I-, Q-, and I/Q-simultaneously bifurcated photonic Ising machines with Kerr nonlinearity

We show that bifurcation exists not only in the I channel but also in the Q channel, noting that the in-phase part I and the quadrature part Q of coherent quadrature amplitude modulation (QAM) communication are simply phase-shifted by 90 degrees from each other. To realize bifurcation in the quadrature, it is important to add an optical phase shift of π/2 and feed it back to the fiber loop as an imaginary amplitude. Then, we report that the bifurcation switching of I-bifurcation and Q-bifurcation occurs for different amounts of nonlinear phase rotation where cos ϕ_NL and sin ϕ_NL become zero, respectively. We also show that stable bifurcation exists where I and Q are coupled through the Kerr effect, where I changes Q and Q changes I. This simultaneous I/Q-bifurcation can be used to maintain a constant intensity and therefore, a constant phase when both are converging to a stable bifurcation. This phenomenon can be used to realize a complex bifurcation machine, i.e., an I/Q-bifurcated photonic Ising machine, where a stable max-cut calculation without a cut-value dip can be performed even in the presence of the Kerr effect. We also report that a new phenomenon named "bifurcation splitting" exists when the Kerr effect has a strong influence on a 50 km-long single fiber-loop propagation.