Magic Wavelength to Make Optical Lattice Clocks Insensitive to Atomic Motion

In a standing wave of light, a difference in spatial distributions of multipolar atom-field interactions may introduce atomic-motion dependent clock uncertainties in optical lattice clocks. We show that the magic wavelength can be defined so as to eliminate the spatial mismatch in electric dipole, magnetic dipole, and electric quadrupole interactions for specific combinations of standing waves by allowing a spatially constant light shift arising from the latter two interactions. Experimental prospects of such lattices used with a blue magic wavelength are discussed.

Figure 1

(a) Spatial distribution of an electromagnetic field for a 1D standing wave. (b) Configuration of the electromagnetic fields and optical lattices for cases (I)–(III), as described in the text. Optical lattice sites inside $|x|$, $|y|$, $|z|<0.9\lambda$ are indicated with their equipotential surfaces given by $q_{E1}(\mathbf{r})=0.3$ and ${\rho }_{\xi }=1$.