Spin Squeezing and Light Entanglement in Coherent Population Trapping

We show that strong squeezing and entanglement can be generated at the output of a cavity containing atoms interacting with two fields in a coherent population trapping situation, on account of a nonlinear Faraday effect experienced by the fields close to a dark-state resonance in a cavity. Moreover, the cavity provides a feedback mechanism allowing to reduce the quantum fluctuations of the ground state spin, resulting in strong steady state spin squeezing