Quantum-fluctuation-driven coherent spin dynamics in small condensates

We have studied the quantum spin dynamics of small condensates of cold sodium atoms. For a condensate initially prepared in a mean-field ground state, we show that coherent spin dynamics is purely driven by quantum fluctuations of collective spin coordinates and can be tuned by quadratic Zeeman coupling and magnetization. This dynamics in small condensates can be probed in a high-finesse optical cavity where the temporal behaviors of the excitation spectra of a coupled condensate-photon system reveal the time evolution of populations of atoms at different hyperfine spin states.