Ultrastable Optical Clock with Neutral Atoms in an Engineered Light Shift Trap

An ultrastable optical clock based on neutral atoms trapped in an optical lattice is proposed. Complete control over the light shift is achieved by employing the $5s^2{}^{1}S_0\to 5s5p{}^{3}P_0$ transition of ${}^{87}\mathrm{S}\mathrm{r}$ atoms as a “clock transition.” Calculations of ac multipole polarizabilities and dipole hyperpolarizabilities for the clock transition indicate that the contribution of the higher-order light shifts can be reduced to less than 1 mHz, allowing for a projected accuracy of better than ${10}^{-17}$.

Figure 1

Simplified optical coupling scheme for ${}^{87}\mathrm{S}\mathrm{r}$. (a) In the limit of large detunings ${\delta }_i$ of the coupling laser compared to the hyperfine splittings ${\delta }_{\mathrm{h}\mathrm{f}\mathrm{s}}$, the squared transition dipole moment of the upper $J$ manifold can be simply added up, resulting in a quasiscalar light shift. (b) 3D optical lattice provides Lamb-Dicke confinement while it prevents atom-atom interactions.

Figure 2

Light shift as a function of the trapping laser wavelength for a laser intensity of $I=10\mathrm{k}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$. The solid and dashed lines show the light shifts for the ${}^{1}S_0$ and ${}^{3}P_0$ states, respectively, which intersect at ${\lambda }_L\approx 800\mathrm{n}\mathrm{m}$. The inset illustrates the insignificance of the polarization-dependent light shifts of the ${}^{3}P_0$ ($F=9/2$) state by taking into account the dipole coupling to the ${}^{3}S_1$ and ${}^{3}D_1$ state at ${\lambda }_L$ in the presence of a magnetic field $B_0=30\mathrm{m}\mathrm{G}$.