Quantum Spin Squeezing Enhanced by a Critical Exceptional Point

Critical exceptional points (CEPs) are non-equilibrium critical points, where multiple collective excitation modes coalesce. We show that, in a broad class of collective-spin models possessing a Liouvillian $\mathcal{PT}$ symmetry, the phase transition point associated with PT symmetry breaking coincides with a CEP. Furthermore, we reveal that the CEP generates steady-state entanglement via strong spin squeezing. 

This proof follows from the covariance-matrix Lyapunov equation: at the CEP, the smallest eigenvalue of the rotated covariance in the plane orthogonal to the mean spin vanishes in the thermodynamic limit $S\to\infty$.