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Probing Physics beyond the Standard Model from Molecules

Periodic Reporting for period 4 - NEWPHYS-MOLECULES (Probing Physics beyond the Standard Model from Molecules)

Reporting period: 2020-03-01 to 2021-11-30

The Standard Model of physics is incomplete. Gravity is not understood at the quantum level, dark matter and dark energy are not explained, and (string)-theories searching to cover these shortcomings are only consistent in higher-dimensional spaces, while only four of those dimensions are observed. The mystery of finely tuned strengths of the fundamental forces, providing us with a Universe of complexity, remains unexplained. This calls for new physics that can be explored also at the atomic scale in the low energy domain. That is the paradigm underlying the present proposal: Effects of new physics - either related to hitherto unknown particles or to symmetry-breaking phenomena - will manifest themselves as minute shifts in the quantum level structures of atoms and molecules, in minute drifts over time or dependencies on environmental conditions.

In the project precision frequency measurements were performed on the hydrogen molecule, the main H2 isotopic species and also the less abundant isotopic species. For this a dedicated molecular beam experiment and a novel laser setup were built to perform two-photon Doppler-free experiments with vacuum-ultraviolet laser radiation. The main results of the project are the precision determination of the dissociation energies (the energy it takes to break the chemical bond of the molecule) of H2, D2 and HD species, all at 10-digit precision. These experimental results are a factor of 30 more accurate than the values known at the beginning of the project. During the course of my experimental project scientists in Poland have calculated these benchmark values via the advanced theory of quantum-electrodynamics (QED). Experiment and theory are found to be in excellent agreement, therewith proving the validity of the Standard Model of Physics in this molecular regime. Moreover, the possibility for the existence of a fifth fourth beyond the four known forces (electromagnetism, gravity, strong and weak nuclear forces) was further constrained: if it exists at a length scale of 1 Angstrom it must be smaller than 10^(-10) times the strength of electromagnetism.

Besides these main results, some additional, connected, results were obtained:
- For the first time precision spectroscopic measurements were performed on the tritium-containing molecular hydrogen species (T2, HT and DT); their vibrational splittings were measured accurately and found in agreement with theory
- The research on neutral hydrogen was extended to the HD+ molecular ion, and a highly accurate measurement was performed by sympathetic laser-cooling in an ion trap. The precision measurement of an overtone vibration comprises a further test of QED.
- As highlighted in the proposal, via photolysis of H2S molecules the hydrogen (H2) molecule can be produced in exotic quantum states. As an important result precision measurements were performed on quasi-bound states (shape resonances) in H2. From these experiments a very precise value for the “scattering length” was determined: this number governs collision between hydrogen atoms.
- As a side issue, defined in the proposal, radio astronomic observations were carried out (with the Atacama Large Millimeter Array in Chile) to further constrain the possibility of varying constants: the proton-electron mass ratio has varied by less than 10^(-7) in the past 7 billion years. Astronomical observations of hydrogen molecules in the optical regime, with the Very Large Telescope, have led to constraints on the same fundamental constants: at distances of up to 12.4 billion years the mass ratio had varied by less than 5 parts per million.

In the project methods of cavity-enhanced molecular detection were developed. We have defined a Proof-of-Concept side-project (BREATHSENS) to sensitively measure acetone molecules in dairy farms (probing cow diseases).
Precision measurements on the hydrogen molecule have been investigated. Results have been obtained in three directions:

1) The measurements of the dissociation energy of H2 have led to a determination of the value of D0 in both ortho-hydrogen and parahydrogen, and importantly the para-ortho splitting between the two lowest rotational levels in the molecule were determined. In addition an alternative method was explored, not following two-photon vacuum ultraviolet radiation, but that of Ramsey-comb spectroscopy using frequency-comb lasers in a direct method. These papers bear i
Next to that the dissociation energies of the D2 and HD isotopologues were also determined at similar accuracies, i.e. a factor of 25 improvement of the previous values.

2) An infrared transition in the HD molecule has been measured a thousand times more accurate then previously. For this an entirely new measurement setup has been built allowing us to measure a "Lamb-dip" so that the Doppler effect could be nullified in a laser experiment.

3) For the first time laser precision measurements could be performed on Tritium molecules, a special form of heavy hydrogen. these measurements were made possible through a collaboration with the Tritium Laboratory at KIT-Karlsruhe.
The measured values are all more accurate than their theoretical evaluation and the results have spurred activity by theorists, now performing calculations on the hydrogen isotopes, including relativistic and QED effects. Measurements were performed for all three isotopologues: T2, HT and DT.

4) As discussed in the proposal the photolysis of H2S molecules would lead to exotic quantum states in the H2 molecule. In the proposal the focus was on preparing translationally cold states, i.e. molecules moving at very low speeds in the laboratory frame. An important result from our experiments starting from two-photon photolysis of H2S is the production of quasi-bound states. These shape resonances or states bound by the centrifugal part of the potential could be measured for combinations of high vibrational and rotational quantum numbers in a unique fashion for H2.

5) While the core of the work is focused on experimental studies of neutral hydrogen molecules, my team also explores measurements on the HD+ ion. Measurements on Doppler-free two-photon transitions were measured that provide a sensitive test of QED-theory and the Standard Model in a three-particle system. The measurements lead to an improved values for the proton-electron mass ratio at the part-per-trillion level. This represents the most accurate determination of that mass-ratio, and for the first time that such result was obtained form optical frequency measurements in a molecular species.

6) A number of studies were carried out via radio astronomy using various telescopes probing the methanol molecule, the most sensitive molecular species for detecting possible variations of fundamental constants. The study with the ALMA telescope, published in 2021 yields a rigorous constraint on the variation of the proton-electron mass ratio of 10^(-7) for cosmological distances of 7 billion light years.
The central result is that the dissociation energies of all three hydrogen isotopologues (H2, D2 and HD) have been measured with an accuracy of about a factor of 25 better than previous. Agreement was found with theoretical results from QED calculations. Hence the Standard Model of physics was tested at a higher level of accuracy.
Figure: Progress on accurate measurements of the dissociation energy of the hydrogen molecule