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Ultraviolet spectroscopy provides unique insights into the structure of matter with applications ranging from fundamental tests to photochemistry in the Earth's atmosphere and astronomical observations from space telescopes 1-8 . At longer wavelengths, dual-comb spectroscopy, using two interfering laser frequency combs, has become a powerful technique capable of simultaneously providing a broad spectral range and very high resolution 9 . Here we demonstrate a photon-counting approach that can extend the unique advantages of this method into ultraviolet regions where nonlinear frequency conversion tends to be very inefficient. Our spectrometer, based on two frequency combs with slightly different repetition frequencies, provides a wide-span, high-resolution frequency calibration within the accuracy of an atomic clock, and overall consistency of the spectra. We demonstrate a signal-to-noise ratio at the quantum limit and an optimal use of the measurement time, provided by the multiplexed recording of all spectral data on a single photon-counter 10 . Our initial experiments are performed in the near-ultraviolet and in the visible spectral ranges with alkali-atom vapour, with a power per comb line as low as a femtowatt. This crucial step towards precision broadband spectroscopy at short wavelengths paves the way for extreme-ultraviolet dual-comb spectroscopy, and, more generally, opens up a new realm of applications for photon-level diagnostics, as encountered, for example, when driving single atoms or molecules., (© 2024. The Author(s).)

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.

Time-resolved near-infrared absorption spectroscopy of single non-repeatable transient events is performed at high spectral resolution with a dual-comb interferometer using a continuous-wave laser followed by a single electro-optic amplitude modulator. By sharing high-speed electrical/optical components, our spectrometer greatly simplifies the implementation of dual-comb spectroscopy and offers a high mutual coherence time, measured up to 50 s, without any active stabilization system and/or data processing. The time resolution is as short as 100 µs in our experimental demonstration. For a span of 36 GHz, the mean signal-to-noise ratio of 80, at 100-MHz spectral resolution and 100-µs measurement time, enables precise determination of the parameters of rovibrational lines, including intensity or concentration.

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.

The energy levels of hydrogen-like atomic systems can be calculated with great precision. Starting from their quantum mechanical solution, they have been refined over the years to include the electron spin, the relativistic and quantum field effects, and tiny energy shifts related to the complex structure of the nucleus. These energy shifts caused by the nuclear structure are vastly magnified in hydrogen-like systems formed by a negative muon and a nucleus, so spectroscopy of these muonic ions can be used to investigate the nuclear structure with high precision. Here we present the measurement of two 2S-2P transitions in the muonic helium-4 ion that yields a precise determination of the root-mean-square charge radius of the α particle of 1.67824(83) femtometres. This determination from atomic spectroscopy is in excellent agreement with the value from electron scattering 1 , but a factor of 4.8 more precise, providing a benchmark for few-nucleon theories, lattice quantum chromodynamics and electron scattering. This agreement also constrains several beyond-standard-model theories proposed to explain the proton-radius puzzle 2-5 , in line with recent determinations of the proton charge radius 6-9 , and establishes spectroscopy of light muonic atoms and ions as a precise tool for studies of nuclear properties.

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.)

We probe complex optical spectra at high resolution over a broad span in almost complete darkness. Using a single photon-counting detector at light power levels that are a billion times weaker than commonly employed, we observe interferences in the counting statistics with two separate mode-locked femtosecond lasers of slightly different repetition frequencies, each emitting a comb of evenly spaced spectral lines over a wide spectral span. Unique advantages of the emerging technique of dual-comb spectroscopy, such as multiplex data acquisition with many comb lines, potential very high resolution, and calibration of the frequency scale with an atomic clock, can thus be maintained for scenarios where only few detectable photons can be expected. Prospects include spectroscopy of weak scattered light over long distances, fluorescence spectroscopy of single trapped atoms or molecules, or studies in the extreme-ultraviolet or even soft-X-ray region with comb sources of low photon yield. Our approach defies intuitive interpretations in a picture of photons that exist before detection., (Copyright © 2020 the Author(s). Published by PNAS.)

