Spin squeezing of $10^{11}$ atoms

Atomic ensemble with large number of quantum-correlated particles is desirable for precision measurement. As a type of such quantum state, spin squeezed state (SSS) has been pursued in both cold atom and warm vapor cell systems with the largest atom number $10^{8}$. We report experimental preparation of a SSS in a paraffin-coated macroscopic vapor cell in free space, containing $10^{11}$ $^{87}\text{Rb}$ atoms, by stroboscopic quantum non-demolition measurement and using adiabatic pulse control and motional everaging. We observed $2.38\pm0.23~\text{dB}$ noise reduction, and $1.31\pm0.23~\text{dB}$ spin squeezing \emph{below coherent spin state}. Our result present the highest angular resolution on the Bloch sphere in all SSS up to date, and will open possibilities for quantum metrology and control in large entangled atomic ensembles,with techniques generalizable to other systems such as trapped ions and mechanical oscillators.