Measurement of absolute transition frequencies of ${}^{87}\mathrm{Rb}$ to $\mathit{nS}$ and $\mathit{nD}$ Rydberg states by means of electromagnetically induced transparency

We report the measurement of absolute excitation frequencies of ${}^{87}\mathrm{Rb}$ to $nS$ and $nD$ Rydberg states. The Rydberg transition frequencies are obtained by observing electromagnetically induced transparency on a rubidium vapor cell. The accuracy of the measurement of each state is $\lesssim$1 MHz, which is achieved by frequency stabilizing the two diode lasers employed for the spectroscopy to a frequency comb and a frequency comb calibrated wavelength meter, respectively. Based on the spectroscopic data we determine the quantum defects of ${}^{87}\text{Rb}$, and compare it with previous measurements on ${}^{85}\text{Rb}$. We determine the ionization frequency from the $5S_{1/2}(F=1)$ ground state of ${}^{87}\text{Rb}$ to $1010.029\hspace{0.5em}164\hspace{0.5em}6(3)\mathrm{THz}$, providing the binding energy of the ground state with an accuracy improved by two orders of magnitude.

Figure 1

Energy-level diagram of ${}^{87}\mathrm{Rb}$ and corresponding laser wavelengths for observation of electromagnetically induced transparency using a Rydberg state. The probe laser is stabilized to the lower atomic resonance, while the coupling laser, with a variable detuning $\hslash {\Delta }_{\mathrm{c}}$, is scanned across the Rydberg resonance.

Figure 2

Optical setup (schematic) for the observation of EIT in a rubidium vapor cell. The probe and coupling beams are counterpropagating in the rubidium vapor cell (heated to $~$45${}^{°}$C) and the probe laser intensity is monitored with a photodiode (PD). A chopper in the coupling laser beam provides a reference signal for lock-in detection of the photodiode signal. The probe laser is frequency stabilized to a frequency comb. The coupling beam at 480 nm comes from a frequency-doubled 960-nm laser that is stabilized and scanned by a wavelength meter. The wavelength meter is calibrated with the help of a frequency comb beat signal at 960 nm.

Figure 3

EIT resonance for the $34S_{1/2}$ Rydberg state (exemplary) as recorded by the photodiode, against the coupling laser frequency measured simultaneously by the wavelength meter. A Gaussian shape is fitted for peak frequency determination (solid line).

Figure 4

Difference between measured transition frequencies to $n{S}_{1/2}$ Rydberg states (see Table ) and the transition frequencies calculated with Eq. (1) based on the Rydberg-Ritz parameters and ionization frequency specified in Tables and .