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

We show that bifurcation exists not only in the <i>I</i> channel but also in the <i>Q</i> channel, noting that the in-phase part <i>I</i> and the quadrature part <i>Q</i> 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>I</i>-bifurcation and <i>Q</i>-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>I</i> and <i>Q</i> are coupled through the Kerr effect, where <i>I</i> changes <i>Q</i> and <i>Q</i> changes <i>I.</i> This simultaneous <i>I/Q</i>-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>I/Q</i>-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.