A precision millimeter-wave measurement of the Rydberg frequency

Abstract

The Rydberg frequency, cR[infinity], sets the frequency scale for the spectrum of hydrogen atoms. From a frequency measurement of one transition in hydrogen, cR[infinity] can be extracted and the frequency of any other transition can be predicted, given that the reduced-mass, relativistic, QED, and proton structure corrections can be computed to the desired accuracy. Recent advances in optical frequency techniques applied to transitions involving low-lying states of hydrogen have decreased the uncertainty in cR[infinity], to 7.6 x 10⁻¹². This thesis presents our measurement of cR[infinity] using millimeter-wave transitions between high-lying "circular Rydberg" states of atomic hydrogen with a principle quantum number, n, between 27 and 30. This measurement provides an independent check, in a different regime, of the optical measurements. Our measurement, cR[infinity] = 3 289 841 960 306(69) kHz with an uncertainty of 2.1 x 10⁻¹¹, is consistent with the CODATA 98 recommended value.