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We analyze the generation of spin-squeezed states by coupling three-levelatoms to an optical cavity and continuously measuring the cavity transmissionin order to monitor the evolution of the atomic ensemble. Using analyticaltreatment and microscopic simulations of the dynamics, we show that one canachieve significant spin squeezing even without the continuous feedback that isproposed in optimal approaches. In the adiabatic cavity removal approximationand large number of atoms $N$ limit, we find the scaling exponents $N^{-2/3}$for spin squeezing and $N^{-1/3}$ for the corresponding protocol duration,which are crucially impacted by the collective Bloch sphere curvature. Withfull simulations, we characterize how spin-squeezing generation depends on thesystem parameters and departs from the bad cavity regime, by gradually mixingwith cavity-filling dynamics until metrological advantage is lost. Finally, wediscuss the relevance of this spin-squeezing protocol to state-of-the-artoptical clocks.

Analysis of spin-squeezing generation in cavity-coupled atomic ensembles with continuous measurements