Dynamical control of a quantum Kapitza pendulum in a spin-1 BEC

We demonstrate dynamic stabilization of an unstable strongly interacting quantum many-body system by periodic manipulation of the phase of the collective states. The experiment employs a spin-1 atomic Bose condensate that has spin dynamics analogous to a non-rigid pendulum in the mean-field limit. The condensate spin is initialized to an unstable (hyperbolic) fixed point of the phase space, where subsequent free evolution gives rise to spin-nematic squeezing\footnote{C.D. Hamley, \emph{et al.}, ``Spin-Nematic Squeezed Vacuum in a Quantum Gas,'' Nature Physics 8, 305-308 (2012).} and quantum spin mixing.\footnote{C.S. Gerving, \emph{et al.}, ``Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose-Einstein condensate,'' Nature Communications 3, 1169 (2012).} To stabilize the system, periodic microwave pulses are applied that manipulate the spin-nematic fluctuations and limit their growth. The range of pulse periods and phase shifts with which the condensate can be stabilized is measured and compares well with a linear stability analysis of the problem.\footnote{T.M. Hoang, \emph{et al.}, ``Dynamic stabilization of a quantum many-body system.'' arXiv:1209.4363 (2012).}