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\title{PRECISION SPECTROSCOPY OF TRANSITION FROM THE METASTABLE 2 $^3$S$_1$ STATE OF TO HIGH NP RYDBERG STATES }

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\author{\underline{\FirstName G. \LastName CLAUSEN},
  \FirstName S. \LastName SCHEIDEGGER,\FirstName \,J. A. \LastName AGNER, \FirstName H. \LastName SCHMUTZ, and \FirstName F. \LastName MERKT}
\address{Laboratory of Physical Chemistry, ETH Zurich}


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\fancyhead[C]{{\footnotesize \textit{HRMS, 28th Colloquium, Dijon, France,
  Aug. 28 - Sept. 1, 2023}}}
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The metastable He ((1s)$^1$(2s)$^1$) atom in its singlet ($^1$S$_0$) or triplet ($^3$S$_1$) states is an ideal system to perform tests of ab-initio calculations of two-electron systems that include quantum-electrodynamics and nuclear finite-size effects. The recent determination of the ionization energy of the metastable
$2\,^1$S$_0$ state of $^4$He [1] confirmed a discrepancy between the latest theoretical values of the Lamb shifts in low-lying electronic states of triplet helium [2] and the measured $3\,^3$D $\leftarrow$ 2 $^3$S [3] and $3\,^3$D $\leftarrow$ 2 $^3$P [4] transition frequencies. This discrepancy could not be resolved in the latest calculations [5, 6]. 
\\
Currently, we focus on the development of a new experimental method for the determination of the ionization energy of the
$2\,^3$S$_1$ state of $^4$He via the measurement of transitions from the $2\,^3$S$_1$ state to $n$p Rydberg states. Extrapolation of the $n$p series yields the ionization energy with sub-MHz accuracy. 
\\ In this poster, we present the progress in the development of our experimental setup, which involves (i) the preparation of a cold, supersonic expansion of helium atoms in the $2\,^3$S$_1$ state, (ii) the development and characterization of a laser system for driving the transitions to the $n$p Rydberg states, and (iii) the implementation of a new sub-Doppler, background-free detection method. We present this new spectroscopic method, with which we cancel the $^1$st-order Doppler shift and illustrate its power with a new determination of the ionization energy of $2\,^3$S$_1$ metastable He.  \\ \\
\textbf{References}
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	\small
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[1] G. Clausen \emph{et al.}, 
		{ Phys. Rev. Lett.} {\bfseries 127}, 093001 (2021). \newline
[2] V. Patk\'o\v{s} \emph{et al.}, { Phys. Rev. A.} {\bfseries 103}, 042809 (2021). \newline
[3] C. Dorrer \emph{et al.}, { Phys. Rev. Lett.} {\bfseries 78}, 3658 (1997). \newline 
[4] P.-L. Luo \emph{et al.}, { Phys. Rev. A.} {\bfseries 94}, 062507 (2016). \newline 
[5] V. A. Yerokhin \emph{et al.}, { Eur. Phys. J. D.} {\bfseries 76}, 142 (2022). \newline 
[6] V. A. Yerokhin \emph{et al.}, { Phys. Rev. A.} {\bfseries 107}, 012810 (2023).

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