Coherent population trapping for reservoir engineering and spin squeezing

Spin squeezing has important applications in the field of quantum metrology and quantum information processing. Here we propose that coherent population trapping is well suitable for establishing cavity dissipation mechanism and generating a spin-squeezed state. An ensemble of $N$ double $\mathrm{\Lambda }$-type atoms is placed inside the two-mode optical cavity, where one $\mathrm{\Lambda }$ subsystem is driven resonantly by two strong control fields to form a dark resonance and the other $\mathrm{\Lambda }$ subsystem is coupled by two cavity vacuum fields and two external fields with large detunings. Due to the dark resonance, the atoms are trapped in a dark state and one has the maximal coherence between the two ground states. Two double off-resonance stimulated Raman scattering interactions are induced between fields and dressed atoms to establish a dissipative quantum dynamical process based on a collective cavity reservoir. As a result, strong stable spin squeezing is generated, which is verified by our numerical and analytical results.