Proton-electron mass ratio from laser spectroscopy of HD+ at the part-per-trillion level.

Recent mass measurements of light atomic nuclei in Penning traps have indicated possible inconsistencies in closely related physical constants such as the proton-electron and deuteron-proton mass ratios. These quantities also influence the predicted vibrational spectrum of the deuterated molecular hydrogen ion (HD+) in its electronic ground state. We used Doppler-free two-photon laser spectroscopy to measure the frequency of the v = 0→9 overtone transition (v, vibrational quantum number) of this spectrum with an uncertainty of 2.9 parts per trillion. By leveraging high-precision ab initio calculations, we converted our measurement to tight constraints on the proton-electron and deuteron-proton mass ratios, consistent with the most recent Penning trap determinations of these quantities. This results in a precision of 21 parts per trillion for the value of the proton-electron mass ratio.

Extreme ultraviolet lensless imaging without object support through rotational diversity in diffractive shearing interferometry.

We report on a method that allows microscopic image reconstruction from extreme-ultraviolet diffraction patterns without the need for object support constraints or other prior knowledge about the object structure. This is achieved by introducing additional diversity through rotation of an object in a rotationally asymmetric probe beam, produced by the spatial interference between two phase-coherent high-harmonic beams. With this rotational diffractive shearing interferometry method, we demonstrate robust image reconstruction of microscopic objects at wavelengths around 30 nm, using images recorded at only three to five different object rotations.

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

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.

Determination of the Interval between the Ground States of Para- and Ortho-H_{2}.

Nuclear-spin-symmetry conservation makes the observation of transitions between quantum states of ortho- and para-H_{2} extremely challenging. Consequently, the energy-level structure of H_{2} derived from experiment consists of two disjoint sets of level energies, one for para-H_{2} and the other for ortho-H_{2}. We use a new measurement of the ionization energy of para-H_{2} [E_{I}(H_{2})/(hc)=124 417.491 098(31) cm^{-1}] to determine the energy separation [118.486 770(50) cm^{-1}] between the ground states of para- and ortho-H_{2} and thus link the energy-level structure of the two nuclear-spin isomers of this fundamental molecule. Comparison with recent theoretical results [M. Puchalski et al., Phys. Rev. Lett. 122, 103003 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103003] enables the derivation of an upper bound of 1.5 MHz for a hypothetical global shift of the energy-level structure of ortho-H_{2} with respect to that of para-H_{2}.

Broadband extreme ultraviolet dispersion measurements using a high-harmonic source.

We demonstrate direct dispersion measurements of various thin films at extreme ultraviolet (EUV) wavelengths, using a table-top laser-driven high-harmonic generation (HHG) source. In this method, spatially separated identical EUV pulses are generated through HHG with a pair of phase-locked infrared pulses. The EUV pulses are re-imaged to a sample plane using a single toroidal mirror, such that one pulse illuminates the target thin film, while the other pulse passes through a reference aperture. By comparing the EUV interference with and without a sample, we are able to extract the dispersion properties of the sample, integrated over the full film thickness. We have measured thin films of titanium, nickel, copper, and silicon nitride, demonstrating that this technique can be applied to a wide range of materials, only requiring a film thin, enough for sufficient EUV transmission.

Dissociation Energy of the Hydrogen Molecule at 10

The ionization energy of ortho-H_{2} has been determined to be E_{I}^{o}(H_{2})/(hc)=124 357.238 062(25) cm^{-1} from measurements of the GK(1,1)-X(0,1) interval by Doppler-free, two-photon spectroscopy using a narrow band 179-nm laser source and the ionization energy of the GK(1,1) state by continuous-wave, near-infrared laser spectroscopy. E_{I}^{o}(H_{2}) was used to derive the dissociation energy of H_{2}, D_{0}^{N=1}(H_{2}), at 35 999.582 894(25) cm^{-1} with a precision that is more than one order of magnitude better than all previous results. The new result challenges calculations of this quantity and represents a benchmark value for future relativistic and QED calculations of molecular energies.

Sub-Doppler Frequency Metrology in HD for Tests of Fundamental Physics.

Weak transitions in the (2,0) overtone band of the hydrogen deuteride molecule at λ=1.38 µm were measured in saturated absorption using the technique of noise-immune cavity-enhanced optical heterodyne molecular spectroscopy. Narrow Doppler-free lines were interrogated with a spectroscopy laser locked to a frequency comb laser referenced to an atomic clock to yield transition frequencies [R(1)=217105181895(20) kHz; R(2)=219042856621(28) kHz; R(3)=220704304951(28) kHz] at three orders of magnitude improved accuracy. These benchmark values provide a test of QED in the smallest neutral molecule, and they open up an avenue to resolve the proton radius puzzle, as well as constrain putative fifth forces and extra dimensions.

Diffractive shear interferometry for extreme ultraviolet high-resolution lensless imaging.

