Ultrafast Laser Physics and Precision Metrology For Fundamental Tests

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1S-2S spectroscopy of trapped singly-ionized helium

Introduction He+ experiment

We aim to measure the 1S-2S transition frequency of the helium+ ion for the first time using advanced laser techniques, including frequency comb lasers, ion trapping, and (sympathetic) laser cooling. This will enable us to explore this exciting new system for finding new physics by investigating Quantum-Electrodynamics (QED), the Rydberg constant, and the charge radius of the alpha particle. With the latter we contribute to the solution of the so-called Proton-Size Puzzle [1-4]. The uncertainties in the 1S-2S transition due to the Rydberg constant, QED and alpha-particle charge radius are in fact of the same order of magnitude, so that one actually has to look at these aspects collectively.

So what is this all about? Quantum electrodynamics is arguably the best-tested theory in physics. Based on e.g. the anomalous magnetic moment and precision spectroscopy on e.g. the 1S-2S transition in atomic hydrogen, it was thought that QED is basically correct. However, to compare the spectroscopy with QED calculations, one also has to take into account the effect of the finite proton size and the value of the Rydberg constant. Assuming that QED is correct, the spectroscopy and theory can be used to figure out how large the proton charge radius is and the value of the Rydberg constant. This gave a number of about 0.88 fm for the charge radius, which agreed before 2010 well with electron-scattering experiments. However, in 2010 the 2S-2P transition was measured by the CREMA collaboration in muonic hydrogen, where the electron is replaced with a muon (which is just like the electron, but 200 times heavier). The effects of QED and proton size are much bigger in muonic hydrogen, and from the spectroscopy a 10 times more accurate proton size could be derived [2,3] (and now also the deuteron size from muonic deuterium [4]). However, the proton appeared to be 4% smaller (the radius is approximately 0.84 fm). For a long time there was no real solution to this "proton size puzzle", despite a lot of theoretical and experimental effort.
In 2017 a result for the proton radius was published [5] based on 1S-4P spectroscopy of normal hydrogen (MPQ in Munich, Germany) that agreed with the muonic results obtained before. One might think this solved the puzzle, but then in early 2018 the proton radius from 1S-3S spectroscopy [6] of hydrogen (Paris) agreed with the previous electronic hydrogen results (therefore not with the muonic results). More measurements like the 2S-2P re-measurement by the group of Eric Hessels (Canada) agreed with the smaller value, and most recently electron scattering now also confirmed the smaller radius. This has great repercussions for the Rydberg constant too as it is nearly 100% correlated, leading to a big adjustment (way beyond the old error bar) in the CODATA 2018 determination of the fundamental constants. The fact that all these things are interconnected makes it quite complicated to test theory.

Above: A schematic of the 1S-2S He+ experiment, and excitation scheme.

One way to find new clues for possible new physics is to test QED & nuclear size influences in different systems, such as Helium+ ions. The CREMA collaboration has measured the 2S-2P transition in muonic helium+ ions (both 3He and 4He), and evaluation of the results is in progress. What we like to do is to measure the 1S-2S transition in normal helium+ for the first time so that it can be compared to the muonic helium+ measurements. In combination with the measurements in atomic hydrogen, this could lead to a better test of (higher-order) QED, or it can be used to check the value of the Rydberg constant, or to determine a more accurate charge radius of the alpha particle (the nucleus of Helium+).

In a paper we wrote in 2019 (which you can find here) we explain in more detail what we can learn from He+ spectroscopy, and how we intend to do it.

We are now building the setup to realize 1S-2S excitation of He+ trapped in a linear Paul trap, with a co-trapped Be+ ion for sympathetic cooling (1 mK by Doppler cooling, or below by side-band cooling). Spectroscopy will be performed with our Ramsey-comb method [7-9] that combines high-energy (mJ-level) phase-stable ultrafast laser pulses with kHz or better frequency precision. We will use a combination of 32 nm made by high-harmonic generation from 790 nm, and the 790 nm itself, for the two-photon transition to enhance the transition rate compared to the more obvious equal-photon scheme (2x60 nm).