Atomically thin crystals of transition metal dichalcogenides (TMDs) host excitons with strong binding energies and sizable light-matter interactions. Coupled to optical cavities, monolayer TMDs routinely reach the regime of strong light-matter coupling, where excitons and photons admix coherently to form polaritons up to room temperature. Here, we explore the two-dimensional nature of TMD polaritons with scanning-cavity hyperspectral imaging. We record a spatial map of polariton properties of extended WS 2 monolayers coupled to a tunable micro cavity in the strong coupling regime, and correlate it with maps of exciton extinction and fluorescence taken from the same flake with the cavity. We find a high level of homogeneity, and show that polariton splitting variations are correlated with intrinsic exciton properties such as oscillator strength and linewidth. Moreover, we observe a deviation from thermal equilibrium in the resonant polariton population, which we ascribe to non-Markovian polariton-phonon coupling. Our measurements reveal a promisingly consistent polariton landscape, and highlight the importance of phonons for future polaritonic devices.

Mid-infrared high-resolution spectroscopy has proven an invaluable tool for the study of the structure and dynamics of molecules in the gas phase. The advent of frequency combs advances the frontiers of precise molecular spectroscopy. Here we demonstrate, in the important 3-µm spectral region of the fundamental CH stretch in molecules, dual-comb spectroscopy with experimental coherence times between the combs that exceed half an hour. Mid-infrared Fourier transform spectroscopy using two frequency combs with self-calibration of the frequency scale, negligible contribution of the instrumental line shape to the spectral profiles, high signal-to-noise ratio, and broad spectral bandwidth opens up opportunities for precision spectroscopy of small molecules. Highly multiplexed metrology of line shapes may be envisioned., Competing Interests: The authors declare no conflict of interest., (Copyright © 2019 the Author(s). Published by PNAS.)

Laser frequency combs emit a spectrum with hundreds of thousands of evenly spaced phase-coherent narrow lines. A comb-enabled instrument, the dual-comb interferometer, exploits interference between two frequency combs and attracts considerable interest in precision spectroscopy and sensing, distance metrology, tomography, telecommunications, etc. Mutual coherence between the two combs over the measurement time is a pre-requisite to interferometry, although it is instrumentally challenging. At best, the mutual coherence reaches about 1 s. Computer-based phase-correction techniques, which often lead to artifacts and worsened precision, must be implemented for longer averaging times. Here with feed-forward relative stabilization of the carrier-envelope offset frequencies, we experimentally realize a mutual coherence over times approaching 2000 s, more than three orders of magnitude longer than that of state-of-the-art dual-comb systems. An illustration is given with near-infrared Fourier transform molecular spectroscopy with two combs of slightly different repetition frequencies. Our technique without phase correction can be implemented with any frequency comb generator including microresonators or semiconductor lasers.

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.

Sub-Doppler broadband multi-heterodyne spectroscopy is proposed and experimentally demonstrated. Using two laser frequency combs of slightly different repetition frequencies, we have recorded Doppler-free two-photon dual-comb spectra of atomic rubidium resonances of a width of 6 MHz, while simultaneously interrogating a spectral span of 10 THz. The atomic transitions are uniquely identified via the intensity modulation of the observed fluorescence radiation. To the best of our knowledge, these results represent the first demonstration of Doppler-free Fourier transform spectroscopy and extend the range of applications of broadband spectroscopy towards precision nonlinear spectroscopy.

Absorption spectroscopy of fundamental ro-vibrational transitions in the mid-infrared region provides a powerful tool for studying the structure and dynamics of molecules in the gas phase and for sensitive and quantitative gas sensing. Laser frequency combs permit novel approaches to perform broadband molecular spectroscopy. Multiplex dual-comb spectroscopy without moving parts can achieve particularly high speed, sensitivity and resolution. However, achieving Doppler-limited resolution in the mid-infrared still requires overcoming instrumental challenges. Here we demonstrate a new approach based on difference-frequency generation of frequency-agile near-infrared frequency combs that are produced using electro-optic modulators. The combs have a remarkably flat intensity distribution, and their positions and line spacings can be freely selected by simply dialing a knob. Using the proposed technique, we record, in the 3-μm region, Doppler-limited absorption spectra with resolved comb lines within milliseconds, and precise molecular line parameters are retrieved. Our technique holds promise for fast and sensitive time-resolved studies of, for example, trace gases., Competing Interests: The authors declare no conflict of interest.

