Sensitive detection of spin flip using spin-mixing dynamics of $^{87}$Rb Bose-Einstein condensates

We revisit experimentally the spin-mixing dynamics in $^{87}$Rb spinor Bose-Einstein condensates, starting with all atoms in the $F=1$, $m_F=0$ Zeeman sublevel. We show that the short-time dynamics in the parametric amplification regime [1] is extremely sensitive to the initial number of atoms in the $m_F=\pm1$ state. This behavior is utilized to precisely characterize the degree of spin flip down to a few atoms. The longer-time evolution beyond the undepleted approximation is also investigated both experimentally and theoretically by considering the atom loss, as well as background radio-frequency noise. \\\\ {[1] D. Linnemann et al., Phys. Rev. Lett. 117, 013001 (2016)}