Metrology of Rydberg states of the hydrogen atom

Abstract

We present a method to precisly 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 $k=\pm 2$ Stark states, which are used to calibrate the electric field strength. We illustrate this method with measurements of transitions from the $2\text{s}(f=0\text{ and }1)$ 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 $\left(-c{R}_{\mathrm{H}}/n^2\right)$. 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 $2\text{s}$ state by taking the difference between transition frequencies from the $2\text{s}(f=0\text{ and }1)$ 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.

References in corpus (8)

• High-precision determination of the electric and magnetic form factors of the proton
• Dispersion analysis of the nucleon form factors including meson continua
• Measurement of the $2$S${}_{1/2}-8$D${}_{5/2}$ transition in hydrogen
• High-precision determination of the electric and magnetic radius of the proton
• Proton radius from electron-proton scattering and chiral perturbation theory
• SI-traceable frequency dissemination at 1572.06 nm in a stabilized fiber network with ring topology
• Calculation of Hydrogenic Bethe Logarithms for Rydberg States
• Precision millimetre-wave spectroscopy and calculation of the Stark manifolds in high Rydberg states of para-H${}_2$

Cited by in corpus (4)

• Sub-part-per-trillion test of the Standard Model with atomic hydrogen
• Intensity-dependent precision two-photon Doppler-free spectroscopy of Xe using narrow-bandwidth long-pulse deep-UV laser radiation
• The Stark effect in molecular Rydberg states: Calculation of Rydberg-Stark manifolds of H${}_2$ and D${}_2$ including fine and hyperfine structures
• Narrowline Laser Cooling and Spectroscopy of Molecules via Stark States