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

We propose a stroboscopic method to dynamically decouple the effects of two-body atom-atom interactions for ultracold bosonic 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 bosons quenched in an optical lattice, we can measure the three-body interaction strength with a precision proportional to ${\overline{n}}^{-5/2}$ using homodyne quadrature interferometry, and ${\overline{n}}^{-7/4}$ using conventional collapse-and-revival techniques, where $\overline{n}$ is the mean number of atoms per lattice site. Both precision scalings surpass the nonlinear scaling of ${\overline{n}}^{-3/2}$, which was previously proposed and achieved 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.

Figure 1

Visibility as a function of time showing the effects of two- and three-body interactions in the quench dynamics of ultracold atoms in an optical lattice, where $\overline{n}=2.67$. The solid line (red) is for the combined $U_2$ and $U_3$ dynamics, while the dashed and dot-dashed lines are for $U_2$-only and $U_3$-only dynamics, respectively. To extract the three-body scaling, we need to isolate the $U_3$-only dynamics from the combined time trace.

Figure 2

Schematic of the dynamical decoupling protocol which turns off the two-body interactions and isolates the dynamics due to the three-body interactions. Panel (a) shows the switching of the sign of $U_2$ as a function of time, achieved via the use of a Feshbach resonance. The three-body strength $U_3$ remains constant and negative. Panel (b) shows the visibility (solid line) as a function of time under the influence of the periodically changing $U_2$ shown in panel (a), and $\overline{n}=2.67$. The dashed line is the time evolution due to only $U_3$. The two curves intersect after each interval of duration $T$, indicated by the green markers. Panel (c) shows intersection points (green markers) for a time interval $T$ that is ten times smaller, coinciding even more closely with the pure three-body time trace. The solid line shows the dynamics for $U_3$-only evolution.

Figure 3

The derivative of visibility $\mathcal{V}$ as a function of time for two-body-only (dot-dashed line), three-body-only (solid), and cubic nonlinearity (dashed) simulations. We use $\overline{n}=2.67$.

Figure 4

Panel (a) shows quadrature dynamics $\langle x_i\rangle$ as a function of time for two-body-only and three-body-only interactions with $\overline{n}=4.68$ and $\zeta =0$. Panel (b) shows the evolution of quadrature fluctuations for three-body-only interactions for $\zeta =0,\pi /2$ and $\overline{n}=4.68$.