Cooperative squeezing of internal and collective spins in an atomic ensemble

Abstract: Creating highly spin-squeezed states for quantum metrology surpassing the standard quantum limit is a topic of great interest. Spin squeezing has been achieved by either entangling different atoms in an ensemble, or by controlling the multi-level internal spin state of an atom. Here, we experimentally demonstrate combined internal and collective spin squeezing in a hot atomic ensemble with $\sim 10^{11}$ rubidium atoms. By synergistically combining these two types of squeezing and carefully aligning their squeezing quadratures, we have achieved a metrologically relevant spin squeezing of $-6.21\pm0.84$ dB, significantly outperforming the results obtained by utilizing either type of squeezing alone. Our approach provides a new perspective on fully harnessing the degrees of freedom inherent in quantum states of an atomic ensemble.