We demonstrate a novel imaging approach and associated reconstruction algorithm for far-field coherent diffractive imaging, based on the measurement of a pair of laterally sheared diffraction patterns. The differential phase profile retrieved from such a measurement leads to improved reconstruction accuracy, increased robustness against noise, and faster convergence compared to traditional coherent diffractive imaging methods. We measure laterally sheared diffraction patterns using Fourier-transform spectroscopy with two phase-locked pulse pairs from a high-harmonic source. Using this approach, we demonstrate spectrally resolved imaging at extreme ultraviolet wavelengths between 28 and 35 nm.

Spectrally resolved single-shot wavefront sensing of broadband high-harmonic sources.

Wavefront sensors are an important tool to characterize coherent beams of extreme ultraviolet radiation. However, conventional Hartmann-type sensors do not allow for independent wavefront characterization of different spectral components that may be present in a beam, which limits their applicability for intrinsically broadband high-harmonic generation (HHG) sources. Here we introduce a wavefront sensor that measures the wavefronts of all the harmonics in a HHG beam in a single camera exposure. By replacing the mask apertures with transmission gratings at different orientations, we simultaneously detect harmonic wavefronts and spectra, and obtain sensitivity to spatiotemporal structure such as pulse front tilt as well. We demonstrate the capabilities of the sensor through a parallel measurement of the wavefronts of 9 harmonics in a wavelength range between 25 and 49 nm, with up to λ/32 precision.

Deep-Ultraviolet Frequency Metrology of H_{2} for Tests of Molecular Quantum Theory.

Molecular hydrogen and its isotopic and ionic species are benchmark systems for testing quantum chemical theory. Advances in molecular energy structure calculations enable the experimental verification of quantum electrodynamics and potentially a determination of the proton charge radius from H_{2} spectroscopy. We measure the ground state energy in ortho-H_{2} relative to the first electronically excited state by Ramsey-comb laser spectroscopy on the EF^{1}Σ_{g}^{+}-X^{1}Σ_{g}^{+}(0,0) Q1 transition. The resulting transition frequency of 2 971 234 992 965(73) kHz is 2 orders of magnitude more accurate than previous measurements. This paves the way for a considerably improved determination of the dissociation energy (D_{0}) for fundamental tests with molecular hydrogen.

High-energy Nd:YAG laser system with arbitrary sub-nanosecond pulse shaping capability.

We report on a laser system capable of generating high-energy (>270 mJ) temporally shaped pulses at 1064 nm with 0.43-ns shaping resolution. The pulses are generated by modulation of a continuous-wave seed laser and subsequent amplification by a dual-stage grazing-incidence Nd:YVO4 "bounce" amplifier and a Nd:YAG power amplifier (all quasi-continuous diode-pumped). The system produces pulses with a high-quality top-hat spatial beam profile with up to 0.6 GW of peak power and 44 W of average power, a power stability of 0.22% rms, and fully programmable complex temporal shapes.

High-Precision Ramsey-Comb Spectroscopy at Deep Ultraviolet Wavelengths.

High-precision spectroscopy in systems such as molecular hydrogen and helium ions is very interesting in view of tests of quantum electrodynamics and the proton radius puzzle. However, the required deep ultraviolet and shorter wavelengths pose serious experimental challenges. Here we show Ramsey-comb spectroscopy in the deep ultraviolet for the first time, thereby demonstrating its enabling capabilities for precision spectroscopy at short wavelengths. We excite ^{84}Kr in an atomic beam on the two-photon 4p^{6}→4p^{5}5p[1/2]_{0} transition at 212.55 nm. It is shown that the ac-Stark shift is effectively eliminated, and combined with a counterpropagating excitation geometry to suppress Doppler effects, a transition frequency of 2 820 833 101 679(103) kHz is found. The uncertainty of our measurement is 34 times smaller than the best previous measurement, and only limited by the 27 ns lifetime of the excited state.

Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD(.).

The simplest molecules in nature, molecular hydrogen ions in the form of H2(+) and HD(+), provide an important benchmark system for tests of quantum electrodynamics in complex forms of matter. Here, we report on such a test based on a frequency measurement of a vibrational overtone transition in HD(+) by laser spectroscopy. We find that the theoretical and experimental frequencies are equal to within 0.6(1.1) parts per billion, which represents the most stringent test of molecular theory so far. Our measurement not only confirms the validity of high-order quantum electrodynamics in molecules, but also enables the long predicted determination of the proton-to-electron mass ratio from a molecular system, as well as improved constraints on hypothetical fifth forces and compactified higher dimensions at the molecular scale. With the perspective of comparisons between theory and experiment at the 0.01 part-per-billion level, our work demonstrates the potential of molecular hydrogen ions as a probe of fundamental physical constants and laws.

Effect of soil temperature on optical frequency transfer through unidirectional dense-wavelength-division-multiplexing fiber-optic links.

