Improved Measurement of the Hydrogen 1S - 2S Transition Frequency (1107.3101v1)

Abstract: We have measured the 1S - 2S transition frequency in atomic hydrogen via two photon spectroscopy on a 5.8 K atomic beam. We obtain $f_{1S-2S} = 2 466 061 413 187 035 (10)$ Hz for the hyperfine centroid. This is a fractional frequency uncertainty of $4.2\times 10^{-15}$ improving the previous measure- ment by our own group [M. Fischer et al., Phys. Rev. Lett. 92, 230802 (2004)] by a factor of 3.3. The probe laser frequency was phase coherently linked to the mobile cesium fountain clock FOM via a frequency comb.

• The paper demonstrates a 3.3× improvement in the hydrogen 1S–2S frequency measurement using two-photon spectroscopy on a 5.8 K atomic beam.
• It details methodological innovations including a sub-1 Hz diode laser system and direct 2S velocity distribution measurement to reduce systematic uncertainties.
• The refined measurement enhances the determination of fundamental constants and tests of QED, strengthening high-precision atomic metrology.

Improved Measurement of the Hydrogen $1S - 2S$ Transition Frequency

The paper "Improved Measurement of the Hydrogen $1S - 2S$ Transition Frequency" presents a significant advancement in the precision measurement of the $1S - 2S$ transition in atomic hydrogen using two-photon spectroscopy on a 5.8 K atomic beam. The authors report achieving a transition frequency of $f_{1S-2S} = 2,466,061,413,187,035(10) \text{ Hz}$, with a fractional frequency uncertainty of $4.2 \times 10^{-15}$, representing a factor of 3.3 improvement over the previous best measurement from 2004.

Methodological Enhancements

The authors attribute this achievement to several key advancements in their experimental setup:

1. Diode Laser System: The replacement of a dye laser with a diode laser has improved frequency stability, providing more reliable measurements across sessions. The diode laser exhibits a line width of less than 1 Hz and a fractional frequency drift of $1.6 \times 10^{-16} \, \text{s}^{-1}$.
2. Velocity Distribution Measurement: A direct measurement of the $2S$ velocity distribution contributes to a more accurate determination of the second-order Doppler effect, essential for reducing systematic uncertainties significantly.
3. Quench Laser Implementation: An innovative use of a quench laser reset the population to the ground state immediately after hydrogen emerges from the nozzle, mitigating issues such as frequency shifts associated with high atom density and potential Stark shifts in the setup.

Detailed Experimentation

The beam apparatus characterized includes differential pumping to maintain lower pressures favorable for spectroscopy, and the transition is excited via a standing wave formed by a laser cavity of finesse 120. The atomic hydrogen, dissociated and cooled, goes through this apparatus, allowing for precise excitation and detection of $2S$ states via quenching with an electric field that leads to Lyman-α photon emission. The probe laser frequency is phase-locked to a cesium fountain clock, ensuring order-of-magnitude improvement in frequency accuracy.

Systematic Effect Compensation

Two significant systematic effects are meticulously addressed:

• Second Order Doppler Effect: The authors employ time-resolved detection techniques and velocity distribution measurements to robustly correct and compensate the second-order Doppler effect, achieving an uncertainty of $2.0 \times 10^{-15}$.
• ac Stark Shift: The contribution due to ac Stark shifts is minimized through linear extrapolation after accounting for non-linear effects, with additional modeling validated through Monte Carlo simulations, resulting in an uncertainty reduction to $0.8 \times 10^{-15}$.

Data Analysis and Uncertainty Budget

The authors provide a comprehensive view of their measurement's precision by presenting an exhaustive uncertainty budget where contributions from spectroscopic statistical uncertainty, Doppler effect corrections, and ac Stark shifts represent the majority. Lesser contributions include Zeeman shifts and other configuration-induced effects, maintaining the results' integrity.

Implications and Future Directions

This refined measurement of the $1S - 2S$ transition is instrumental in determining the Rydberg constant and testing QED predictions. The improved precision also enhances hydrogen-based CPT tests, facilitating comparison with antihydrogen. For fundamental physics, the precision limits set on transition frequencies offer a robust platform to challenge potential variations in fundamental constants and Lorentz invariance principles. Future developments could see further enhancements in frequency stability and control mechanisms, potentially stimulating more precise explorations in atomic physics and fundamental constant reevaluations.

Conclusion

The reported enhancements within this paper underscore the importance of innovation in laser technology, beam manipulation, and systematic error compensation. This advancement strengthens the utility of the hydrogen $1S - 2S$ transition as a benchmark in high-precision metrology, quantum mechanics testing, and beyond. Continued efforts in this research area are poised to expand the boundaries of experimental physics precision and theoretical validation.