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.

We theoretically show that a dipole externally driven by a pulse with a lower-bounded temporal width, and placed inside a cylindrical hollow waveguide, can generate a train of arbitrarily short and focused electromagnetic pulses. The waveguide encloses vacuum with perfect electric conducting walls. A dipole driven by a single short pulse, which is properly engineered to exploit the linear spectral filtering of the cylindrical hollow waveguide, excites longitudinal waveguide modes that are coherently refocused at some particular instances of time, thereby producing arbitrarily short and focused electromagnetic pulses. We numerically show that such ultrafocused pulses persist outside the cylindrical waveguide at distances comparable to its radius.

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 extend the technique of multiplex coherent Raman spectroscopy with two femtosecond mode-locked lasers to oscillators of a pulse repetition frequency of 1 GHz. We demonstrate a spectra of liquids, which span 1100  cm -1 of Raman shifts. At a resolution of 6  cm -1 , their measurement time may be as short as 5 μs for a refresh rate of 2 kHz. The waiting period between acquisitions is improved 10-fold compared to previous experiments with two lasers of 100-MHz repetition frequencies.

We study the mechanical stability of a tunable high-finesse microcavity under ambient conditions and investigate light-induced effects that can both suppress and excite mechanical fluctuations. As an enabling step, we demonstrate the ultra-precise electronic stabilization of a microcavity. We then show that photothermal mirror expansion can provide high-bandwidth feedback and improve cavity stability by almost two orders of magnitude. At high intracavity power, we observe self-oscillations of mechanical resonances of the cavity. We explain the observations by a dynamic photothermal instability, leading to parametric driving of mechanical motion. For an optimized combination of electronic and photothermal stabilization, we achieve a feedback bandwidth of 500 kHz and a noise level of 1.1 × 10 -13 m rms.

The deuteron is the simplest compound nucleus, composed of one proton and one neutron. Deuteron properties such as the root-mean-square charge radius rd and the polarizability serve as important benchmarks for understanding the nuclear forces and structure. Muonic deuterium μd is the exotic atom formed by a deuteron and a negative muon μ(-). We measured three 2S-2P transitions in μd and obtain r(d) = 2.12562(78) fm, which is 2.7 times more accurate but 7.5σ smaller than the CODATA-2010 value r(d) = 2.1424(21) fm. The μd value is also 3.5σ smaller than the r(d) value from electronic deuterium spectroscopy. The smaller r(d), when combined with the electronic isotope shift, yields a "small" proton radius r(p), similar to the one from muonic hydrogen, amplifying the proton radius puzzle., (Copyright © 2016, American Association for the Advancement of Science.)

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.

Raman spectroscopy reveals chemically specific information and provides label-free insight into the molecular world. However, the signals are intrinsically weak and call for enhancement techniques. Here, we demonstrate Purcell enhancement of Raman scattering in a tunable high-finesse microcavity, and utilize it for molecular diagnostics by combined Raman and absorption imaging. Studying individual single-wall carbon nanotubes, we identify crucial structural parameters such as nanotube radius, electronic structure and extinction cross-section. We observe a 320-times enhanced Raman scattering spectral density and an effective Purcell factor of 6.2, together with a collection efficiency of 60%. Potential for significantly higher enhancement, quantitative signals, inherent spectral filtering and absence of intrinsic background in cavity-vacuum stimulated Raman scattering render the technique a promising tool for molecular imaging. Furthermore, cavity-enhanced Raman transitions involving localized excitons could potentially be used for gaining quantum control over nanomechanical motion and open a route for molecular cavity optomechanics.

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.

