High-precision spectroscopy experiments with simple atomic and molecular systems provide important benchmarks for tests of bound-state Quantum Electrodynamics (QED). In recent years there has been significant progress in both experiment [1,2] and theory [3] for QED tests in H₂. Even investigations of the proton radius puzzle [4] might become feasible in this molecule if the dissociation energy can be determined at a level of 10 kHz [3]. For this latter target, we developed an excitation method, Ramsey-comb spectroscopy, that enables kHz-level precision spectroscopy in the deep-UV. The method is based on excitation with amplified and upconverted frequency comb laser pulses [5]. It has allowed us to measure the EF¹ Σ_g⁺ − X¹ Σ_g⁺(0,0) Q1 two-photon transition at 202 nm with an accuracy of 73 kHz [6]. This result is two orders of magnitude better than obtained with previous experiments, and combined with future improved measurements of the EF ionization energy, this could lead to a dissociation energy with an uncertainty below 100 kHz. New measurements from V=1 and N=0 are now in preparation. Moreover, a new setup has been constructed to extend Ramsey-comb spectroscopy to the vacuum- and extreme-ultraviolet spectral region through high-harmonic generation, and an experiment is in preparation to demonstrate this. [1] J. Liu et al., J. Chem. Phys. 130, 174306 (2009) [2] W. Ubachs et al., J. Mol. Spectr. 320, 1-12 (2016) [3] M. Puchalski et al., Phys. Rev. A 95, 052506 (2017) [4] R. Pohl et al., Science 353, 669 (2016) [5] J. Morgenweg et al., Nature Physics 10, 30-33 (2014) [6] R.K. Altmann et al., Phys. Rev. Lett. 120, 043204 (2018)

Predicting the energy-level structure of molecules from first principles is one of the major goals and tasks of theoretical molecular physics and chemistry. Few-electron molecules are particularly attractive systems for comparison with experimental results because numerically "exact" predictions of molecular properties can in principle be obtained, i.e., predictions that are only limited in accuracy by the uncertainties of fundamental constants. We present absolute-frequency measurements of transitions from rotational levels of the a ³Σ_\textu⁺ (v"=0) metastable state of He₂ to np Rydberg states. The transition frequencies are determined by one-photon UV spectroscopy in slow molecular beams using a narrow-band laser system referenced to a frequency comb. The ionization energy of metastable He₂ and the rotational structure of the X^{+ 2}Σ_\textu⁺ (v⁺=0) ground state of He₂⁺ have been determined with unprecedented precision and accuracy using Rydberg-series extrapolation.

The hydroxyl radical, OH, is a prototypical open-shell diatomic molecule that is important in a variety of fields, including atmospheric chemistry, interstellar chemistry, crossed beam molecular collision studies, and Stark deceleration. In laboratory studies, OH is commonly detected with rotational state selectivity by measuring laser-induced fluorescence from ultraviolet A ²Σ⁺ − X ²Π transitions. Previous studies have determined the absolute frequencies of these transitions to within approximately 0.003 cm⁻¹(100 MHz) G. Stark et al. J. Opt. Soc. Am. B, 11:3-32, 1994 This level of accuracy is quite sufficient for excitation with commonly-used frequency-doubled pulsed dye lasers, which typically have a bandwidth on the order of 0.1 cm⁻¹, but for driving the transitions with a continuous-wave (CW) laser with a linewidth on the order of 1 MHz or less, the transition frequencies must be known much more exactly. In this talk, I would like to present our recent high-precision measurements of the A ²Σ⁺,v′=0 ← X ²Π_3/2,v"=0,J"=3/2 transitions in ¹⁶OH and ¹⁶OD. Using a frequency-doubled CW dye laser which is stabilized and monitored with the help of an optical frequency comb, we have measured transitions to the 12 lowest levels of the A ²Σ⁺,v′=0 vibronic state of ¹⁶OH with an uncertainty of less than 100 kHz (10⁻¹⁰ relative uncertainty) and are currently completing measurements of transitions to the 16 lowest A levels in ¹⁶OD with an expected uncertainty of 100-200 kHz. These measurements have enabled us to determine the ¹⁶OH A ²Σ⁺,v′=0 band origin with three orders of magnitude higher precision and the rotational constant with two orders of magnitude higher precision than previously possible. Similar improvements are expected in the corresponding constants of ¹⁶OD, as well as in its spin-rotation constant γ, which has not been measured in microwave double-resonance experiments as in ¹⁶OH J. J. ter Meulen et al. Chem. Phys. Lett., 129:533-537, 1986

