  We propose a stroboscopic method to dynamically decouple the effects of
two-body atom-atom interactions for ultracold atoms, and realize a system
dominated by elastic three-body interactions. Using this method, we show that
it is possible to achieve the optimal scaling behavior predicted for
interaction-based quantum metrology with three-body interactions. Specifically,
we show that for ultracold atoms quenched in an optical lattice, we can measure
the three-body interaction strength with a precision proportional to ${\bar
n}^{-5/2}$ using homodyne quadrature interferometry, and ${\bar n}^{-7/4}$
using conventional collapse-and-revival techniques, where ${\bar n}$ is the
mean number of atoms per lattice site. Both precision scalings surpass the
nonlinear scaling of ${\bar n}^{-3/2}$, the best so far achieved or proposed
with a physical system. Our method of achieving a decoupled three-body
interacting system may also have applications in the creation of exotic
three-body states and phases.
