Precision Spectroscopy of the Hydrogen Hyperfine Structure

Precision spectroscopy nowadays is made with tunable laser beams send on cold atoms at rest to induce transitions. In combination with a frequency comb a relative energy resolution down to 10^-13 and in absolute values 10^-12 eV was reached for the 2S-1S transition in hydrogen. With components of a Lamb-shift polarimeter and a so-called Sona transition unit it was now possible to observe transitions between the hyperfine substates of hydrogen with an energy difference of a few neV. In this case a beam of metastable atoms in a single hyperfine substates is sent through a static magnetic field of two solenoids with opposite direction. The longitudinal field component has a nearly sinusoidal shape and, thus, the through going atom is experiencing an oscillating magnetic field in its rest frame. The effective value of the maximum fields in the center of the coils define the average magnetic field seen by the atom, which corresponds to the x-axis in the Breit-Rabi diagram. The time-of-flight Δt depends on the velocity of the beam v and the distance of the coils that determines the wavelength λ. Therefore, the frequency corresponds to f = 1/Δt = v/λ and the energy of the photons is following the Planck-Einstein relation E = h · f = h · v/λ. Here it should be mentioned that for the hydrogen atom the velocity of the incoming radio-field oscillation is not the speed of light but just the velocity of the atoms in the laboratory system itself and is on a level of 10⁵ m/s. The beam velocity and the wavelength can be measured with a relative uncertainty of 10^-3 and, thus, the total uncertainty can be 10^-12 eV, a similar level like in the most precise measurements before. In addition, all odd integer multiples of this energy will induce transitions too, until the energy difference between the hyperfine substates will fit at the corresponding magnetic field in the Breit-Rabi diagram. The photon energy can be changed by either changing the distance between the coils or modifying the velocity of the beam. By that a huge number of measurements is possible to determine the energy differences in the Breit-Rabi diagram and in this way the corrections due to QED on a level of 10^-12 eV are in range. Further improvements are possible …

As shown in the figure above, the experimental setup starts with an electron-impact ionizer that is producing an intense beam of protons at a sharp energy in the few keV range. As next a Wien filter is used to separate the protons from all other ions produced by the source and it even helps to specify the beam velocity more precisely. By charge exchange with cesium vapor metastable hydrogen atoms in all four hyperfine substates are produced. A subsequent spinfilter of a Lamb-shift polarimeter will separate a single hyperfine substate, either α1 (m_J=+1/2, m_I=+1/2) or α2 (m_J=+1/2, m_I=-1/2). The oscillating static field of the Sona transition unit has two effects on the occupation numbers: First of all, it is inducing an exchange of the occupation numbers of the substates α1 and β3 (m_J=-1/2, m_I=-1/2) by exchanging the magnetic field direction non-adiabatically. In parallel the magnetic field oscillation can be interpreted as a single ‘radio-wave laser-pulse’ that can induce transitions between the hyperfine substates, i.e. β3 -> α2 and afterwards α2 -> α1, until the energy difference between this states corresponds to an odd integer multiple of the basic energy E = h · v/λ. A second spinfilter will transmit metastable atoms either in the state α1 or α2 and their amount is measured by quenching them into the ground state due to a strong electric field (Stark effect). The results can be seen in the following figure.

This new method allows to directly induce transitions between quantum states in an energy range below 10 neV. Thus, it should be possible to test the expected QED corrections on the binding energies. In the figure above deformations of the peaks are obvious that are produced by the interference of the transitions between the three states. Nevertheless, the spinfilter can be modified that they transmit both α states at the same time. By that a transition of atoms in the β3 state into a superposition of both α states can be observed. Another possible upgrade of this experiments would be a new type of spinfilter that is under development. This modified spinfilter will allow to measure the occupation numbers of both β states separately and by that the measurements will be overdetermined.