Quantum correlation in degenerate optical parametric oscillators with mutual injections

We theoretically and numerically study the quantum dynamics of two degenerate optical parametric oscillators with mutual injections. The cavity mode in the optical coupling path between the two oscillator facets is explicitly considered. Stochastic equations for the oscillators and mutual injection path based on the positive $P$ representation are derived. The system of two gradually pumped oscillators with out-of-phase mutual injections is simulated, and its quantum state is investigated. When the incoherent loss of the oscillators other than the mutual injections is small, the squeezed quadratic amplitudes $\hat{p}$ in the oscillators are positively correlated near the oscillation threshold. It indicates finite quantum correlation, estimated via Gaussian quantum discord, and the entanglement between the intracavity subharmonic fields. When the loss in the injection path is low, each oscillator around the phase transition point forms macroscopic superposition even under a small pump noise. It suggests that the squeezed field stored in the low-loss injection path weakens the decoherence in the oscillators.Comment: 14 pages, 9 figures; v3: author added, minor updat

Valence-band structure of ferromagnetic semiconductor (InGaMn)As

To clarify the whole picture of the valence-band structures of prototype ferromagnetic semiconductors (III,Mn)As (III: In and Ga), we perform systematic experiments of the resonant tunneling spectroscopy on [(In_0.53Ga_0.47)_1-x Mn_x]As (x=0.06-0.15) and In_0.87Mn_0.13As grown on AlAs/ In_0.53Ga_0.47As:Be/ p+InP(001). We show that the valence band of InGaMnAs almost remains unchanged from that of the host semiconductor InGaAs, that the Fermi level exists in the band gap, and that the p-d exchange splitting in the valence band is negligibly small in (InGaMn)As. In the In0.87Mn0.13As sample, although the resonant peaks are very weak due to the large strain induced by the lattice mismatch between InP and InMnAs, our results also indicate that the Fermi level exists in the band gap and that the p-d exchange splitting in the valence band is negligibly small. These results are quite similar to those of GaMnAs obtained by the same method, meaning that there are no holes in the valence band, and that the impurity-band holes dominate the transport and magnetism both in the InGaMnAs and In_0.87Mn_0.13As films. This band picture of (III,Mn)As is remarkably different from that of II-VI-based diluted magnetic semiconductors.Comment: 21 pages, 6 figures, accepted for publication in Phys. Rev.

Network of Time-Multiplexed Optical Parametric Oscillators as a Coherent Ising Machine

Finding the ground states of the Ising Hamiltonian [1] 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 Hamiltonian [2-6]. Here we report a novel 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 injections [7]. 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 programed the smallest non-deterministic polynomial time (NP)- hard Ising problem on the machine, and in 1000 runs of the machine no computational error was detected

Improved design and experimental demonstration of ultrahigh-Q C6{}_\text{6}-symmetric H1 hexapole photonic crystal nanocavities

An H1 photonic crystal nanocavity 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 nanocavity with a $Q$ factor exceeding $10^8$. We achieved such extremely high-$Q$ conditions by designing only four structural modulation parameters thanks to the ${\rm C_{6}}$ symmetry of the mode, despite the need of more complicated optimizations for many other nanocavities. The fabricated silicon photonic crystal nanocavities 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 cavities with loaded $Q$ factors over one million ($1.2 \times 10^6$ maximum). 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 $4.5 \times 10^8$, which is two orders of magnitude higher than in the previous studies. Our work elevates the performance of the H1 nanocavity to the ultrahigh-$Q$ level and paves the way for its large-scale arrays with unconventional functionalities

光パラメトリック発振器を用いたコヒーレント計算機の量子論及び実装実験

学位の種別: 課程博士審査委員会委員 : (主査)東京大学准教授 田浦 健次朗, 東京大学教授 安達 淳, 東京大学教授 大津 元一, 東京大学教授 菊池 和朗, 東京大学教授 合原 一幸, 科学技術振興機構プログラムマネージャー 山本 喜久University of Tokyo(東京大学