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In Sec. 6 (polarization monitor) of our recent publication [Opt. Express29(5), 7024 (2021)10.1364/OE.417455], we assumed a small value of δ. This is however incorrect. The correct approximation for small β leads to the updated Eqs. (10)-(11), resulting in a corrected Fig. 12.

We present an improved active fiber-based retroreflector (AFR) providing high-quality wavefront-retracing anti-parallel laser beams in the near UV. We use our improved AFR for first-order Doppler-shift suppression in precision spectroscopy of atomic hydrogen, but our setup can be adapted to other applications where wavefront-retracing beams with defined laser polarization are important. We demonstrate how weak aberrations produced by the fiber collimator may remain unobserved in the intensity of the collimated beam but limit the performance of the AFR. Our general results on characterizing these aberrations with a caustic measurement can be applied to any system where a collimated high-quality laser beam is required. Extending the collimator design process by wave optics propagation tools, we achieved a four-lens collimator for the wavelength range 380-486 nm with the beam quality factor of M 2  ≃ 1.02, limited only by the not exactly Gaussian beam profile from the single-mode fiber. Furthermore, we implemented precise fiber-collimator alignment and improved the collimation control by combining a precision motor with a piezo actuator. Moreover, we stabilized the intensity of the wavefront-retracing beams and added in-situ monitoring of polarization from polarimetry of the retroreflected light.

We have performed two-photon ultraviolet direct frequency comb spectroscopy on the 1S-3S transition in atomic hydrogen to illuminate the so-called proton radius puzzle and to demonstrate the potential of this method. The proton radius puzzle is a significant discrepancy between data obtained with muonic hydrogen and regular atomic hydrogen that could not be explained within the framework of quantum electrodynamics. By combining our result [ f 1S-3S = 2,922,743,278,665.79(72) kilohertz] with a previous measurement of the 1S-2S transition frequency, we obtained new values for the Rydberg constant [ R ∞ = 10,973,731.568226(38) per meter] and the proton charge radius [ r p = 0.8482(38) femtometers]. This result favors the muonic value over the world-average data as presented by the most recent published CODATA 2014 adjustment., (Copyright © 2020, American Association for the Advancement of Science.)

Optical frequency combs were introduced around 20 years ago as a laser technology that could synthesize and count the ultrafast rate of the oscillating cycles of light. Functioning in a manner analogous to a clockwork of gears, the frequency comb phase-coherently upconverts a radio frequency signal by a factor of [Formula: see text] to provide a vast array of evenly spaced optical frequencies, which is the comb for which the device is named. It also divides an optical frequency down to a radio frequency, or translates its phase to any other optical frequency across hundreds of terahertz of bandwidth. We review the historical backdrop against which this powerful tool for coherently uniting the electromagnetic spectrum developed. Advances in frequency comb functionality, physical implementation, and application are also described., (Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.)

The quantum Zeno effect (QZE) is not only interesting as a manifestation of the counterintuitive behavior of quantum mechanics, but may also have practical applications. When a spectroscopy laser is applied to target atoms or ions prepared in an initial state, the Rabi flopping of an auxiliary transition sharing one common level can be inhibited. This effect is found to be strongly dependent on the detuning of the spectroscopy laser and offers a sensitive spectroscopy signal which allows for high precision spectroscopy of transitions with a small excitation rate. We demonstrate this method with direct frequency comb spectroscopy using the minute power of a single mode to drive a dipole allowed transition in a single trapped ion. Resolving the individual modes of the frequency comb demonstrates that the simple instantaneous quantum collapse description of the QZE can not be applied here, as these modes need several pulses to build up.

At the core of the "proton radius puzzle" is a four-standard deviation discrepancy between the proton root-mean-square charge radii ( r p ) determined from the regular hydrogen (H) and the muonic hydrogen (µp) atoms. Using a cryogenic beam of H atoms, we measured the 2S-4P transition frequency in H, yielding the values of the Rydberg constant R ∞ = 10973731.568076(96) per meterand r p = 0.8335(95) femtometer. Our r p value is 3.3 combined standard deviations smaller than the previous H world data, but in good agreement with the µp value. We motivate an asymmetric fit function, which eliminates line shifts from quantum interference of neighboring atomic resonances., (Copyright © 2017 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.)

We demonstrate nonlinear pulse compression by multi-pass cell spectral broadening (MPCSB) from 860 fs to 115 fs with compressed pulse energy of 7.5 µJ, average power of 300 W and close to diffraction-limited beam quality. The transmission of the compression unit is >90%. The results show that this recently introduced compression scheme for peak powers above the threshold for catastrophic self-focusing can be scaled to smaller pulse energies and can achieve a larger compression factor than previously reported. Good homogeneity of the spectral broadening across the beam profile is verified, which distinguishes MPCSB among other bulk compression schemes.