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Footnotes:

G. Stark et al. J. Opt. Soc. Am. B, 11:3-32, 1994. J. J. ter Meulen et al. Chem. Phys. Lett., 129:533-537, 1986.

H₂⁺ is the simplest of all molecules and as such an important system for the development of molecular quantum mechanics. The rovibrational energy-level structure of this one-electron system can be calculated extremely precisely by quantum-chemical methodsV. I. Korobov, L. Hilico, and J.-Ph. Karr, Phys. Rev. A 89, 032511 (2014) By comparison with the results of precise spectroscopic measurements of rovibrational intervals, fundamental constants or particle properties, such as the proton-to-electron mass ratio or the proton size, can be determinedJ.-Ph. Karr, L. Hilico, J. C. J. Koelemeij, and V. I. Korobov, Phys. Rev. A 94, 050501(R) (2016) Because the rotational and vibrational transitions of H₂⁺ are electric-dipole forbidden, the experimental data on its energy-level structure are limited. We present the determination of spin-rovibrational intervals in H₂⁺ from high-resolution measurements of the Rydberg spectrum of H₂ and Rydberg-series extrapolation using multichannel quantum defect theoryD. Sprecher, Ch. Jungen and F. Merkt, J. Chem. Phys. 140, 104303:1-18 (2014) Choosing suitable double-well valence states of H₂, characterized by long lifetimes and favorable Franck-Condon factors to different vibrational states in the ion, allows us to excite Rydberg states that converge on selected rovibrational levels of H₂⁺. For the excitation of Rydberg states, a resonant three-photon excitation scheme was employed, using pulsed VUV and VIS laser sources to reach the intermediate valence state and a continuous-wave (cw) near-infrared laser source for the excitation to the Rydberg states. The valence state - Rydberg state intervals could be measured with a relative accuracy of 3E-10 using an optical frequency comb for the frequency calibration of the cw laser and minimizing systematic uncertaintiesM. Beyer, N. Hölsch, J. A. Agner, J. Deiglmayr, H. Schmutz, and F. Merkt, Phys. Rev. A 97, 012501 (2018)

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Footnotes:

V. I. Korobov, L. Hilico, and J.-Ph. Karr, Phys. Rev. A 89, 032511 (2014). J.-Ph. Karr, L. Hilico, J. C. J. Koelemeij, and V. I. Korobov, Phys. Rev. A 94, 050501(R) (2016). D. Sprecher, Ch. Jungen and F. Merkt, J. Chem. Phys. 140, 104303:1-18 (2014). M. Beyer, N. Hölsch, J. A. Agner, J. Deiglmayr, H. Schmutz, and F. Merkt, Phys. Rev. A 97, 012501 (2018).

I will present our recent results on the use of a femtosecond frequency comb to coherently drive stimulated Raman transitions between terahertz-spaced atomic energy levels [1]. More specifically, we address the 3d ²D_3/2 and 3d ²D_5/2 fine structure levels of a single trapped ⁴⁰Ca⁺ ion and spectroscopically resolve the transition frequency with a relative accuracy of 5.5×10⁻¹² ! The achieved accuracy is nearly a factor of five better than the previous best Raman spectroscopy [2], and is currently limited by the inaccuracy of our atomic clock reference. Using direct frequency comb Raman spectroscopy on four other isotopes ^42,44,46,48Ca⁺, in combination with precise measurements of the 4s ²S_1/2−3d ²D_5/2 transition, we were also able to improve bounds on new physics beyond the standard model [3,4].
Furthermore, I will discuss the population dynamics of frequency-comb-driven Raman transitions which can be fully predicted from the spectral properties of the femtosecond frequency comb. We achieved Rabi oscillations with a contrast of 99.3(6)% and milliseconds coherence time (see figure)!
The technique can be easily generalized to transitions in the sub-kHz [5] to tens of THz range and should be applicable for driving, e.g., spin-resolved rovibrational transitions in molecules and hyperfine transitions in highly charged ions.
[9]r[0pt]0pt [1] C. Solaro et al. arXiv:1712.07429 (2017) [2] R. Yamazaki et al. PRA 77,012508 (2008) [3] S. Meyer et al. in preparation [4] J.C. Berengut et al. arXiv:1704.05068 (2017) [5] D. Hayes et al. PRL 104,140501 (2010)

