Optical Lattice Induced Light Shifts in an Yb Atomic Clock

We present an experimental study of the lattice-induced light shifts on the optical clock transition () in neutral ytterbium. The “magic” frequency for the isotope was determined to be , which leads to a first order light shift uncertainty of 0.38 Hz. We also investigated the hyperpolarizability shifts due to the nearby , , and two-photon resonances at 759.708, 754.23, and 764.95 nm, respectively. By measuring the corresponding clock transition shifts near these two-photon resonances, the hyperpolarizability shift was estimated to be 170(33) mHz for a linear polarized, deep, lattice at the magic wavelength. These results indicate that the differential polarizability and hyperpolarizability frequency shift uncertainties in a Yb lattice clock could be held to well below .

Figure 1

Relevant energy levels of Yb, including expanded view of states nearly resonant through two-photon excitation at the magic wavelength. The two-photon detunings are expressed in terms of the one photon frequency.

Figure 2

(a) The shift of the Yb optical clock frequency versus lattice power for 12 separate lattice wavelengths. As the lattice wavelength is increased, the differential polarizability (slope of the lines) goes from large and negative, through zero at the magic frequency, ${\nu }_{\mathrm{magic}}=394799475(35)\mathrm{MHz}$, (${\lambda }_{\mathrm{magic}}\approx 759.3537\mathrm{nm}$), to large and positive. The data are individually offset so the fit lines pass through the origin. (b) Differential polarizability plotted as a function of lattice frequency. The fit line was used to interpolate the magic frequency with an uncertainty of 35 MHz.

Figure 3

ac Stark shift on the clock transition with the lattice tuned near the $6s6p{}^{3}P_0\leftrightarrow 6s8p{}^{3}P_0$ two-photon resonance with linear (solid points) and circular (open squares) lattice polarization. Extrapolating the dispersion shaped fit to the magic wavelength gives a shift of 200(30) mHz for a $500E_r$ trap depth. The resonance disappears in the circular polarized case due to selection rules.

Figure 4

ac stark shifts on the Yb optical clock frequency with the lattice laser tuned near the $6s6p{}^{3}P_0\to 6s5f{}^{3}F_2$ two-photon resonances. The two resonances are the $F=5/2$, $3/2$ hyperfine components of the ${}^{3}F_2$ state in the ${}^{171}\mathrm{Yb}$ isotope, and are split by 4240(20) MHz. The fit gives a total clock shift of 3.5 mHz when extrapolated to the magic wavelength.