Systematic Study of the ${}^{87}\mathrm{Sr}$ Clock Transition in an Optical Lattice

With ultracold ${}^{87}\mathrm{Sr}$ confined in a magic wavelength optical lattice, we present the most precise study (2.8 Hz statistical uncertainty) to date of the ${}^{1}S_0\mathrm{\text{−}}{}^{3}P_0$ optical clock transition with a detailed analysis of systematic shifts (19 Hz uncertainty) in the absolute frequency measurement of 429 228 004 229 869 Hz. The high resolution permits an investigation of the optical lattice motional sideband structure. The local oscillator for this optical atomic clock is a stable diode laser with its hertz-level linewidth characterized by an octave-spanning femtosecond frequency comb.

Figure 1

Measurement of probe laser (698 nm) linewidth by comparison to a reference laser at 1064 nm using an octave spanning (573–1146 nm) fs laser. Linewidth of the heterodyne beat at 1064 nm is 3 Hz.

Figure 2

Partial diagram of ${}^{87}\mathrm{Sr}$ energy levels and the schematic of the optical layout delivering the probe and lattice laser to the atoms. P: polarizer, DM: dichroic mirror, PMT: photo-multiplier tube. The strong longitudinal and weak transverse confinement of the 1D lattice creates 2D trapping regions. The lattice and probe lasers share an identical polarization. Branching ratios from the ${}^{3}S_1$ to the ${}^{3}P$ states are $5/9(J=2)$, $3/9(J=1)$, and $1/9(J=0)$.

Figure 3

(a) Spectroscopic trace of saturated, elastic ${}^{1}S_0\mathrm{\text{−}}{}^{3}P_0$ electronic transition and the inelastic motional sidebands at 80 kHz detuning from the center transition. (b) Lattice band structure derived from exact solution of ${cos}^2(kz)$ dependent longitudinal lattice potential. (c) Fit to the blue sideband of (a) where the sideband is composed of multiple $n\to n+1$ transitions. Here the trap depth is $\sim 20\mu \mathrm{K}$ while the atomic sample temperature is $5\mu \mathrm{K}$. The short vertical bars (blue online) denote the position of each $n\to n+1$ transition from (b). (d) Narrow ${}^{1}S_0\mathrm{\text{−}}{}^{3}P_0$ elastic carrier spectrum. Typical scan time for each spectrum is $\sim 100\mathrm{s}$.

Figure 4

The measured ${}^{1}S_0\mathrm{\text{−}}{}^{3}P_0$ transition frequency versus (a) lattice intensity ($I_0=10\mathrm{kW}/{\mathrm{cm}}^2$), (b) atomic density, and (c) magnetic field. (d) JILA measurements over a 3 month period, with each data point representing an averaged daily frequency measurement. The results reported in this work (lower bars) and in Ref. 6 (upper bars) are both shown with the total (outer box) and statistical (inner shaded area) errors.