### Speaker

Mr
Lothar Maisenbacher
(Max Planck Institute of Quantum Optics)

### Description

Precision measurements of atomic hydrogen (H) have long been successfully used to extract fundamental constants and to test bound-state quantum electrodynamics. Both the Rydberg constant $R_\infty$ and the proton root mean square charge radius $r_\mathrm{p}$ can be determined by H spectroscopy, requiring the measurement of at least two transition frequencies. With the very precisely measured 1S-2S transition frequency serving as a corner stone [1], the current limitation is the measurement precision of other H transition frequencies. Moreover, the CODATA 2014 value [2] for $r_\mathrm{p}$, containing the H spectroscopy world data and elastic scattering results, disagrees by 5.6 standard deviations ($\sigma$) with the much more precise value extracted from spectroscopy of muonic hydrogen ($\mu$p) [3].
Using a cryogenic beam of H atoms optically excited to the initial 2S state, we measured the 2S-4P transition in H with a relative uncertainty of 4 parts in $10^{12}$ [4]. Combining our result with the 1S-2S transition frequency yields the values of the Rydberg constant $R_\infty = 10973731.568076(96)$ m$^{-1}$ and $r_\mathrm{p} = 0.8335(95)$ fm. Our $r_\mathrm{p}$ value is 3.7$\sigma$ smaller than the CODATA value, but in good agreement with the $\mu$p value.
[1] C.G. Parthey $\textit{et al.}$, Phys. Rev. Lett. $\textbf{107}$, 203001 (2011).
[2] P.J. Mohr $\textit{et al.}$, Rev. Mod. Phys. $\textbf{88}$, 035009 (2016).
[3] A. Antognini $\textit{et al.}$, Science $\textbf{339}$, 417 (2013).
[4] A. Beyer $\textit{et al.}$, Science $\textbf{358}$, 79 (2017).

[email protected] |

### Primary author

Mr
Lothar Maisenbacher
(Max Planck Institute of Quantum Optics)

### Co-authors

Mr
Alexey Grinin
(Max Planck Institute of Quantum Optics)
Dr
Arthur Matveev
(Max Planck Institute of Quantum Optics)
Dr
Beyer Axel
(Max Planck Institute of Quantum Optics)
Dr
Ksenia Khabarova
(Lebedev Physical Institute)
Dr
Nikolai Kolachevsky
(Lebedev Physical Institute)
Prof.
Randolf Pohl
(Max Planck Institute of Quantum Optics; Johannes Gutenberg University Mainz)
Prof.
Theodor W. Hänsch
(Max Planck Institute of Quantum Optics; Ludwig Maximilians University Munich)
Dr
Thomas Udem
(Max Planck Institute of Quantum Optics)
Mr
Vitaly Andreev
(Max Planck Institute of Quantum Optics)