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

Cascaded half-harmonic generation of femtosecond frequency combs in mid-IR

For the growing demand of frequency combs in mid-infrared (mid-IR), known as the "molecular fingerprint" region of the spectrum [1], down conversion of near-IR frequency combs through half- harmonic generation offers numerous benefits including high conversion efficiency and intrinsic phase and frequency locking to the near-IR pump [2]. Hence cascaded half-harmonic generation promises a simple path towards extending the wavelength coverage of stable frequency combs. Here, we report a two-octave down-conversion of a frequency comb around 1 {\mu}m through cascaded half-harmonic generation with ~64% efficiency in the first stage, and ~18% in the second stage. We obtain broadband intrinsically-frequency-locked frequency combs with ~50-fs pulses at ~2 {\mu}m and ~110-fs pulses at ~4 {\mu}m. These results indicate the effectiveness of half-harmonic generation as a universal tool for efficient phase- and frequency-locked down-conversion, which can be beneficial for numerous applications requiring long-wavelength coherent sources

A Coherent Ising Machine Based On Degenerate Optical Parametric Oscillators

A degenerate optical parametric oscillator network is proposed to solve the NP-hard problem of finding a ground state of the Ising model. The underlying operating mechanism originates from the bistable output phase of each oscillator and the inherent preference of the network in selecting oscillation modes with the minimum photon decay rate. Computational experiments are performed on all instances reducible to the NP-hard MAX-CUT problems on cubic graphs of order up to 20. The numerical results reasonably suggest the effectiveness of the proposed network.Comment: 18 pages, 6 figure

Design of a Single-Feed Dual-Band Dual-Polarized Printed Microstrip Antenna Using a Boolean Particle Swarm Optimization

A novel dual-frequency dual-linear-polarization printed antenna element benefiting from a single-feed single-layer structure is introduced in this paper. The Boolean particle swarm optimization algorithm in conjunction with the method of moments (MoM) is employed to optimize the geometry of the antenna after considering three objectives: cross polarization, return loss, and boresight direction in both bands. A fuzzy-logic based ordered weighted averaging operator allows us to efficiently implement the multi-objective optimization technique. Prototypes of the optimized designs have been fabricated and tested. The measured results show excellent performance with more than 15 dB of return loss and 10 dB of cross polarization in both frequency bands of operation, i.e., 12 and 14 GHz. A gain of 4.8 dBi has been measured for both frequency bands

Realizing spin-Hamiltonians in nanoscale active photonic lattices

Spin models arise in the microscopic description of magnetic materials and have been recently used to map certain classes of optimization problems involving large degrees of freedom. In this regard, various optical implementations of such Hamiltonians have been demonstrated to quickly converge to the global minimum in the energy landscape. Yet, so far, an integrated nanophotonic platform capable of emulating complex magnetic materials is still missing. Here, we show that the cooperative interplay among vectorial electromagnetic modes in coupled metallic nanolasers can be utilized to implement certain types of spin Hamiltonians. Depending on the topology/geometry of the arrays, these structures can be governed by a classical XY Hamiltonian that exhibits ferromagnetic and antiferromagnetic couplings, as well as geometrical frustration. Our results pave the way towards a scalable nanophotonic platform to study spin exchange interactions and could address a variety of optimization problems

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