# 2S-nP Rydberg Project

## General

The 2S-nP project is our most recent experiment and the main focus of many of our current activities. This project is aiming for a new determination of the Rydberg constant and the proton r.m.s. charge radius from precision spectroscopy of atomic hydrogen. The precise extraction of these parameters is a essential ingredient for stringent tests of the internal consistency of QED and other fundamental applications, e.g. the determination of fundamental constants which can be related to each other via the Rydberg constant:

$$R_\infty=\frac{m_e \alpha^2c}{2h}$$

Currently, there is a four sigma discrepancy between the proton r.m.s. charge radius determined from laser spectroscopy of muonic hydrogen and the corresponding results from precision spectroscopy of electronic hydrogen. An even larger discrepancy of 7 sigma is obtained, when a set of electron-proton-scattering data is included in the analysis. This discrepancy, referred to as the "proton size puzzle", exists since four years now and suggested possible ways to resolve it span the entire spectrum from experimental errors up to physics beyond the standard model.

Figure 1: Proton charge radius determined from hydrogen spectroscopy. Violet: radio frequency measurements, blue and green: optical measurements.

Utilizing the 1S-2S beam apparatus as a well controlled and reliable cryogenic source of hydrogen atoms in the meta-stable 2S state, we believe that measurements of transition frequencies from the 2S state to higher lying P-states in our lab are well suited to shed new light on the electronic hydrogen part of the puzzle. In particular, we are currently studying the 2S-4P transition at 486nm. In parallel, we are also setting up laser systems capable of probing higher 2S-nP transitions: a laser system for the 2S-6P transition at 410nm is fully operational in our lab and another system covering the wavelength range between 380nm and 390nm (2S-8/9/10P) is under construction. Once demonstrated on the 2S-4P transition, our measurement scheme can be applied to these transitions with a few setup modifications.

Achieving the desired accuracy of a few parts in {$10^{-12}$} is an technologically and experimentally challenging task. Determining the position of the atomic line resonance to an uncertainty on the order of {$10^{-4}$} of it's width requires both, a sophisticated and well characterized experimental system as well as a deep theoretical understanding of the atomic dynamics involved. The latter is brought by a number of numerical simulations, the most computational intensive being performed using facilities provided by the MPG/IPP Rechenzentrum Garching.

## Experimental setup

Figure 2: 3D View of the beam and detector setup for 2S-4P spectroscopy.

A schematic view of the beam and detector setup for the 2S-4P spectroscopy is shown in figure 2. Atomic hydrogen thermalizes at the inner walls of a copper nozzle which is temperature stabilized to 5.8\,K by a liquid helium flow cryostat. An atomic beam is collimated from the atoms leaving the nozzle to the left by two diaphragms and excitation of the two photon 1S-2S transition at 243nm takes place collinear to the atomic beam axis. In contrast to electron-impact excitation, the standard scheme of 2S excitation in the optical experiments shown in figure 1, the optical excitation of the 2S state preserves the atoms' low thermal velocity and only populates desired substates which are determined by the frequency of the exciting laser. Excitation of the 2S-4P transition takes place in a second separated region. The laser to atomic beam angle is close to 90°, which reduces the first order Doppler (FOD) effect on the one photon 2S-4P transition. Although our atoms' mean thermal velocity is more than one order of magnitude lower than typical velocities in previous experiments, the FOD has to be reduced by more than six orders of magnitude in total and is the largest systematic effect that needs to be taken care of. This high suppression is possible by combining the active fiber-based retroreflector (AFR) developed in our lab with the time-of-flight-resolved detection scheme also used in 1S-2S spectroscopy. Lyman-$\gamma$ photons which are emitted upon the rapid 4P-1S decay are detected by channel electron multipliers (CEM1 and CEM2) via photoemission of electrons from the graphite coating within the detector region and clicks are recorded with their arrival time. From their time distribution, signals with different effective velocities down to about 70m/s can be constructed, assisting the proper characterization of the FOD. A third detector (CEM3) is observing the number of 2S atoms remaining after the 2S-4P interaction and giving complementary information in addition to CEMs 1&2.