity power to build, which enables additional cavity modes to oscillate through nonlinear wave mixing [10]. FC formation has now been demonstrated in a variety of Kerr nonlinear materials such as silica [9,14-18], silicon nitride (Si 3 N 4 ) [19-21], aluminum nitride [22], CaF 2 [23], and MgF 2 [24]. Recently, dissipative Kerr solitons have also been demonstrated in MgF 2 and Si 3 N 4 optical microresonators [25,26]. Out of these materials, stoichiometric Si 3 N 4 has distinctive 2334-2536/16/111171-10 Journal

We present, experimentally and numerically, the observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in a high-Q SiN microresonator. Breather solitons can be excited by increasing the pump power at a relatively small pump phase detuning in microresonators. Out of phase power evolution is observed for groups of comb lines around the center of the spectrum compared to groups of lines in the spectral wings. The evolution of the power spectrum is not symmetric with respect to the spectrum center. Numerical simulations based on the generalized Lugiato-Lefever equation are in good agreement with the experimental results and unveil the role of stimulated Raman scattering in the symmetry breaking of the power spectrum evolution. Our results shows that optical microresonators can be exploited as a powerful platform for the exploration of soliton dynamics.The Fermi-Pasta-Ulam (FPU) recurrence was first raised by Fermi and his colleagues in the 1950s [1]. In a numerical simulation of string oscillation with nonlinear coupling between different modes to test thermalization theory, they found at a certain point the energy will return to the fundamentally excited mode, rather than distributing homogenously among different modes. This discovery triggered the rigorous investigation on plasma physics by Zubusky and Kruskal [2], which led to the discovery of solitons. Solitons and their related theory have revolutionized the research in diverse arenas, including fluid dynamics [3], optics [4,5], Bose-Eistein condensation [6,7].In optics, the FPU recurrence was first demonstrated based on the modulation instability (MI) in optical fibers [8]. As a feature of the FPU recurrence, the powers of the pump mode and the signal mode in MI evolves periodically with a phase delay of π. The collision between solitons in fibers also facilitated the observation of FPU recurrence in an active cavity [9]. Furthermore, optical breathers, e.g., the Akhmediev breather (AB) in the nonlinear schrödinger equation (NLSE) [10][11][12], are an important manifestation of FPU recurrence. Since collisions between breathers and solitons can result in optical rogue waves [13][14][15], studying FPU recurrence and the control of the transition between solitons and breathers may contribute to the understanding of optical rogue waves.Recently, maturity in the fabrication of high-Q microresonators [16] has fueled rapid progress on Kerr frequency comb generation [17][18][19][20][21][22]. In the frequency domain, microresonators based frequency comb synthesis has promising applications in optical clock [23], optical arbitrary waveform generation [24], and microwave photonics [25,26] etc. In the time domain, microresonators provide a new and important approach to realize optical solitons [21,[27][28][29][30]. Different from mode-locked lasers, passive microresonators have no active gain or saturable absorber, making them free from the influence of the complex gain dynamics. Hence, soliton generation in microresonators can exhibit excellent predicta...