Method for High-Resolution Frequency Measurements in the Extreme Ultraviolet Regime: Random-Sampling Ramsey Spectroscopy R. Eramo, 1,2 S. Cavalieri, 2,3 C. Corsi, 2 I. Liontos, 2 and M. Bellini 1,2 1 Istituto Nazionale di Ottica (INO-CNR), L.go E. Fermi 6, 50125 Florence, Italy 2 European Laboratory for non linear Spectroscopy (LENS), 50019 Sesto Fiorentino, Florence, Italy 3 Department of Physics, University of Florence, 50019 Sesto Fiorentino, Florence, Italy (Received 16 December 2010; published 27 May 2011) 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. DOI: 10.1103/PhysRevLett.106.213003 PACS numbers: 32.30.Jc, 42.62.Eh, 42.65.Ky, 82.53.Kp High-order laser harmonics are a convenient source of coherent radiation in the extreme ultraviolet regions of the electromagnetic spectrum, where investigations of simple atomic species and highly developed calculations promise new accurate tests of bound-state electrodynamics [1]. The use of high-order laser harmonics as a spectroscopic tool in the extreme ultraviolet (XUV) has been recently proven possible by means of Ramsey-like techniques [2–7], based on the idea first introduced by Ramsey in 1950 [8] and relying on the extension of the effective interrogation time by using pairs (or sequences) of phase- coherent [9–11], time-delayed XUV ultrashort excitation pulses [12–15]. Low-order laser harmonics [16,17] and broadband XUV pulses [18] have been also used in the same context. Just like in standard Fourier transform spec- troscopy (FTS), the effective spectral resolution of these methods scales inversely with the maximum time delay between the exciting pulses, and the achievable resolving power corresponds to the number of optical periods con- tained in such a delay. This is closely related to the intuitive rule according to which, in order to increase the accuracy of a frequency measurement, one has to correspondingly increase the measuring time so as to count more and more oscillation periods. An experiment performed on high-lying bound states of Argon [14] has recently demonstrated a potential resolving power higher than the best currently available in synchro- tron facilities by measuring Ramsey quantum interferences in the excitation signal at delays larger than 100 ps. Indeed, if a Michelson-type interferometer is used to introduce the interpulse delay, and in the case of XUV radiation with wavelengths in the 30–100 nm range, just a few mm of mirror displacement are sufficient to obtain a resolving power larger than 10 5 . However, if accurate measurements of transition frequencies are to be performed, all the atomic quantum interference fringes have to be accurately followed over a long time interval. While this is the norm for standard FTS in the visible and ir regions, following this approach for Ramsey spectroscopy in the XUV is far from straightforward and technically almost impossible. In fact, since these measurements are normally performed in an ion-electron counting regime, they are intrinsically very slow and one has to face long acquisition times that pose severe constraints on the overall system stability. Here we demonstrate a novel method, theoretically pro- posed by our group [19], to overcome these constraints and make measurement times substantially shorter, by acquir- ing fringes only over a limited subset of randomly chosen delay intervals in the whole delay range T that is needed for a given target spectral resolution. By significantly reducing the experimental difficulty of XUV Ramsey-like spectroscopy, we are able to perform the first high- resolution absolute measurement of an XUV atomic transition frequency with a simple pulse-splitting interfer- ometer. The method is nevertheless very general and can thus be advantageously exploited also in more sophisti- cated schemes and/or in other spectral regions. A Ramsey-like experiment consists in exciting an atomic system by a first pulse and then probing the induced coherence with a second pulse delayed by t and with a fixed phase relation to the first pulse. Any observable related to the atomic excitation will exhibit Ramsey oscillations with a period given by the inverse of the atomic transition frequency. By scanning the delay t between successive excitations, the effects of such oscillations can be trans- ferred to state populations and subsequently detected. It is worth examining in some detail a few different cases, assuming that we are dealing with a single resonant atomic transition of negligible linewidth compared to the inverse of the time delay. The simplest case is depicted in Fig. 1(a) where the atomic interference fringes are acquired while spanning the delay t in a single time window between t 0 PRL 106, 213003 (2011) PHYSICAL REVIEW LETTERS week ending 27 MAY 2011 0031-9007= 11=106(21)=213003(4) 213003-1 Ó 2011 American Physical Society