Cooperative squeezing of internal and collective spins in an atomic ensemble

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 multilevel 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.