Optical frequency combs have revolutionized the measurement of optical frequencies and improved the precision of spectroscopic experiments. Besides their importance as a frequency-measuring ruler, the frequency combs themselves can excite target transitions (direct frequency comb spectroscopy). The direct frequency comb spectroscopy may extend the optical frequency metrology into spectral regions unreachable by continuous wave lasers. In high precision spectroscopy, atoms/ions/molecules trapped in place have been often used as a target to minimize systematic effects. Here, we demonstrate direct frequency comb spectroscopy of single 25 Mg ions confined in a Paul trap, at deep-UV wavelengths. Only one mode out of about 20,000 can be resonant at a time. Even then we can detect the induced fluorescence with a spatially resolving single photon camera, allowing us to determine the absolute transition frequency. The demonstration shows that the direct frequency comb spectroscopy is an important tool for frequency metrology for shorter wavelengths where continuous wave lasers are unavailable.Frequency combs are useful tools in high precision measurement including atomic transitions and atomic clocks. Here the authors demonstrate direct frequency comb spectroscopy to shorter wavelengths by probing a transition frequency in a trapped Mg+ ion using a single mode of a UV frequency comb.

We present an active fiber-based retroreflector providing high quality phase-retracing anti-parallel Gaussian laser beams for precision spectroscopy of Doppler sensitive transitions. Our design is well-suited for a number of applications where implementing optical cavities is technically challenging and corner cubes fail to match the demanded requirements, most importantly retracing wavefronts and preservation of the laser polarization. To illustrate the performance of the system, we use it for spectroscopy of the 2S-4P transition in atomic hydrogen and demonstrate an average suppression of the first order Doppler shift to 4 parts in 10 6 of the full collinear shift. This high degree of cancellation combined with our cryogenic source of hydrogen atoms in the metastable 2S state is sufficient to enable determinations of the Rydberg constant and the proton charge radius with competitive uncertainties. Advantages over the usual Doppler cancellation based on corner cube type retroreflectors are discussed as well as an alternative method using a high finesse cavity.

A power-scalable concept for carrier-envelope-phase stabilization is presented. It takes advantage of simultaneous pumping of the zero- and first-phonon absorption line of Yb:YAG at 969 and 940 nm. The concept was implemented to lock the carrier-envelope-offset frequency of a 45 W average power Kerr-lens mode-locked thin-disk oscillator. The lock performance is compared to previous experiments where carrier-envelope-stabilization was realized by means of cavity loss modulation.

We demonstrate Doppler cooling of trapped magnesium ions using a frequency comb at 280 nm obtained from a frequency tripled Ti:sapphire laser. A comb line cools on the 3s_{1/2}-3p_{3/2} transition, while the nearest blue-detuned comb line contributes negligible heating. We observe the cooling-heating transition and long-term cooling of ion chains with several sympathetically cooled ions. Spatial thermometry shows that the ion is cooled to near the Doppler limit. Doppler cooling with frequency combs has the potential to open many additional atomic species to laser cooling by reaching further into the vacuum and extreme ultraviolet via high-harmonic generation and by providing a broad bandwidth from which multiple excitation sidebands can be obtained.

Waveform-stabilized laser pulses have revolutionized the exploration of the electronic structure and dynamics of matter by serving as the technological basis for frequency-comb and attosecond spectroscopy. Their primary sources, mode-locked titanium-doped sapphire lasers and erbium/ytterbium-doped fibre lasers, deliver pulses with several nanojoules energy, which is insufficient for many important applications. Here we present the waveform-stabilized light source that is scalable to microjoule energy levels at the full (megahertz) repetition rate of the laser oscillator. A diode-pumped Kerr-lens-mode-locked Yb:YAG thin-disk laser combined with extracavity pulse compression yields waveform-stabilized few-cycle pulses (7.7 fs, 2.2 cycles) with a pulse energy of 0.15 μJ and an average power of 6 W. The demonstrated concept is scalable to pulse energies of several microjoules and near-gigawatt peak powers. The generation of attosecond pulses at the full repetition rate of the oscillator comes into reach. The presented system could serve as a primary source for frequency combs in the mid infrared and vacuum UV with unprecedented high power levels.

We report on the development and characterization of continuous, narrow-band, and tunable laser systems that use direct second-harmonic generation from blue and green diode lasers with an output power level of up to 11.1 mW in the mid-ultraviolet. One of our laser systems was tuned to the mercury 6(1)S0 → 6(3)P1 intercombination line at 253.7 nm. We could perform Doppler-free saturation spectroscopy on this line and were able to lock our laser to the transition frequency on long time scales.

