Figure 2 : Classical synchronization indicates quantum squeezing and number entanglement.

From: Classical synchronization indicates persistent entanglement in isolated quantum systems

Figure 2

We consider two coupled oscillators, respectively, two quantum modes with variable coupling strength K. (a) The fixed points of the Kuramoto model (4). A stable (solid) and an unstable (dashed) fixed point emerge in a saddle node bifurcation at Kc=|ω|/2. (b) The temporal minimum of the squeezing parameter (refs 13, 19) as a function of the coupling strength K. For U=0 (solid line) the transition to quantum squeezing is located at the critical coupling for classical synchronization, Kc=ω/2. The on-site interaction term U suppresses squeezing such that the transition occurs at a higher value of K for U=0.4/N (dashed line). (c) Long-time average of the entanglement parameter W12 as a function of the coupling strength K. Persistent entanglement W12>0 (see ref. 50 and Methods) emerges with classical synchronization at K>Kc=ω/2, independent of U. The initial quantum state is a two-mode coherent state |z, Δφ〉=|0, π/2〉 with N=100 and ω=1 in all cases.