Method for High-Resolution Frequency Measurements in the Extreme Ultraviolet Regime: Random-Sampling Ramsey Spectroscopy

Ramsey-like schemes have been recently introduced in combination with high-order laser harmonic sources for high-resolution spectroscopic studies in the extreme ultraviolet (XUV). Here we demonstrate a novel method, combining measurements only in a limited subset of randomly chosen time-sampling intervals, which lead us to perform the first high-resolution XUV spectroscopy of atomic argon with a simple split-pulse setup. Providing an experimentally simple and convenient solution to the problem of performing high-resolution absolute frequency measurements in the XUV, our approach will help paving new roads into this challenging spectral territory.

Figure 1

Schemes of different options for scanning the delay (left panels) in a Ramsey spectroscopy experiment with short excitation pulses, and corresponding retrieved spectra (right panels). (a) The acquisition of Ramsey fringes in a single time window of width $\delta t$ provides a spectral resolution proportional to $1/\delta t$. (b) Measuring the Ramsey signal in two short time windows delayed by $T$ provides a potential spectral resolution of $\approx 1/T$ but may lead to ambiguities in the peak determination. (c) A sequence of $N$ randomly spaced Ramsey acquisitions results in an effective cancellation of the satellite peaks and leads to the correct identification of the transition frequency in a fraction of the acquisition time. (d) Finally, a series of two-time window Ramsey acquisitions at random delays $T_i$’s can be combined by taking the product of the individual spectra.

Figure 2

Schematic view of the experimental setup and of the Ar level scheme. An ultrastable Michelson interferometer is used to split the ir pump pulses from the laser into two time-delayed replicas; HHG indicates the process of high-order harmonic generation and the selection of the ninth harmonic order at 87 nm; pairs of identical XUV pulses delayed by time $t$ are thus produced and used to excite the Ar transition in a gas jet. Further excitation by a counterpropagating ir pulse ionizes the atoms and the produced ions are finally detected by a TOF spectrometer.

Figure 3

Products of the $|FT{|}^2$ of $N$ pairs of randomly sampled Ramsey acquisitions. The curves are vertically displaced for presentation purposes and the origin of the frequency axis is taken as the NIST frequency for the investigated transition [20]. From bottom to top, successive plots show that increasing the number $N$ of randomly sampled Ramsey acquisition pairs leads to the progressive cancellation of the satellite spectral peaks and to the identification of the atomic resonance (plot $N=20$, also shown in detail in the top inset). The wide $\sin c^2$ profile corresponding to a mean of the squared FTs of single time window acquisitions is also shown in the main plot. The bottom inset shows a detail of the spectrum around the origin, where the $|FT{|}^2$ of each experimental Ramsey pair is plotted (after rescaling) and compared to the product of the previous ones (black lines). It is worth noting that the different Ramsey pairs were accumulated in experimental runs extending over several days.