To compare the increasing number of optical frequency standards, highly stable optical signals have to be transferred over continental distances. We demonstrate optical-frequency transfer over a 1840-km underground optical fiber link using a single-span stabilization. The low inherent noise introduced by the fiber allows us to reach short term instabilities expressed as the modified Allan deviation of 2×10(-15) for a gate time τ of 1 s reaching 4×10(-19) in just 100 s. We find no systematic offset between the sent and transferred frequencies within the statistical uncertainty of about 3×10(-19). The spectral noise distribution of our fiber link at low Fourier frequencies leads to a τ(-2) slope in the modified Allan deviation, which is also derived theoretically.

We have measured the frequency of the extremely narrow 1S-2S two-photon transition in atomic hydrogen using a remote cesium fountain clock with the help of a 920 km stabilized optical fiber. With an improved detection method we obtain f(1S-2S)=2466 061 413 187 018 (11)  Hz with a relative uncertainty of 4.5×10(-15), confirming our previous measurement obtained with a local cesium clock [C. G. Parthey et al., Phys. Rev. Lett. 107, 203001 (2011)]. Combining these results with older measurements, we constrain the linear combinations of Lorentz boost symmetry violation parameters c((TX))=(3.1±1.9)×10(-11) and 0.92c((TY))+0.40c((TZ))=(2.6±5.3)×10(-11) in the standard model extension framework [D. Colladay, V. A. Kostelecký, Phys. Rev. D. 58, 116002 (1998)].

We investigate how suppressed modes in frequency combs are modified upon frequency doubling and self-phase modulation. We find, both experimentally and by using a simplified model, that these side-modes are amplified relative to the principal comb modes. Whereas frequency doubling increases their relative strength by 6 dB, the growth due to self-phase modulation can be much stronger and generally increases with nonlinear propagation length. Upper limits for this effect are derived in this work. This behavior has implications for high-precision calibration of spectrographs with frequency combs used for example in astronomy. For this application, Fabry-Pérot filter cavities are used to increase the mode spacing to exceed the resolution of the spectrograph. Frequency conversion and/or spectral broadening after non-perfect filtering reamplify the suppressed modes, which can lead to calibration errors.

The best spectrographs are limited in stability by their calibration light source. Laser frequency combs are the ideal calibrators for astronomical spectrographs. They emit a spectrum of lines that are equally spaced in frequency and that are as accurate and stable as the atomic clock relative to which the comb is stabilized. Absolute calibration provides the radial velocity of an astronomical object relative to the observer (on Earth). For the detection of Earth-mass exoplanets in Earth-like orbits around solar-type stars, or of cosmic acceleration, the observable is a tiny velocity change of less than 10 cm s(-1), where the repeatability of the calibration--the variation in stability across observations--is important. Hitherto, only laboratory systems or spectrograph calibrations of limited performance have been demonstrated. Here we report the calibration of an astronomical spectrograph with a short-term Doppler shift repeatability of 2.5 cm s(-1), and use it to monitor the star HD 75289 and recompute the orbit of its planet. This repeatability should make it possible to detect Earth-like planets in the habitable zone of star or even to measure the cosmic acceleration directly.

Optical clocks show unprecedented accuracy, surpassing that of previously available clock systems by more than one order of magnitude. Precise intercomparisons will enable a variety of experiments, including tests of fundamental quantum physics and cosmology and applications in geodesy and navigation. Well-established, satellite-based techniques for microwave dissemination are not adequate to compare optical clocks. Here, we present phase-stabilized distribution of an optical frequency over 920 kilometers of telecommunication fiber. We used two antiparallel fiber links to determine their fractional frequency instability (modified Allan deviation) to 5 × 10(-15) in a 1-second integration time, reaching 10(-18) in less than 1000 seconds. For long integration times τ, the deviation from the expected frequency value has been constrained to within 4 × 10(-19). The link may serve as part of a Europe-wide optical frequency dissemination network.

We present the first (to our best knowledge) femtosecond enhancement cavity in the visible wavelength range for ultraviolet frequency comb generation. The cavity is seeded at 518 nm by a frequency-doubled Yb fiber laser and operates at a peak intensity of 1.2×10(13) W/cm(2). High harmonics of up to the ninth order (~57 nm) are generated in an intracavity xenon gas jet. Intracavity high harmonic powers of several milliwatts for the third harmonic order and microwatts for the fifth harmonic order prove the potential of the "green cavity" as an efficient ultraviolet frequency comb source for future spectroscopic experiments. A limiting degradation effect of the cavity mirrors is avoided by operating at a constant oxygen background pressure.