We carried out Stark-modulation spectroscopy of the ν₃ band of methane [1]. Figure shows observed spectra of the P(4)E, Q(4)E, and R(4)E transitions with the selection rule of ∆M = ±1, where M is the angular momentum quantum number along the Stark filed. Each triplet includes two Lamb-dips from |M"| = 2 to |M′| = 1 and from |M"| = 0 to |M′| = 1 and a crossover resonance (COR) at the middle. The COR is the largest in intensity in the triplet for the Q- and R-branch transitions, and middle for the P-branch transition. The COR of the Λ-type three-level system overlaps in frequency with that of the V-type three-level system of |M"| = 1 and |M′| = 0 and 2, and the relative intensity of the COR to the Lamb dips is analyzed using a steady-state solution of rate equations. The model fairly agrees with the observed relative intensity, and detailed analysis is in progress. [1] S. Okuda, H. Sasada, J. Opt. Soc. Am. B, 34, 2558-2568 (2017). r0pt Figure

Because molecular hydrogen is the simplest molecule, it is considered as the best candidate for a direct comparison of experiment against high level ab initio calculations, both in terms of transition frequencies and line strength. Unfortunately, this apparent simplicity is not only spoiled by the weakness of the transition, but also by its surprisingly complex line profile that hampers accurate parameters to be straightforwardly derived. To address that problem, we have recorded with unprecedented sensitivity pure H₂ Q(1) 2-0 and D₂ S(2) 2-0 transitions around 1.24 and 1.59 μm, respectively, down to a pressure of 100 Pa. A limit of detection of about 2×10⁻¹² cm⁻¹was achieved with the two accurate comb-referenced cavity ring down spectrometers used. Effective parameters were determined for different line profiles (NGP, SDNGP, HTP), allowing line reproduction down to the noise level. The zero pressure parameters will be presented and discussed.

H₂ is a benchmark system for testing quantum electrodynamics and physics beyond the standard model via highly accurate measurements of transition frequencies, which has been the subject of many works during the past decadesL. A. Rahn, R. L. Farrow, and G. J. Rosasco, Physical Review A, 43(11), 6075 (1991).G. D. Dickenson, M. L. Niu, et al., Physical review letters, 110(19), 193601 (2013).S. Kassi and A. Campargue, Journal of Molecular Spectroscopy, 300, 55-59 (2014). However, retrieving the unperturbed transition frequencies requires to measure spectra at very low pressure, where the low density combined with weak quadrupole transition moments makes it challenging to achieve high signal-to-noise ratios. An alternative approach is to model very precisely the transition profiles at higher pressure in order to correct for the strong Dicke narrowing and speed-dependent collisional effects which distort the absorption profiles. We present a new approach to measure H₂ transition frequencies in the fundamental rovibrational band with high accuracy and signal-to-noise ratio. The approach uses an optical frequency comb to calibrate the frequency spacing between a cw pump and a cw Stokes beams that interact with H₂ in a multipass cell by stimulated Raman scattering. Specifically, we focus on the Q(1) transition of the 1-0 band of pure H₂ at 4155.25cm⁻¹. The pump laser emits at 737.8 nm and is kept fixed while the Stokes laser is swept over 0.3cm⁻¹around 1064 nm. The wavelength of the Stokes laser is referenced to a local oscillator, which in turn is locked to an optical frequency comb along with the pump laser. The frequency comb is obtained using an Er:fiber amplified femtosecond laser with stabilized repetition rate and offset frequency to a reference Rb standard. The profiles measured at various pressures, spanning from 0.1 to 5 atm, are fitted using Hartmann-Tran profiles. The retrieved parameters are compared to ab-initio values based on H₂-H₂ quantum scattering calculations.

