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

Dynamically decoupled three-body interactions with applications to interaction-based quantum metrology