In the next section we describe the first demonstration of Ramsey-comb spectroscopy in xenon using high-harmonic generation. This demonstrates that Ramsey-comb spectroscopy works very well with HHG, which is a vital step towards our plans for measuring the 1S-2S He+ transition.

For ion trapping technology we work together with dr. Tanja Mehlstaeubler and prof. Piet Schmidt of the PTB Braunschweig, Germany, and we are currently setting up an advanced ion trap for He+ with their help.

An important advance: Ramsey-comb spectroscopy at 110 nm using high-harmonic generation

The setup for Ramsey-comb excitation based on high-harmonic generation, designed and built by Laura Dreissen. The left part contains the high-harmonic generation (HHG), the right part the xenon excitation chamber with all the diagnostics (like a time-of-flight mass spectrometer). In the middle is an extreme ultraviolet refocusing telescope based on toroidal mirrors.

We excited the 8S transition at 110 nm with the Ramsey-comb method combined with high-harmonic generation (HHG), reaching an unprecedented accuracy of 2.3 x 10^-10 with HHG light. This proves that the Ramsey-comb method works very well together with HHG, and that phase effects in the HHG process (adiabatic, and due to ionization) are no problem. More information will be posted soon, but until then you can read our paper in Phys. Rev. Lett. (2019), and our most recent paper in Phys. Rev. A (2020).

Below: Schematic of the xenon experiment

Towards 1S-2S He+ spectroscopy

We are now converting the xenon setup shown above for the 1S-2S He+ experiment and adding a lot of hardware, electronics and software. In the beginning of 2020 a new ion trap was made that will be used to trap He+ and Be+ (for sympathetic cooling). The trap itself was designed and made by Elmer Grundeman, with generous help and based on previous designs from the group of prof. Tanja Mehlstaeubler at the PTB in Germany. In fact, Elmer went to PTB to use their facilities to put the trap together.

Below on the left you can see a photo of the trap still wrapped in protective foil just after it arrived in our lab in Amsterdam. On the right you see the special trap-mounting construction that will house the ion-trap. It enables alignment of the trap in all degrees of freedom (designed and built by Julian Krauth) and in the picture it is mounted in an interferometric test-setup for stability measurements.

Note for Master and Bachelor students: on several aspects of this project we can define projects. Please contact Kjeld Eikema at k.s.e.eikema@vu.nl

Below: parts of the new Ramsey-comb laser system (no. 2) designed for He+ excitation near 30 nm with extra low phase noise. This system, built and designed by Mathieu Colombon and Charlaine Roth, uses as a starting point a commercial (Menlo Systems) ultra-stable frequency comb laser system (ULN, doubled Er-fiber) that is stabilized to a sub-Hz ultra-stable laser (also Menlo) and a Cs atomic clock. The parts shown below are different components of the new pump laser for the parametric amplifier of the comb laser pulses.

References:

[1] C.G. Parthey et al., PRL 107, 203001 (2011)
[2] R. Pohl et al, Nature, vol. 466, pp. 213-216 (2010)
[3] A. Antognini, et. al., Science 339, 417-420 (2013)
[4] R. Pohl et al., Science 353, 669-673 (2016)
[5] A. Beyer et al., Science 358, 79-85 (2017)
[6] H. Fleurbaey et al., ArXiv 1801.08816v1 (January 2018)
[7] J. Morgenweg, I. Barmes, K.S.E. Eikema, Nature Physics 10, 30-33 (2014)
[8] J. Morgenweg, K.S.E. Eikema, Phys. Rev. A 89, 052510 (2014)
[9] R.K. Altmann, S. Galtier, L.S. Dreissen, and K.S.E. Eikema, Phys. Rev. Lett. 117, 173201 (2016)
[10] J. Liu et al., J. Chem Phys. 130, 174306 (2009)

We gratefully acknowledge financial support from the following organizations:

Questions? Contact: k.s.e.eikema@vu.nl