Quantum Spin Squeezing Enhanced by Critical Exceptional Points

Critical exceptional points (CEPs) are nonequilibrium critical points in open many-body systems at which multiple collective excitation modes coalesce. CEPs are known to amplify classical fluctuations, but their effect on genuinely \textit{quantum} fluctuations remains unclear. Here, we show that dissipative collective-spin systems hosting CEPs exhibit parametrically enhanced steady-state \textit{quantum} spin squeezing. Close to the CEP, the optimally squeezed variance scales as $|Z|$, whereas the anti-squeezed variance diverges as $|Z|^{-1}$, with $Z$ the dimensionless order parameter. Importantly, the anti-squeezed fluctuation direction asymptotically aligns with the coalescing eigenvector of the stability matrix, reflecting the defective nature of the CEP dynamics. These scalings are robust against dephasing channels generated by spin components orthogonal to the coalesced critical collective mode. Our results identify CEPs as a route to engineering steady-state anisotropic quantum fluctuations and correlations in driven-dissipative platforms.