Frequency Shifts in an Optical Lattice Clock Due to Magnetic-Dipole and Electric-Quadrupole Transitions

We report a hitherto undiscovered frequency shift for forbidden $J=0\to J=0$ clock transitions excited in atoms confined to an optical lattice. These shifts result from magnetic-dipole and electric-quadrupole transitions, which have a spatial dependence in an optical lattice that differs from that of the stronger electric-dipole transitions. In combination with the residual translational motion of atoms in an optical lattice, this spatial mismatch leads to a frequency shift via differential energy level spacing in the lattice wells for ground state and excited state atoms. We estimate that this effect could lead to fractional frequency shifts as large as ${10}^{-16}$, which might prevent lattice-based optical clocks from reaching their predicted performance levels. Moreover, these effects could shift the magic wavelength in lattice clocks in three dimensions by as much as 100 MHz, depending on the lattice configuration.

Figure 1

An illustration of optical transitions between vibrational levels for atoms confined to an optical lattice.