Thin-disk laser pump layouts yielding an increased number of passes for a given pump module size and pump source quality are proposed. These layouts result from a general scheme based on merging two simpler pump optics arrangements. Some peculiar examples can be realized by adapting standard, commercially available pump optics with an additional mirror pair. More pump passes yield better efficiency, opening the way for the usage of active materials with low absorption. In a standard multipass pump design, scaling of the number of beam passes brings about an increase in the overall size of the optical arrangement or an increase in the pump source quality requirements. Such increases are minimized in our scheme, making them eligible for industrial applications.

Imaging the optical properties of individual nanosystems beyond fluorescence can provide a wealth of information. However, the minute signals for absorption and dispersion are challenging to observe, and only specialized techniques requiring sophisticated noise rejection are available. Here we use signal enhancement in a high-finesse scanning optical microcavity to demonstrate ultra-sensitive imaging. Harnessing multiple interactions of probe light with a sample within an optical resonator, we achieve a 1,700-fold signal enhancement compared with diffraction-limited microscopy. We demonstrate quantitative imaging of the extinction cross-section of gold nanoparticles with a sensitivity less than 1 nm(2); we show a method to improve the spatial resolution potentially below the diffraction limit by using higher order cavity modes, and we present measurements of the birefringence and extinction contrast of gold nanorods. The demonstrated simultaneous enhancement of absorptive and dispersive signals promises intriguing potential for optical studies of nanomaterials, molecules and biological nanosystems.

Avalanche photodiodes are commonly used as detectors for low energy x-rays. In this work, we report on a fitting technique used to account for different detector responses resulting from photoabsorption in the various avalanche photodiode layers. The use of this technique results in an improvement of the energy resolution at 8.2 keV by up to a factor of 2 and corrects the timing information by up to 25 ns to account for space dependent electron drift time. In addition, this waveform analysis is used for particle identification, e.g., to distinguish between x-rays and MeV electrons in our experiment.

Laser frequency combs, sources with a spectrum consisting of hundred thousands evenly spaced narrow lines, have an exhilarating potential for new approaches to molecular spectroscopy and sensing in the mid-infrared region. The generation of such broadband coherent sources is presently under active exploration. Technical challenges have slowed down such developments. Identifying a versatile highly nonlinear medium for significantly broadening a mid-infrared comb spectrum remains challenging. Here we take a different approach to spectral broadening of mid-infrared frequency combs and investigate CMOS-compatible highly nonlinear dispersion-engineered silicon nanophotonic waveguides on a silicon-on-insulator chip. We record octave-spanning (1,500-3,300 nm) spectra with a coupled input pulse energy as low as 16 pJ. We demonstrate phase-coherent comb spectra broadened on a room-temperature-operating CMOS-compatible chip.

We present the concluding result from an Ives-Stilwell-type time dilation experiment using 7Li+ ions confined at a velocity of β=v/c=0.338 in the storage ring ESR at Darmstadt. A Λ-type three-level system within the hyperfine structure of the 7Li+3S1 →3P2 line is driven by two laser beams aligned parallel and antiparallel relative to the ion beam. The lasers' Doppler shifted frequencies required for resonance are measured with an accuracy of <4×10(-9) using optical-optical double resonance spectroscopy. This allows us to verify the special relativity relation between the time dilation factor γ and the velocity β, γ√1-β2=1 to within ±2.3×10(-9) at this velocity. The result, which is singled out by a high boost velocity β, is also interpreted within Lorentz invariance violating test theories.

A few-cycle, broadband, singly-resonant optical parametric oscillator (OPO) for the mid-infrared based on MgO-doped periodically-poled LiNbO 3 (MgO:PPLN), synchronously pumped by a 20-fs Ti:sapphire laser is reported. By using crystal interaction lengths as short as 250 µm, and careful dispersion management of input pump pulses and the OPO resonator, near-transform-limited, few-cycle idler pulses tunable across the mid-infrared have been generated, with as few as 3.7 optical cycles at 2682 nm. The OPO can be continuously tuned over 2179-3732 nm (4589-2680 cm -1 ) by cavity delay tuning, providing up to 33 mW of output power at 3723 nm. The idler spectra exhibit stable broadband profiles with bandwidths spanning over 422 nm (FWHM) recorded at 3732 nm. The effect of crystal length on spectral bandwidth and pulse duration is investigated at a fixed wavelength, confirming near-transform-limited idler pulses for all grating interaction lengths. By locking the repetition frequency of the pump laser to a radio-frequency reference, and without active stabilization of the OPO cavity length, an idler power stability better than 1.6% rms over >2.75 hours is obtained when operating at maximum output power, in excellent spatial beam quality with TEM 00 mode profile. Photograph shows a multigrating MgO:PPLN crystal used as a nonlinear gain medium in the few-cycle femtosecond mid-IR OPO. The visible light is the result of non-phase-matched sum-frequency mixing between the interacting beams.

