Retrieval of cavity-generated atomic spin squeezing after free-space release

We demonstrate that releasing atoms into free space from an optical lattice does not deteriorate cavity-generated spin squeezing for metrological purposes. In this work, an ensemble of $500\phantom{\rule{0.16em}{0ex}}000$ spin-squeezed atoms in a high-finesse optical cavity with near-uniform atom-cavity coupling is prepared, released into free space, recaptured in the cavity, and probed. Up to $\ensuremath{\sim}10$ dB of metrologically relevant squeezing is retrieved for $700\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{s}$ free-fall times, and decaying levels of squeezing are realized for up to 3 ms free-fall times. The degradation of squeezing results from loss of atom-cavity coupling homogeneity between the initial squeezed state generation and final collective state readout. A theoretical model is developed to quantify this degradation and this model is experimentally validated.