Prospects for Optical Clocks with a Blue-Detuned Lattice

We investigated the properties of optical lattice clocks operated with a repulsive light-shift potential. The magic wavelength, where light-shift perturbation for the clock transition cancels, was experimentally determined to be 389.889(9) nm for ${}^{87}\mathrm{Sr}$. The hyperpolarizability effects on the clock transition were investigated theoretically. With minimal trapping field perturbation provided by the blue-detuned lattice, the fractional uncertainty due to the hyperpolarizability effects was found to be $2\times {10}^{-19}$ in the relevant clock transition.

Figure 1

(a) Energy levels for alkaline earth atoms. The ${}^{1}S_0-{}^{3}P_0$ transition is used for the clock transition. By applying the lattice laser detuned slightly above the nearby state, $nsnp{}^{1}P_1$ and $ns(n+1)d^3{D}_1$, atoms can be trapped near the nodes of the standing wave. (b) The light shift for the ${}^{1}S_0$ (dashed line) and the ${}^{3}P_0$ (solid line) states of Sr as a function of the lattice laser wavelength for laser intensity of $I=10\mathrm{kW}/{\mathrm{cm}}^2$. Intersections of the curves indicate blue magic wavelengths, which include ${\lambda }_b\approx 360$ and 390 nm.

Figure 2

(a) An experimental configuration. Ultracold spin-polarized ${}^{87}\mathrm{Sr}$ atoms were loaded into a one-dimensional optical lattice operated at the (red-detuned) magic wavelength ${\lambda }_r=813.428\mathrm{nm}$. The probe laser measured the frequency difference $\delta (\lambda )$ of the clock transition with and without a UV light near 390 nm. (b) The light shift $\delta (\lambda )$ as a function of the UV laser wavelength $\lambda$ with $I=4.5\mathrm{W}/{\mathrm{cm}}^2$. The blue magic wavelength was determined to be ${\lambda }_b=389.889(9)\mathrm{nm}$.

Figure 3

(a) Real and (b) imaginary parts of the differential hyperpolarizabilities of the Sr atoms calculated near the blue magic wavelength ${\lambda }_{b1}\approx 360\mathrm{nm}$ and ${\lambda }_{b2}\approx 390\mathrm{nm}$. The empty circles and filled squares correspond to linear and circular lattice laser polarizations.