Metrology of Rydberg states of the hydrogen atom

TL;DR

This paper introduces a precise method for measuring high-$n$ Rydberg states of hydrogen, using Stark spectra calibration to avoid systematic shifts from stray electric fields, enabling high-accuracy quantum state measurements.

Contribution

The paper presents a novel calibration technique using Stark spectra of specific hydrogen states to accurately measure Rydberg transition frequencies free from electric field systematic errors.

Findings

Measured transition frequencies agree with Bohr's formula within 10 kHz.

Demonstrated hyperfine splitting determination of the 2s state.

Showed the feasibility of high-precision measurements in high-$n$ hydrogenic states.

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 $k=\pm2$ 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 $\left(-cR_{\mathrm{H}}/n^2\right)$. 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.