Improved design and experimental demonstration of ultrahigh-Q C6-symmetric H1 hexapole photonic crystal nanocavities.

An H1 photonic crystal nanocavity (PCN) is based on a single point defect and has eigenmodes with a variety of symmetric features. Thus, it is a promising building block for photonic tight-binding lattice systems that can be used in studies on condensed matter, non-Hermitian and topological physics. However, improving its radiative quality (Q) factor has been considered challenging. Here, we report the design of a hexapole mode of an H1 PCN with a Q factor exceeding 108. We achieved such extremely high-Q conditions by varying only four structural modulation parameters thanks to the C6 symmetry of the mode, despite the need of more complicated optimizations for many other PCNs. Our fabricated silicon H1 PCNs exhibited a systematic change in their resonant wavelengths depending on the spatial shift of the air holes in units of 1 nm. Out of 26 such samples, we found eight PCNs with loaded Q factors over one million. The best sample was of a measured Q factor of 1.2 × 106, and its intrinsic Q factor was estimated to be 1.5 × 106. We examined the difference between the theoretical and experimental performances by conducting a simulation of systems with input and output waveguides and with randomly distributed radii of air holes. Automated optimization using the same design parameters further increased the theoretical Q factor by up to 4.5 × 108, which is two orders of magnitude higher than in the previous studies. We clarify that this striking improvement of the Q factor was enabled by the gradual variation in effective optical confinement potential, which was missing in our former design. Our work elevates the performance of the H1 PCN to the ultrahigh-Q level and paves the way for its large-scale arrays with unconventional functionalities.

Emulating the local Kuramoto model with an injection-locked photonic crystal laser array.

The Kuramoto model is a mathematical model for describing the collective synchronization phenomena of coupled oscillators. We theoretically demonstrate that an array of coupled photonic crystal lasers emulates the Kuramoto model with non-delayed nearest-neighbor coupling (the local Kuramoto model). Our novel strategy employs indirect coupling between lasers via additional cold cavities. By installing cold cavities between laser cavities, we avoid the strong coupling of lasers and realize ideal mutual injection-locking with effective non-delayed dissipative coupling. First, after discussing the limit cycle interpretation of laser oscillation, we demonstrate the synchronization of two indirectly coupled lasers by numerically simulating coupled-mode equations. Second, by performing a phase reduction analysis, we show that laser dynamics in the proposed device can be mapped to the local Kuramoto model. Finally, we briefly demonstrate that a chain of indirectly coupled photonic crystal lasers actually emulates the one-dimensional local Kuramoto chain. We also argue that our proposed structure, which consists of periodically aligned cold cavities and laser cavities, will best be realized by using state-of-the-art buried multiple quantum well photonic crystals.

Photonic Topological Insulating Phase Induced Solely by Gain and Loss.

We reveal a one-dimensional topological insulating phase induced solely by gain and loss control in non-Hermitian optical lattices. The system comprises units of four uniformly coupled cavities, where the successive two have loss; the others experience gain, and they are balanced under two magnitudes. The gain and loss parts are effectively dimerized, and a bulk band gap, topological transition, midgap topological edge, and interface states in finite systems can all be achieved by controlled pumping. We also clarify non-Hermitian topological invariants and edge states in gapless conditions.

A 16-bit Coherent Ising Machine for One-Dimensional Ring and Cubic Graph Problems.

Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to finding a ground state of the Ising Hamiltonian, thus various physical systems have been studied to emulate and solve this Ising problem. Recently, networks of mutually injected optical oscillators, called coherent Ising machines, have been developed as promising solvers for the problem, benefiting from programmability, scalability and room temperature operation. Here, we report a 16-bit coherent Ising machine based on a network of time-division-multiplexed femtosecond degenerate optical parametric oscillators. The system experimentally gives more than 99.6% of success rates for one-dimensional Ising ring and nondeterministic polynomial-time (NP) hard instances. The experimental and numerical results indicate that gradual pumping of the network combined with multiple spectral and temporal modes of the femtosecond pulses can improve the computational performance of the Ising machine, offering a new path for tackling larger and more complex instances.

Binary phase oscillation of two mutually coupled semiconductor lasers.

A two-site Ising model is implemented as an injection-locked laser network consisting of a single master laser and two mutually coupled slave lasers. We observed ferromagnetic and antiferromagnetic orders in the in-phase and out-of-phase couplings between the two slave lasers. Their phase difference is locked to either 0 or π even if the coupling path is continuously modulated. The system automatically selects the oscillation frequency to satisfy the in-phase or out-of-phase coupling condition, when the mutual coupling dominates over the injection-locking by the master laser.

Mapping of Ising models onto injection-locked laser systems.

We propose a mapping protocol to implement Ising models in injection-locked laser systems. The proposed scheme is based on optical coherent feedback and can be potentially applied for large-scale Ising problems.