Energy levels in atomic hydrogen

An experiment is underway at NPL to make accurate measurements of the frequency of a series of two-photon transitions in atomic hydrogen. This work will contribute towards an improved determination of the Rydberg constant.

Hydrogen is unique among optical frequency standards in providing a range of calculable reference frequencies, from radio frequencies into the vacuum ultraviolet region, which are linked by well-defined atomic theory and are provided by the same atomic system. The scaling factor for these transition frequencies is the Rydberg constant, which is currently known to 6.6 parts in 10^{12 [1]}. Although the 1S-2S transition frequency in hydrogen has been measured to 1.4 parts in 10^{14 [2]}, this is not sufficient to determine the Rydberg constant with higher accuracy because of quantum electrodynamic and nuclear size corrections to the energy levels. To separate out these effects additional transition frequencies must be measured.

Jeff Flowers working on the
NPL hydrogen atomic beam

In our experiment we are studying the 2S-nS,D transitions by Doppler-free two-photon laser spectroscopy on a metastable hydrogen atomic beam^[3]. In the atomic beam, metastable atoms are produced by electron impact excitation and detected by electric field quenching of the metastable state^[4]. To induce the 2S-nS,D transitions we use a Ti:sapphire laser which is stabilized to a high-finesse ultralow-expansion cavity and which is collinear with the metastable atomic beam. A build-up cavity constructed around the atomic beam produces the counter-propagating beams required for the Doppler-free two-photon excitation and increases the excitation rate. The transitions are detected by monitoring the reduction in the number of metastable atoms reaching the far end of the beam as the laser frequency is swept through the resonance.

We have recently observed the first laser-induced signals from our apparatus and made a preliminary measurement of the 2S_1/2–8D_5/2 transition frequency using a hydrogen-maser-referenced femtosecond optical frequency comb. Detailed studies of systematic frequency shifts are in progress.  The femtosecond comb provides the capability to study all optical transitions with n > 4 under nominally identical conditions. This enables us to carry out more stringent tests of a number of systematic effects than in previous experiments.

243 nm laser source for optical
excitation of the 2S state in
atomic hydrogen

The limiting systematic effects in this first experiment are expected to be ac Stark shifts and saturation effects associated with the high laser power required to induce the two-photon 2S–nS,D transitions. To reduce these effects, we propose in a later stage of the experiment to produce the metastable 2S state by two-photon optical excitation from the ground state using a stabilised 243 nm laser source. Optical excitation, in contrast to electron impact excitation, imparts no additional momentum to the atoms and so should generate an intense, well-collimated source of metastable atoms, which can be cooled to increase further the atomic density in the beam. This in turn would enable the 2S–nS,D transitions to be excited using lower laser power, reducing the light shifts. A separate apparatus is being constructed to test the optical excitation efficiency, while electron impact excitation continues to be used for initial experiments in the primary apparatus.

This work is being carried out in collaboration with Dr Patrick Baird from the University of Oxford.

1. P. J. Mohr and B. N. Taylor, Rev. Mod. Phys. 77, 1 (2005).
2. T. W. Hänsch et al., Phil. Trans. Roy. Soc. A 363, 2155 (2005).
3. J. L. Flowers et al., IEEE Trans. Instrum. Meas. 56, 331 (2007).
4. F. Biraben et al., Rev. Sci. Instrum. 61, 1468 (1990).