Rydberg Spectroscopy in an Optical Lattice: Blackbody Thermometry for Atomic Clocks

We show that optical spectroscopy of Rydberg states can provide accurate in situ thermometry at room temperature. Transitions from a metastable state to Rydberg states with principal quantum numbers of 25–30 have 200 times larger fractional frequency sensitivities to blackbody radiation than the strontium clock transition. We demonstrate that magic-wavelength lattices exist for both strontium and ytterbium transitions between the metastable and Rydberg states. Frequency measurements of Rydberg transitions with ${10}^{-16}$ accuracy provide 10 mK resolution and yield a blackbody uncertainty for the clock transition of ${10}^{-18}$.

Figure 1

(a) Rydberg atoms trapped in an optical lattice can be sensitive thermometers. (b) Energy levels for Sr. Transitions from the metastable ${}^{3}P_0$ state to high Rydberg states (dashed line) have a frequency sensitivity of $16\mathrm{Hz}/\mathrm{K}$, which can enable a temperature accuracy of $\pm 10\mathrm{mK}$. To achieve this accuracy using transitions between Rydberg levels (inset, solid line), only a modest fractional frequency accuracy of ${10}^{-13}$ is required, but, for Sr, the transition linewidths would require lines to be split by more than ${10}^6$. For $l\le 4$ states, transitions between ${}^{3}P_0$ and ${}^{3}D_1$ states have the largest sensitivity, $\approx 1\mathrm{Hz}/\mathrm{K}$; their precise energies are not known.

Figure 2

The Farley-Wing function [17] is plotted versus normalized transition frequency $y={\omega }_{n^{\prime }n}/k_{B}T$. It gives the blackbody radiation shift of state $n$ due to $n^{\prime }$, Eq. (3).

Figure 3

BBR Stark shifts of the (a) triplet and (b) singlet $5sn\ell$ Rydberg states of Sr. The shifts asymptote to 2.4 kHz for high principal quantum numbers $n$.