Scalable spin squeezing using multilevel atoms in an optical cavity

Ultracold atoms in optical cavity setups are promising candidates for the creation of metrologically useful entangled states. Up to date, however, most of the effort has been restricted to atomic systems that use two relevant internal levels to encode a spin-1/2 degree of freedom. Here, we report on expanded opportunities for entanglement generation offered by multilevel atoms in cavities using two complementary protocols. In the first, we describe how to prepare two-mode squeezed states via near-unitary cavity-mediated spin-exchange interactions between atoms featuring four relevant internal levels. We find that the squeezing is scalable and robust to intrinsic experimental decoherence and can be easily exploited for metrology by mapping a conventional Ramsey sequence to our four-level system. In the second protocol, we demonstrate how dissipative relaxation to a dark state in multilevel atoms can enable the preparation of entangled states with up to four different squeezed quadratures, and how the squeezing is scalable. These ideas open new directions for quantum-enhanced sensing through the manipulation of cavity mediated interactions in multi-level atoms.