Metrology of high-n Rydberg states of molecular hydrogen with Δv/v=2 x 10-10 accuracy

Precision spectroscopy of molecular Rydberg states of high principal quantum number (n >= 50) followed by Rydberg series extrapolation currently represents the most accurate method of determining the ionization energies of neutral molecules. Until recently, such determinations relied on the use of pulsed laser radiation and supersonic molecular beams, which limited the spectral linewidths and induced ac Stark shifts, thus causing undesirable statistical and systematic uncertainties. We report on the combination of single-mode continuous-wave laser radiation, calibrated with a frequency comb, with slow supersonic beams expanding from low-temperature reservoirs, to record transitions to high-n molecular Rydberg states with unprecedented accuracy. As illustration, we present the result of a measurement, with a relative frequency accuracy of Delta nu/nu = 2 x 10(-10) and an absolute accuracy of 64 kHz, of the transition from the GK (1)Sigma(+)(g)(upsilon = 0,N = 2) state of H-2 to the n = 50 f Rydberg state belonging to a series converging on the X+ 2 Sigma(+)(g)(upsilon(+)= 0, N+= 0) ground state of H-2(+). The accuracy of the result [nu(NIR)=380132832.236(0.035)(stat)(0.054)(sys)MHz] approaches the accuracy that can be achieved in similar measurements on ultracold alkali-metal-atom samples, although the dominant sources of uncertainties are different. The implications of our result for precision measurements of the adiabatic ionization energy of H-2 and of the energy-level structure of H-2(+) are discussed.