Metrology of Rydberg states of the hydrogen atom

We present a method to precisely measure the frequencies of transitions to high-n Rydberg states of the hydrogen atom which are not subject to uncontrolled systematic shifts caused by stray electric fields. The method consists in recording Stark spectra of the field-insensitive k = 0 Stark states and the field-sensitive k = +/- 2 Stark states, which are used to calibrate the electric field strength. We illustrate this method with measurements of transitions from the 2s(f = 0 and 1) hyperfine levels in the presence of intentionally applied electric fields with strengths in the range between 0.4 and 1.6 Vcm-1. The slightly field-dependent k = 0 level energies are corrected with a precisely calculated shift to obtain the corresponding Bohr energies (-cRH/n2). The energy difference between n = 20 and n = 24 obtained with our method agrees with Bohr's formula within the 10-kHz experimental uncertainty. We also determined the hyperfine splitting of the 2s state by taking the difference between transition frequencies from the 2s(f = 0 and 1) levels to the n = 20, k = 0 Stark states. Our results demonstrate the possibility of carrying out precision measurements in high-n hydrogenic quantum states.