High-Precision Ramsey-Comb Spectroscopy Based on High-Harmonic Generation

Abstract

High-harmonic generation (HHG) is widely used for up-conversion of amplified (near) infrared ultrafast laser pulses to short wavelengths. We demonstrate that Ramsey-comb spectroscopy, based on two such pulses derived from a frequency-comb laser, enables us to observe phase effects in this process with a few mrad precision. As a result, we could perform the most accurate spectroscopic measurement based on light from HHG, illustrated with a determination of the 5p 6 → 5p 5 8s 2 [3/2]1 transition at 110 nm in 132 Xe. We improve its relative accuracy 10 4 times to a value of 2.3 × 10 −10 . This is 3.6 times better than shown before involving HHG, and promising to enable 1S − 2S spectroscopy of He + for fundamental tests.High-precision spectroscopy in calculable atomic and molecular systems is at the heart of the most precise tests of bound-state quantum electrodynamics (QED) and searches for new physics beyond the Standard Model [1][2][3][4][5][6]. Instrumental in this development was the invention of the optical frequency comb (FC) [7,8] which enables precise optical frequency measurements referenced to an atomic clock. However, uncertainties in finite nuclearsize effects are hampering further progress [9]. Instead, spectroscopy has been used to measure the proton size in atomic and muonic hydrogen, but with partly conflicting results [10][11][12][13][14][15][16]. High-precision spectroscopy of the 1S − 2S transition in He + would provide new possibilities for fundamental tests as the uncertainty there is less dominated by nuclear size effects [17]. Combined with muonic He + spectroscopy [18,19] one can extract e.g. the alpha particle radius or the Rydberg constant. A major experimental challenge arises from the requirement of extreme ultraviolet (XUV) light at 60 nm (or shorter), to excite the transition. A similar challenge exist for spectroscopy of highly-charged ions [5], or the Thorium nuclear clock transition near 150 nm in the vacuum ultraviolet (VUV) [20,21]. At those wavelengths a relative accuracy of 0.1 ppm has been achieved with Fouriertransform spectroscopy techniques [22], and 0.03 ppm with low harmonics from nanosecond pulsed lasers [23]. A higher accuracy can be reached with light from highharmonic generation (HHG), induced by focusing ultrafast high-energy laser pulses in a noble gas at intensities of ∼ 10 14 W/cm 2 . The process can be understood using the three-step model [24,25], involving tunnel-ionization and recollision of an electron. This highly coherent process leads to the generation of a series of odd harmonics, which are tightly linked to the fundamental wave [26][27][28][29][30]. In combination with frequency-comb lasers, it has been used to achieve a spectroscopic accuracy of about 1 ppb at VUV and XUV wavelengths [31,32]. To improve on this we recently developed the Ramseycomb spectroscopy (RCS) method [33,34], based on pairs of powerful amplified FC pulses in a Ramsey-type [35] excitation scheme. Using only two pulses can compro-mise the accuracy provided by the FC laser [31], but th...

High-resolution Fourier-transform spectroscopy and deperturbation analysis of the A1Π(v = 1) level in 12C18O

“…The recorded absorption bands are analysed line-by-line with a full accounting of their lineshapes, instrumental effects, and contaminating absorption by hot bands and other isotopologues. An absolute frequency calibration is made uniformly to all measured spectra showing B 1 + ← − X 1 + and C 1 + ← − X 1 + by comparison with a highly-accurate absolute measurement of the Xe 5p 6 -5p 5 8s 2 [3/2] transition at 110 nm by Dreissen et al [56] . This line appears in our spectra because of a Xe gas-filter chamber located upstream and used to remove higher-frequency harmonics generated by the beamline undulator.…”

Interrogating the Temporal Coherence of EUV Frequency Combs with Highly Charged Ions

“…Through intracavity high-order harmonic generation (HHG) [10] of femtosecond infrared (IR) pulse trains, coherent extreme-ultraviolet (EUV) pulse trains representing EUV FCs have been demonstrated [11,12]. This could allow for high-precision spectroscopy in the EUV regime [13,14] and enable next-generation atomic clocks based on EUV transitions [15][16][17]. However, due to the lack of cw EUV reference lasers, the temporal coherence of an EUV FC is mainly investigated by splitting the EUV pulse train into two pathways and then recombing them to perform Michelson interference [12,18].…”

“…These values are calculated employing multiconfiguration Dirac-Hartree-Fock (MCDHF) theory [37,38] and referenced with the experimental values available from the NIST atomic database [39]. In contrast to the EUV transitions in neutral atoms that usually decay within 100 ns [13,14,[40][41][42][43][44], the EUV transitions in Table I possess lifetimes around both 1 μs and 1 s. Therefore, they can be used to investigate the coherence time of an EUV pulse train for harmonics from the 9th to the 19th order and beyond. By extending the light-matter interaction to account for phase fluctuations in the pulse train, we show that the coherence time can be determined either through DFCS, where millions of pulses interact with the ion [13,45], or via Ramsey frequency comb spectroscopy (RFCS) [14,40,41,43,44,46], where only two pulses separated in time interact with the ion.…”

“…While the first term in the curly bracket of Eq. (7) describes the excitations resulting from two independent pulses (each contributes 1=2), the cosine term represents the Ramsey interference between the two pulses, thus generates Ramsey fringes and determines the transition frequency [14,43,44,46]. The derivation of Eq.…”

High complexity femtosecond pulse duplicator

“…With the development of extreme ultra-violet (XUV) sources of coherent emission, many experimental techniques developed in the optical range have been transferred to the short wavelength domain. This includes techniques making use of two XUV pulses with adjustable delay such as Ramsey spectroscopy [1,2], heterodyne spectroscopy [3,4] and Fourier transform spectroscopy [5][6][7][8][9][10], interferometry [11] and pump/probe experiments [12][13][14]. Experimental schemes providing two XUV pulses of adjustable delays are also central in ultrafast spectroscopy, may it be attosecond-pump/attosecond-probe [8] or attosecond interferometry experiments [15].…”