Results of optical frequency transfer over a carrier-grade dense-wavelength-division-multiplexing (DWDM) optical fiber network are presented. The relation between soil temperature changes on a buried optical fiber and frequency changes of an optical carrier through the fiber is modeled. Soil temperatures, measured at various depths by the Royal Netherlands Meteorology Institute (KNMI) are compared with observed frequency variations through this model. A comparison of a nine-day record of optical frequency measurements through the 2×298 km fiber link with soil temperature data shows qualitative agreement. A soil temperature model is used to predict the link stability over longer periods (days-months-years). We show that optical frequency dissemination is sufficiently stable to distribute and compare, e.g., rubidium frequency standards over standard DWDM optical fiber networks using unidirectional fibers.

Fundamental vibration of molecular hydrogen.

The fundamental ground tone vibration of H(2), HD, and D(2) is determined to an accuracy of 2×10(-4) cm(-1) from Doppler-free laser spectroscopy in the collisionless environment of a molecular beam. This rotationless vibrational splitting is derived from the combination difference between electronic excitation from the X(1)Σ(g)(+), v=0, and v=1 levels to a common EF(1)Σ(g)(+), v=0 level. Agreement within 1σ between the experimental result and a full ab initio calculation provides a stringent test of quantum electrodynamics in a chemically bound system.

Multi-delay, phase coherent pulse pair generation for precision Ramsey-frequency comb spectroscopy.

We demonstrate the generation of phase-stable mJ-pulse pairs at programmable inter-pulse delays up to hundreds of nanoseconds. A detailed investigation of potential sources for phase shifts during the parametric amplification of the selected pulses from a Ti:Sapphire frequency comb is presented, both numerically and experimentally. It is shown that within the statistical error of the phase measurement of 10 mrad, there is no dependence of the differential phase shift over the investigated inter-pulse delay range of more than 300 ns. In combination with nonlinear upconversion of the amplified pulses, the presented system will potentially enable short wavelength (<100 nm), multi-transition Ramsey-frequency comb spectroscopy at the kHz-level.

Frequency comb generation by CW laser injection into a quantum-dot mode-locked laser.

We report on frequency comb generation at 1.5 µm by injection of a CW laser in a hybridly mode-locked InAs/InP two-section quantum-dot laser (HMLQDL). The generated comb has > 60 modes spaced by ∼ 4.5 GHz and a -20 dBc width of > 100 GHz (23 modes) at > 30 dB signal to background ratio. Comb generation was observed with the CW laser (red) detuned more than 20 nm outside the HMLQDL spectrum, spanning a large part of the gain spectrum of the quantum dot material. It is shown that the generated comb is fully coherent with the injected CW laser and RF frequency used to drive the hybrid mode-locking. This method of comb generation is of interest for the creation of small and robust frequency combs for use in optical frequency metrology, high-frequency (> 100 GHz) RF generation and telecommunication applications.

Tailored pulse sequences from an 880 nm pumped Nd:YVO4 bounce amplifier.

We report on an 880 nm quasi-continuously pumped Nd:YVO4 grazing-incidence "bounce" amplifier, operating at a 300 Hz repetition rate. More than 70 dB small signal gain is achieved with a single crystal. Combined with fast programmable modulators, high-contrast and near-diffraction-limited pulse sequences at the 100 µJ level are produced and can be tailored in terms of pulse duration, amplitude, and a temporal spacing well into the microsecond range. This system could significantly improve extreme-UV comb generation based on parametric amplification and harmonic upconversion of two near-IR comb laser pulses.

Full phase stabilization of a Yb:fiber femtosecond frequency comb via high-bandwidth transducers.

We present full phase stabilization of an amplified Yb:fiber femtosecond frequency comb using an intracavity electro-optic modulator and an acousto-optic modulator. These transducers provide high servo bandwidths of 580 kHz and 250 kHz for f(rep) and f(ceo), producing a robust and low phase noise fiber frequency comb. The comb was self-referenced with an f-2f interferometer and phase locked to an ultrastable optical reference used for the JILA Sr optical clock at 698 nm, exhibiting 0.21 rad and 0.47 rad of integrated phase errors (over 1 mHz-1 MHz), respectively. Alternatively, the comb was locked to two optical references at 698 nm and 1064 nm, obtaining 0.43 rad and 0.14 rad of integrated phase errors, respectively.

Frequency metrology in quantum degenerate helium: direct measurement of the 2 3S1 --> 2 1S0 transition.

Precision spectroscopy of simple atomic systems has refined our understanding of the fundamental laws of quantum physics. In particular, helium spectroscopy has played a crucial role in describing two-electron interactions, determining the fine-structure constant and extracting the size of the helium nucleus. Here we present a measurement of the doubly forbidden 1557-nanometer transition connecting the two metastable states of helium (the lowest energy triplet state 2 (3)S(1) and first excited singlet state 2 (1)S(0)), for which quantum electrodynamic and nuclear size effects are very strong. This transition is weaker by 14 orders of magnitude than the most predominantly measured transition in helium. Ultracold, submicrokelvin, fermionic (3)He and bosonic (4)He atoms are used to obtain a precision of 8 × 10(-12), providing a stringent test of two-electron quantum electrodynamic theory and of nuclear few-body theory.