The Stefan Meyer Institute works on hyperfine spectroscopy using beams of hydrogen and deuterium in order to search for physics beyond the Standard Model of particle physics. The experiments are performed as support for tests of the carge-parity-time (CPT) symmetry by measurements of the hyperfine splitting of antihydrogen at the antiproton decelerator of CERN as pursued by the ASACUSA collaboration. In addition direct searches for CPT and Lorentz Invariance Violation (LIV) are possible and a quest for production of ever colder atomic beams has started within the newly formed GRASIAN collaboration.

In these experiments atomic beams pass an interaction region, where microwaves of 1.42 GHz for (anit-) hydrogen or 327 MHz for deuterium, i.e. at the hyperfine splitting (HfS), are provided. Rabi spectroscopy uses a single interaction region, whereas Ramsey spectroscopy relies on two such regions for improved precision. The HÿDRA project embraces these set-ups and goals as expressed in its acronym, which stands for Hydrogen and Deuterium Ramsey/Rabi Apparatus.

The original plan was a sort of jack of all trades device as shown below, where all transitions of hydrogen and deuterium could have been studied. Eventually the efforts towards deuterium have been separated to become a pure matter project, while projects including hydrogen are also targeting antihydrogen. 

The Hyperfine Structure

The interaction of the magnetic moments of the electron and the proton leads to the hyperfine structure of the hydrogen atom. In the absence of any external magnetic field the ground-state hyperfine structure consists of a singlet (F=0) and a degenerate triplet state (F=1). An external static magnetic field lifts this degeneracy due to different Zeeman shifts of the sublevels.

The figure below shows the so-called Breit-Rabi diagram, which summarizes this structure of the energy levels as a function of an external magnetic field. The Zeeman shift of two states of the triplet (MF=0,1) increases the energy level, making them to low-field-seekers, i.e. they feel a force towards lower magnetic field when exposed to a field gradient. The remaining triplet state (MF=-1) and the singlet state are high-field-seekers. The two states with magnetic quantum number equal to zero (MF=0) have a hyperbolic, i.e. only a second order, dependence on the external magnetic field. The other two states have a linear dependence. An oscillating magnetic field of matching frequency w.r.t. the splitting between two energy levels can drive transitions from one hyperfine sub-state to the other. The transition between the two states with MF=0 is called σ-transition and features the weakest magnetic field sensitivity. The π-transitions include one of the states with linear Zeeman shifts and are much more sensitive to magnetic fields.

While the hyperfine structure of hydrogen is explained by the magnetic interaction of two spin 1/2 particles, the nucleus of deuterium (deuteron = one proton and one neutron) is a spin 1 particle and therefore a richer structure is observed. The figure below shows the Breit-Rabi diagram for the case of deuterium and separately the frequency of the observable transitions. In addition the electron cyclotron resonance (ECR) frequency is plotted, which shall be used for an absolute calibration of the external magnetic field.

Standard Model Extension

The Standard Model Extension (SME) by Kostelecký and co-workers [] systematically explores all possible Lagrangian terms violating CPT or Lorentz invariance. Each term is connected to a coefficient that can be tested or constrained by matching experiments. HÿDRA can map the expected field dependence of the transition frequencies over a wide range to distinguish between the CPT broken and unbroken scenarios. Searches for sidereal or annual variations combined with swaps of the magnetic field address SME coefficients relating to LIV. Deuterium is of special relevance in direct tests (i.e. without comparison to antimatter) as the much increased momentum of the proton in the nucleus of deuterium when compared to hydrogen leads to a billionfold (or even higher) increase of sensitivity to certain SME coefficients.

Rabi and Ramsey Spectroscopy

In-beam spectroscopy on atomic species proceeds in the following three steps: (i) production of a polarised atomic beam, (ii) resonant excitation of transitions, and (iii) state-selective detection of atoms. An illustrative sketch itentifying those three steps is provided  below showing the setup as used at CERN in 2016.

Beams are produced from hydrogen molecules by dissociation in a microwave driven plasma. The beam is guided through a cryogenic tubing and nozzle in order to reduce the beam velocity. It can be modulated by a chopper to facilitate background suppression and time-of-flight measurements. A sextupole magnetic field provides strong gradients, which separate low- and high-field-seeking states. This field configuration leads to two-dimensional refocussing of low-field-seekers.

The geometry of the interaction region depends on the system under study and the method (Rabi/Ramsey) to be used. In every case an extremely homogenous external magnetic guiding field, that gives precise control over the Zeeman splitting is mandatory. This is achieved by an adequate coil configuration and a passive mu-metal shielding around it to suppress residual magnetic fields. Inside the coils a microwave structure provides the oscillating magnetic field needed to stimulate the hyperfine transitions.

A second set of sextupole magnets analyses the beam, i.e. if low-field-seekers have been turned into high-field-seekers in the interaction region they get removed from the beam. The detection uses ionization, mass selection and single ion counting on a channeltron. Switching from electron impact ionization to more selective laser ionization is currently prepared. If the microwave frequency is not in resonance with the hyperfine transition the full beam is detected. On resonance a drop in count rate is observed. A fit to the obtained count rate spectrum yields the transition frequency.

For the technical details of the beam production we refer to our publications [].

With a similar setup we've perfomed the most precise in-beam measurement of the hyperfine splitting of hydrogen, reaching 2.7 ppm [].

The Deuterium Rabi Experiment

more information available soon.


Core Team at SMI:

  Prof. Dr. Eberhard Widmann 
  Dr. Martin Simon
  Carina Killian
  Amit Nanda

RF support by CERN:

  Dr. Fritz Caspers
  M.Eng. Manfred Wendt


This project continues the hydrogen experiments in support of the antihydrogen physics program of ASACUSA, which started during 2012 to 2017 under the Advanced Grant "HBAR-HFS" no. 291242 of the European Research Council awarded to Prof. Dr. Eberhard Widmann [].
The position of Amit Nanda has been funded from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 721559 []. Funding continued from the FWF through DKPI (Doktoratskolleg Particles and Interactions, W 1252) [].
The HyDRA project received funding for the subtopic DRabi from the investment initiative 2020 of the Austrian academy of sciences.