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The Proton Size Puzzle: Testing QED at Extreme Wavelengths

Periodic Reporting for period 4 - QED-PROTONSIZE (The Proton Size Puzzle: Testing QED at Extreme Wavelengths)

Reporting period: 2021-03-01 to 2022-08-31

With lasers it is possible to investigate at which wavelengths light is absorbed by atoms and molecules, when the energy of the photon matches an internal energy interval of the electrons. For the simplest systems, such as atomic hydrogen, it can then be compared to theoretical predictions with extreme precision to test our current understanding of physics, called the Standard Model. In particular, Quantum Electrodynamics (QED) is tested in this way, which is in fact the best tested and most successful part of the Standard Model. Precision spectroscopy also enables to determine some of the fundamental constants of Nature that are required to do accurate calculations with the theory. Any deviation found experimentally from theory could hint at new physics, which we know must be there, e.g. given the existence of 'dark matter' and 'dark energy'. Previous measurements based on e.g. atomic hydrogen, and exotic varieties of it such as muonic-hydrogen, have shown contradicting results.

The aim of this project is to enable precision measurements for the first time on singly-ionised helium on the 1S-2S transition, to contribute to solving the aforementioned issues. Singly-ionized helium is like hydrogen, but has much bigger QED effects. A major challenge is that its internal energy structure requires light at extreme wavelengths for which no lasers exist. We are developing a new laser spectroscopy method, called Ramsey-Comb spectroscopy (RCS), that combines the precision of low-power frequency comb lasers (which get their accuracy from an atomic clock) with high-power laser pulses that can be converted to the extreme ultraviolet by high-harmonic generation (HHG). It required development of a complex laser system, a state-of-the-art ion trap (realized through a collaboration with T. Mehlstäubler from PTB in Germany), laser cooling via a different ion to the lowest quantum-mechanical energy state, and methods to detect that the transition was made.

While the He+ trapping was not completely ready yet during the project, we realized nearly all of the components to do precision spectroscopy of the 1S-2S transition in He+ in the near future. Experiments were conducted on other atoms and molecules to demonstrate the principles and potential of our developed methods. This led to e.g. a more than two orders of magnitude improved molecular spectroscopy of H2 and D2, and in a collaboration with F. Merkt from the ETH Zurich, in improved dissociation energies, which is the benchmark for tests of molecular quantum theory. We now reached an accuracy 3 times better than the influence of the finite proton size in H2. Another important demonstration for the project was the first demonstration of RCS combined with HHG. This enabled us to do the most precise spectroscopic measurement ever performed with light from high-harmonic generation, using our Ramsey-comb technique, which we applied on a transition in xenon at 110 nm (improving the accuracy by 10 000 times).

In the final period of the project, again a major advance was made when we demonstrated the first excitation of the 1S-2S transition in He+, with properties as predicted (and confirmed by theoretical simulations). Although this was not yet a precision measurement, it does prove the excitation principle with 32 nm + 790 nm works very well. Therefore we have demonstrated all the ingredients to do an actual precision determination of the 1S-2S transition, which seems tantalizingly close now. We will pursue this in a follow-up project.
During the project we developed and built up a new Ramsey-comb laser system that is optically locked to a sub-Hz ultra-stable laser and a Cs atomic clock. This laser system produces double-pulses near 790 nm with very high phase and timing stability (30 times per second, with a delay up to microseconds, and attosecond accuracy). We also developed a complex 8-chamber vacuum setup, for high-harmonic generation (HHG) from the 790 nm pulses, refocusing of the HHG wavelengths (including 32 nm) in an interaction region where the ion trap is mounted, production of He+ with an atomic beam, optical detection of ions in the trap, and diagnostic equipment to characterize the HHG light. In a demonstration experiment with this setup, we performed precision spectroscopy of xenon atoms at 110 nm, improving the accuracy of the measured transition 10 000 times (published in two papers, and presented at conferences). In other demonstration experiments we showed 201 nm two-photon spectroscopy of H2 and D2 on the X-EF transition, improving the accuracy by 2 orders of magnitude and derived a dissociation potential with 30 times improved value in a collaboration. We published several papers on this topic and conference presentations were given.
For the laser cooling of helium+ we constructed a laser system in the UV at 313 nm with all frequencies to enable ground-state cooling of He+ via a single Be+ ion, and developed darkening-resistant single-mode fibers for 313 nm. We completed the design and construction of the ion trap for He+ in a collaboration with T. Mehlstäubler of the PTB in Braunschweig, Germany, and developed the electronics and control program. The ion-trap will be installed on a special mechanical construction (also ready) that was designed to enable “6D”-alignment of the ion trap from outside of the ultra-high vacuum chamber with 1 micrometer accuracy (unpublished).

In the last period of the project, we constructed a 3He recycling apparatus and produced 3He+ by ionization of a neutral helium atomic beam with the 17th harmonic of the 790 nm beam. With the He+ ions we then demonstrated, for the first time, excitation of the two-photon 1S-2S transition of He+ with a combination of 32 nm and 790 nm. Publication and conference contributions are in preparation.
After updating the first Ramsey-comb laser (then the only one in the world, producing coherent ultrafast pulse pairs), we have built a second one with much improved stability based on an ultra-stable frequency comb laser and LBO as parametric amplifier crystal. With this system we have generated up to the required 32 nm for the project through high-harmonic generation in the form of two mutual-coherent pulses.

We demonstrated the most accurate spectroscopic measurement with light produced via high-harmonic generation and Ramsey-comb spectroscopy combined. A fractional accuracy of 0.2 parts per billion was reached, which is 3.6 times better than demonstrated before using HHG. We showed this on a transition in xenon atoms at 110 nm (vacuum-ultraviolet) with an excited state lifetime of only 23 ns.

Applying the Ramsey-comb method to molecular hydrogen, we improved the accuracy of the ground-state to first-excited state energy interval (X-EF) by 2 orders of magnitude and with this improved the dissociation energy and ionization energy of this molecule by a factor 30 in a collaborative effort with the ETH in Zurich, reaching an accuracy that clearly shows the influence of the proton radius.

And finally, we demonstrated, for the first time, excitation of the 1S-2S two-photon transition in a He+ ion (3He) using a combination of 32 nm and 790 nm. This is the first laser excitation of He+ from the ground state, and together with the demonstrated Ramsey-comb spectroscopy method, it will enable us in a follow-up project to probe the nuclear size of helium and perform one of the best tests of Quantum Electrodynamic theory to date.
Helium+ experiment with the HHG chamber in the foreground
Installing the time-of-flight detector for the xenon experiment
View from the spectroscopy vacuum chamber of the helium+ experiment
Background: Ramsey-comb laser no. 1, foreground: H2 experiment