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Footnotes:

L. A. Rahn, R. L. Farrow, and G. J. Rosasco, Physical Review A, 43(11), 6075 (1991).

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Footnotes:

S. Kassi and A. Campargue, Journal of Molecular Spectroscopy, 300, 55-59 (2014)..

The simplest polyatomic molecule, H₃⁺, serves as an important benchmark for ab initio theory and is an important constituent of the interstellar medium (ISM). In the ISM, H₃⁺ initiates a chain of ion-neutral reactions which leads to more complex chemistry, and observations of H₃⁺ can be used to measure interstellar conditions such as the cosmic ray ionization rate.N. Indriolo, Phil. Trans. R. Soc. A, 370, 5142 (2012).or ab initio theorists, accurate calculations of the rovibrational structure of H₃⁺ require going beyond the Born-Oppenheimer approximation, and for its low-lying rovibrational states, agreement between theory and experiment has reached 0.001 cm⁻¹.L. G. Diniz, J. R. Mohallem, A. Alijah, M. Pavanello, L. Adamowicz, O. L. Polyansky, and J. Tennyson, Phys. Rev. A., 88, 032506 (2013).s these calculations begin to rival experimental measurements, new data are needed to benchmark future ab initio approaches. Using the technique Noise-Immune Cavity-Enhanced Optical Heterodyne Velocity Modulation Spectroscopy (NICE-OHVMS)J. N. Hodges, A. J. Perry, P. A. Jenkins II, B. M. Siller, and B. J. McCall, J. Chem. Phys, 139, 164201 (2013).o perform sub-Doppler spectroscopy and an optical frequency comb to accurately calibrate the frequency, we have expanded our survey of H₃⁺ to include transitions from higher rotational levels in the fundamental band and transitions in the 2ν₂²← ν₂¹ hot band. Using combination differences, we have determined a number of energy level spacings in the ground state with an accuracy of  ∼ 5 MHz, which are directly compared with state of the art ab initio calculations. We also discuss our progress towards calculating "forbidden" rotational transitions, including a possible astrophysical maser,J. H. Black, Phil. Trans. R. Soc. A, 358, 2515 (2000)hich requires our newly measured hot band transitions.

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Footnotes:

N. Indriolo, Phil. Trans. R. Soc. A, 370, 5142 (2012).F L. G. Diniz, J. R. Mohallem, A. Alijah, M. Pavanello, L. Adamowicz, O. L. Polyansky, and J. Tennyson, Phys. Rev. A., 88, 032506 (2013).A J. N. Hodges, A. J. Perry, P. A. Jenkins II, B. M. Siller, and B. J. McCall, J. Chem. Phys, 139, 164201 (2013).t J. H. Black, Phil. Trans. R. Soc. A, 358, 2515 (2000)w

Molecular hydrogen has evolved into a benchmark quantum test system for fundamental physics. Accurate results on the vibrational splitting in hydrogen isotopologues can be exploited to provide a test of QED in the smallest neutral molecule, and open up an avenue to resolve the proton radius puzzle, as well as constrain putative fifth forces and extra dimensions. We will present the first sub-Doppler determination of weak dipole transitions in the (2,0) overtone band of HD at λ ∼ 1.38 μm. To saturate and detect the weak absorption we have implemented a technique called Noise-Immune Cavity-Enhanced Optical Heterodyne Molecular Spectroscopy (NICE-OHMS). To obtain an absolute frequency during the measurements, the spectroscopy laser is simultaniously locked onto a Cs-clock referenced optical frequency comb. The obtained Doppler-free linewidth of  ∼ 300 kHz (FWHM) could give access and insight into the underlying hyperfine structure. Our current determination of the obtained transition frequencies is around 30 kHz; a 1000-fold improvement on the previous Doppler-broadened determination.