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
initialized to an unstable (hyperbolic) fixed point of the spin-nematic phase
space, where subsequent free evolution gives rise to squeezing and quantum spin
mixing. To stabilize the system, periodic microwave pulses are applied that
manipulate the spin-nematic many-body fluctuations and limit their growth. The
range of pulse periods and phase shifts for which the condensate can be
stabilized is measured and the resulting stability diagram compares well with a
linear stability analysis of the problem.Comment: Main text 6 pages, 4 figures; Supplement 5 pages, 1 figur