Extreme Ultraviolet Frequency Comb Metrology

The remarkable precision of frequency-comb (FC) lasers is transferred to the extreme ultraviolet (XUV, wavelengths shorter than 100 nm), a frequency region previously not accessible to these devices. A frequency comb at XUV wavelengths near 51 nm is generated by amplification and coherent up-conversion of a pair of pulses originating from a near-infrared femtosecond FC laser. The phase coherence of the source in the XUV is demonstrated using helium atoms as a ruler and phase detector. Signals in the form of stable Ramsey-like fringes with high contrast are observed when the FC laser is scanned over $P$ states of helium, from which the absolute transition frequency in the XUV can be extracted. This procedure yields a ${}^4\mathrm{He}$ ionization energy at $h\times 5945204212(6)\mathrm{MHz}$, improved by nearly an order of magnitude in accuracy, thus challenging QED calculations of this two-electron system.

Figure 1

(a) Spectral and temporal structure of the generated light (left to right): FC of the continous coherent pulse train from the FC laser, the cosine-modulated spectrum of a pair of amplified pulses, and odd harmonics of the amplified FC laser pulses each containing a cosine-modulated XUV comb corresponding to the XUV pulse pair. (b) Simplified ${}^4\mathrm{He}$ level scheme, XUV comb excitation at 51.5 nm from the $1s^2$ ground state to the $1s5p$ excited state and state-selective ionization by a pulse at 1064 nm. (c) Schematic of the experimental setup. $D$: beam mask, $L$: focusing lens, $f=50\mathrm{cm}$, $I$: iris to separate XUV from IR. The pump laser provides both the 532 nm for pumping the OPA as well as 1064 nm for ionization of helium.

Figure 2

Measured excitation probability (blue circles) of helium at 51.5 nm on the $1s^2$ ${}^{1}S_0-1s5p{}^{1}P_1$ transition, normalized by the XUV pulse energy, as a function of the repetition rate $f_{\mathrm{rep}}$ of the frequency-comb laser. In this example $f_{\mathrm{CEO}}$ is locked at 46.21 MHz, and a $1:5$ $\mathrm{He}:\mathrm{Ne}$ mixture is used for the atomic beam. The red line is a fit to the data.

Figure 3

(top) ${}^4\mathrm{He}$ ground state ionization energy $\pm n\times f_{\mathrm{rep}}$ based on the $1s^2$ ${}^{1}S_0-1s5p{}^{1}P_1$ (blue circles) and the $1s^2$ ${}^{1}S_0-1s4p{}^{1}P_1$ transition (red squares). (bottom) Zoom at the coincidence point for all repetition frequencies. The vertical line at $+38(6)\mathrm{MHz}$ represents the weighted mean. All values are relative to the theoretical value of 5 945 204 174 MHz [26]. (square point slightly shifted up for visibility).