XUV frequency-comb metrology on the ground state of helium

The operation of a frequency comb at extreme ultraviolet (xuv) wavelengths based on pairwise amplification and nonlinear upconversion to the 15th harmonic of pulses from a frequency-comb laser in the near-infrared range is reported. It is experimentally demonstrated that the resulting spectrum at 51 nm is fully phase coherent and can be applied to precision metrology. The pulses are used in a scheme of direct-frequency-comb excitation of helium atoms from the ground state to the 1s4p and 1s5p ¹  P₁ states. Laser ionization by auxiliary 1064 nm pulses is used to detect the excited-state population, resulting in a cosine-like signal as a function of the repetition rate of the frequency comb with a modulation contrast of up to 55%. Analysis of the visibility of this comb structure, thereby using the helium atom as a precision phase ruler, yields an estimated timing jitter between the two upconverted-comb laser pulses of 50 attoseconds, which is equivalent to a phase jitter of 0.38  (6) cycles in the xuv at 51 nm. This sets a quantitative figure of merit for the operation of the xuv comb and indicates that extension to even shorter wavelengths should be feasible. The helium metrology investigation results in transition frequencies of 5  740  806  993  (10) and 5  814  248  672  (6) MHz for excitation of the 1s4p and 1s5p ¹  P₁ states, respectively. This constitutes an important frequency measurement in the xuv, attaining high accuracy in this windowless part of the electromagnetic spectrum. From the measured transition frequencies an eight-fold-improved ⁴He ionization energy of 5  945  204  212  (6) MHz is derived. Also, a new value for the ⁴He ground-state Lamb shift is found of 41  247  (6) MHz. This experimental value is in agreement with recent theoretical calculations up to order m⁶ and m²/M⁵, but with a six-times-higher precision, therewith providing a stringent test of quantum electrodynamics in bound two-electron systems.