A multipass laser cavity is presented which can be used to illuminate an elongated volume from a transverse direction. The illuminated volume can also have a very large transverse cross section. Convenient access to the illuminated volume is granted. The multipass cavity is very robust against misalignment, and no active stabilization is needed. The scheme is suitable for example in beam experiments, where the beam path must not be blocked by a laser mirror, or if the illuminated volume must be very large. This cavity was used for the muonic-hydrogen experiment in which 6 μm laser light illuminated a volume of 7 × 25 × 176 mm3, using mirrors that are only 12 mm in height. We present our measurement of the intensity distribution inside the multipass cavity and show that this is in good agreement with our simulation.

The spectrum of a laser frequency comb consists of several hundred thousand equally spaced lines over a broad spectral bandwidth. Such frequency combs have revolutionized optical frequency metrology and they now hold much promise for significant advances in a growing number of applications including molecular spectroscopy. Despite an intriguing potential for the measurement of molecular spectra spanning tens of nanometres within tens of microseconds at Doppler-limited resolution, the development of dual-comb spectroscopy is hindered by the demanding stability requirements of the laser combs. Here we overcome this difficulty and experimentally demonstrate a concept of real-time dual-comb spectroscopy, which compensates for laser instabilities by electronic signal processing. It only uses free-running mode-locked lasers without any phase-lock electronics. We record spectra spanning the full bandwidth of near-infrared fibre lasers with Doppler-limited line profiles highly suitable for measurements of concentrations or line intensities. Our new technique of adaptive dual-comb spectroscopy offers a powerful transdisciplinary instrument for analytical sciences.

Advances in optical spectroscopy and microscopy have had a profound impact throughout the physical, chemical and biological sciences. One example is coherent Raman spectroscopy, a versatile technique interrogating vibrational transitions in molecules. It offers high spatial resolution and three-dimensional sectioning capabilities that make it a label-free tool for the non-destructive and chemically selective probing of complex systems. Indeed, single-colour Raman bands have been imaged in biological tissue at video rates by using ultra-short-pulse lasers. However, identifying multiple, and possibly unknown, molecules requires broad spectral bandwidth and high resolution. Moderate spectral spans combined with high-speed acquisition are now within reach using multichannel detection or frequency-swept laser beams. Laser frequency combs are finding increasing use for broadband molecular linear absorption spectroscopy. Here we show, by exploring their potential for nonlinear spectroscopy, that they can be harnessed for coherent anti-Stokes Raman spectroscopy and spectro-imaging. The method uses two combs and can simultaneously measure, on the microsecond timescale, all spectral elements over a wide bandwidth and with high resolution on a single photodetector. Although the overall measurement time in our proof-of-principle experiments is limited by the waiting times between successive spectral acquisitions, this limitation can be overcome with further system development. We therefore expect that our approach of using laser frequency combs will not only enable new applications for nonlinear microscopy but also benefit other nonlinear spectroscopic techniques.

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.

Atom interferometers covering macroscopic domains of space-time are a spectacular manifestation of the wave nature of matter. Because of their unique coherence properties, Bose-Einstein condensates are ideal sources for an atom interferometer in extended free fall. In this Letter we report on the realization of an asymmetric Mach-Zehnder interferometer operated with a Bose-Einstein condensate in microgravity. The resulting interference pattern is similar to the one in the far field of a double slit and shows a linear scaling with the time the wave packets expand. We employ delta-kick cooling in order to enhance the signal and extend our atom interferometer. Our experiments demonstrate the high potential of interferometers operated with quantum gases for probing the fundamental concepts of quantum mechanics and general relativity.

