We propose a critical dissipaive quantum metrology schemes for single
parameter estimation which are based on a quantum probe consisting of
coherently driven ensemble of N spin-1/2 particles under the effect of
squeezed, collective spin decay. The collective spin system exhibits a
dissipative phase transition between thermal and ferromagnetic phases, which is
characterized with nonanalytical behavior of the spin observables. We show that
thanks to the dissipative phase transition the sensitivity of the parameter
estimation can be significantly enhanced. Furthermore, we show that our steady
state is an entangled spin squeezed state which allow to perform parameter
estimation with sub shot-noise limited measurement uncertainty.Comment: 7 pages, 5 figure