TL;DR: In this article, a network of four degenerate optical parametric oscillators (OPOs) is employed to find the ground state of the Ising Hamiltonian, and a small non-deterministic polynomial time-hard problem is solved on a 4-OPO Ising machine.
Abstract: A network of four degenerate optical parametric oscillators (OPOs) is employed to find the ground state of the Ising Hamiltonian. The good performance of the network reveals the potential of OPOs for many similar problems. Finding the ground states of the Ising Hamiltonian1 maps to various combinatorial optimization problems in biology, medicine, wireless communications, artificial intelligence and social network. So far, no efficient classical and quantum algorithm is known for these problems and intensive research is focused on creating physical systems—Ising machines—capable of finding the absolute or approximate ground states of the Ising Hamiltonian2,3,4,5,6. Here, we report an Ising machine using a network of degenerate optical parametric oscillators (OPOs). Spins are represented with above-threshold binary phases of the OPOs and the Ising couplings are realized by mutual injections7. The network is implemented in a single OPO ring cavity with multiple trains of femtosecond pulses and configurable mutual couplings, and operates at room temperature. We programmed a small non-deterministic polynomial time-hard problem on a 4-OPO Ising machine and in 1,000 runs no computational error was detected.
TL;DR: In this article, the authors describe the current state of OPO research, including OPOs pumped by high-repetition-rate (>30 kHz) Q-switched diode-pumped solid state lasers, and CW singly resonant OPOs with >3W output power in the 3-4/spl mu/m range.
Abstract: Since their introduction two years ago, quasi-phase-matched (QPM) optical parametric oscillators (OPOs) have moved into the mainstream of OPO research. This has been made possible by continuing improvements and availability of the microstructured nonlinear material periodically poled lithium niobate (PPLN). Demonstrations of PPLN OPOs now span the range of pulse formats and power levels. The most significant area of development is low-peak-power devices where operation with conventional materials is difficult. In this paper, we describe the current state of this research, including OPOs pumped by high-repetition-rate (>30 kHz) Q-switched diode-pumped solid state lasers, and CW singly resonant OPOs with >3-W output power in the 3-4-/spl mu/m range.
TL;DR: In this article, an on-chip lithium niobate optical parametric oscillator at the telecom wavelengths using a quasi-phase-matched, high-quality microring resonator, whose threshold power (∼30µW) is 400 times lower than that in previous integrated photonics platforms.
Abstract: Materials with strong second-order (χ(2)) optical nonlinearity, especially lithium niobate, play a critical role in building optical parametric oscillators (OPOs). However, chip-scale integration of low-loss χ(2) materials remains challenging and limits the threshold power of on-chip χ(2) OPO. Here we report an on-chip lithium niobate optical parametric oscillator at the telecom wavelengths using a quasi-phase-matched, high-quality microring resonator, whose threshold power (∼30µW) is 400 times lower than that in previous χ(2) integrated photonics platforms. An on-chip power conversion efficiency of 11% is obtained from pump to signal and idler fields at a pump power of 93 µW. The OPO wavelength tuning is achieved by varying the pump frequency and chip temperature. With the lowest power threshold among all on-chip OPOs demonstrated so far, as well as advantages including high conversion efficiency, flexibility in quasi-phase-matching, and device scalability, the thin-film lithium niobate OPO opens new opportunities for chip-based tunable classical and quantum light sources and provides a potential platform for realizing photonic neural networks.
TL;DR: In this article, phase-matched AlN microring resonators were used to demonstrate low-threshold parametric oscillation in the telecom infrared band with an on-chip efficiency up to 17% and milliwatt-level output power.
Abstract: Optical parametric oscillators (OPOs) have been widely used for decades as tunable, narrow-linewidth, and coherent light sources for reaching long wavelengths and are attractive for applications such as quantum random number generation and Ising machines. To date, waveguide-based OPOs have suffered from relatively high thresholds on the order of hundreds of milliwatts. With the advance in integrated photonic techniques demonstrated by high-efficiency second-harmonic generation in aluminum nitride (AlN) photonic microring resonators, highly compact and nanophotonic implementation of parametric oscillation is feasible. Here we employ phase-matched AlN microring resonators to demonstrate low-threshold parametric oscillation in the telecom infrared band with an on-chip efficiency up to 17% and milliwatt-level output power. A broad phase-matching window is observed, enabling tunable generation of signal and idler pairs over a 180 nm bandwidth across the C band. This result establishes an important milestone in integrated nonlinear optics and paves the way towards chip-based quantum light sources and tunable, coherent radiation for spectroscopy and chemical sensing.
TL;DR: It is demonstrated that the two OPOs show stable spatial and temporal interference and are mutually locked in frequency and in phase and deterministically choose between the two frequency states corresponding to the two sets of modes shifted with respect to each other by half of the laser pulse repetition rate.
Abstract: We study coherence properties of a χ(2) optical parametric oscillator (OPO), which produces 2/3-octave-wide spectrum centered at the subharmonic (3120 nm) of the femtosecond pump laser. Our method consists of interfering the outputs of two identical, but independent OPOs pumped by the same laser. We demonstrate that the two OPOs show stable spatial and temporal interference and are mutually locked in frequency and in phase. By observing a collective heterodyne beat signal between the two OPOs we show that one can deterministically choose, by cavity length adjustment, between the two frequency states corresponding to the two sets of modes shifted with respect to each other by half of the laser pulse repetition rate. Moreover, we observe that the existence of two opposite phase states, a known common feature of a parametrically driven n = 2 subharmonic oscillator, reveals itself in our experiment as a common phase, 0 or π, being established through the whole set of some 300 thousand longitudinal modes.