Optical Devices based on Limit Cycles and Amplification in Semiconductor Optical Cavities

At strong pump powers, a semiconductor optical cavity passes through a Hopf bifurcation and undergoes self-oscillation. We simulate this device using semiclassical Langevin equations and assess the effect of quantum fluctuations on the dynamics. Below threshold, the cavity acts as a phase-insensitive linear amplifier, with noise $\sim 5\times$ larger than the Caves bound. Above threshold, the limit cycle acts as an analog memory, and the phase diffusion is $\sim 10\times$ larger than the bound set by the standard quantum limit. We also simulate entrainment of this oscillator and propose an optical Ising machine and classical CNOT gate based on the effect.