Spin squeezing in driven, superradiant gas: an integrated method to describe cooperative effects

Driving a superradiant system can produce spin squeezing. To show this, we introduce an integrated method to describe cooperative radiation in many-body systems, and apply the method to an optically dense gas of two-level atoms. For a non-driven system, physical observables such as superradiant decay rate and the many-body induced broadening scale with the optical depth of the sample. When the gas is driven by an external field, steady states are found, which give rise to spin squeezing in the atoms. Different optical depths and driving strengths are examined in order to find the maximum squeezed state.