Cold-collision-shift cancellation and inelastic scattering in a Yb optical lattice clock

Recently, $p$-wave cold collisions were shown to dominate the density-dependent shift of the clock transition frequency in a ${}^{171}$Yb optical lattice clock. Here we demonstrate that by operating such a system at the proper excitation fraction, the cold-collision shift is canceled below the $5\times {10}^{-18}$ fractional frequency level. We report inelastic two-body loss rates for ${}^3{P}_0$-${}^3{P}_0$ and ${}^1{S}_0$-${}^3{P}_0$ scattering. We also measure interaction shifts in an unpolarized atomic sample. Collision measurements for this spin-1/2 ${}^{171}$Yb system are relevant for high-performance optical clocks as well as strongly interacting systems for quantum information and quantum simulation applications.

Figure 1

(a) Cold-collision shift as a function of excitation fraction for a polarized sample (density of $3\times {10}^{11}$ cm${}^{-3}$) in a 1D optical lattice oriented vertically (solid triangles) or horizontally (solid circles). Open squares are with an unpolarized atomic sample. (b) Cold-collision-shift cancellation: the measurement uncertainty for this cancellation is shown, given by the total deviation (similar to two-sample Allan deviation [23]). (c) Measurement of the residual cold-collision shift when operating at $51\%$ excitation and an atomic density of ${\rho }_{1d}$. The red dashed line indicates the weighted mean of the seven measurements, $+$2.5 mHz, while the solid lines give the 1$\sigma$ error bars of $\pm 2.4$ mHz.

Figure 2

(a) ${}^1{S}_0$ trap loss (black triangles) with an exponential fit (dashed curve). ${}^3{P}_0$ trap loss (blue circles) with a one- and two-body loss fit (solid curve). The inset shows ${}^1{S}_0$ loss for a pure ${}^1{S}_0$ sample (black triangles) and a mixed sample of ${}^1{S}_0$ and ${}^3{P}_0$ atoms (blue circles). The former is fit with a simple exponential, and the latter is fit with ${}^3{P}_0$-${}^3{P}_0$ and ${}^1{S}_0$-${}^3{P}_0$ two-body losses. (b) Two-body loss rates as a function of temperature, calculated with $p_{\mathrm{ls}}=1$ (dashed curves) and with $p_{\mathrm{ls}}=0.8$ and $\delta =0.51\pi$ (solid curves). Black is for a nuclear-spin-polarized sample of ${}^3{P}_0$ atoms (${\beta }_{ee}$), and red is for an unpolarized sample of ${}^3{P}_0$ atoms ($[{\beta }_{ee}+{\tilde{\beta }}_{ee}]/2$). Points give experimental measurements; the black circle is for ${\beta }_{ee}$, and the blue triangle is for ${\beta }_{eg}$.

Figure 3

Cold-collision shift as a function of excitation and for different Ramsey times. These data are for a polarized sample in a 2D lattice with a density ${\rho }_{2d}$ corresponding to $25\%$ of the atoms doubly occupied in a lattice site with a density of $4\times {10}^{12}$ atoms/cm${}^3$. Points correspond to experimental measurements, and solid curves are theoretical calculations [19]. Blue (circles) is a Ramsey time of $T=10$ ms, red (diamonds) is 40 ms, black (squares) is 80 ms, green (triangles) is 160 ms, and orange (inverted triangle) is 210 ms.