Accurate knowledge of the charge and Zemach radii of the proton is essential, not only for understanding its structure but also as input for tests of bound-state quantum electrodynamics and its predictions for the energy levels of hydrogen. These radii may be extracted from the laser spectroscopy of muonic hydrogen (μp, that is, a proton orbited by a muon). We measured the 2S(1/2)(F=0)-2P(3/2)(F=1) transition frequency in μp to be 54611.16(1.05) gigahertz (numbers in parentheses indicate one standard deviation of uncertainty) and reevaluated the 2S(1/2)(F=1)-2P(3/2)(F=2) transition frequency, yielding 49881.35(65) gigahertz. From the measurements, we determined the Zemach radius, r(Z) = 1.082(37) femtometers, and the magnetic radius, r(M) = 0.87(6) femtometer, of the proton. We also extracted the charge radius, r(E) = 0.84087(39) femtometer, with an order of magnitude more precision than the 2010-CODATA value and at 7σ variance with respect to it, thus reinforcing the proton radius puzzle.

The mid-infrared spectral range (λ~2-20 μm) is of particular importance as many molecules exhibit strong vibrational fingerprints in this region. Optical frequency combs--broadband optical sources consisting of equally spaced and mutually coherent sharp lines--are creating new opportunities for advanced spectroscopy. Here we demonstrate a novel approach to create mid-infrared optical frequency combs via four-wave mixing in a continuous-wave pumped ultra-high Q crystalline microresonator made of magnesium fluoride. Careful choice of the resonator material and design made it possible to generate a broadband, low-phase noise Kerr comb at λ=2.5 μm spanning 200 nm (≈10 THz) with a line spacing of 100 GHz. With its distinguishing features of compactness, efficient conversion, large mode spacing and high power per comb line, this novel frequency comb source holds promise for new approaches to molecular spectroscopy and is suitable to be extended further into the mid-infrared.

Dual-comb spectroscopy is extended to the visible spectral range with two short-pulse frequency-doubled free-running ytterbium-doped fiber lasers. When the spectrum is shifted to other domains by nonlinear frequency conversion, tracking the relative fluctuations of the femtosecond oscillators at their fundamental wavelength automatically produces the correction signal needed for the recording of distortion-free spectra. The dense rovibronic spectrum of iodine around 19,240 cm(-1) is recorded within 12 ms at Doppler-limited resolution.

We report on the first (to our knowledge) demonstration of nonlinear dual-frequency-comb spectroscopy. In multi-heterodyne femtosecond Raman-induced Kerr-effect spectroscopy, the Raman gain resulting from the coherent excitation of molecular vibrations by a spectrally narrow pump is imprinted onto the femtosecond laser frequency comb probe spectrum. The birefringence signal induced by the nonlinear interaction of these beams and the sample is heterodyned against a frequency comb local oscillator with a repetition frequency slightly different from that of the comb probe. Such time-domain interference provides multiplex access to the phase and amplitude Raman spectra over a broad spectral bandwidth within a short measurement time.

Frequency stabilization of a diode laser locked to a whispering gallery mode (WGM) reference resonator made of a MgF 2 single crystal is demonstrated. The strong thermal dependence of the difference frequency between two orthogonally polarized TE an TM modes (dual-mode frequency) of the optically anisotropic crystal material allows sensitive measurement of the resonator's temperature within the optical mode volume. This dual-mode signal was used as feedback for self-referenced temperature stabilization to nanokelvin precision, resulting in frequency stability of 0.3 MHz/h at 972 nm, which was measured by comparing with an independent ultrastable laser.

We investigate the suitability of various commercially available pump lasers for operation with a carrier-envelope offset frequency stabilized Ti:sapphire oscillator. Although the tested pump lasers differ in their setup and properties (e.g., single vs. multi-mode), we find that they are all well-suited for the purpose. The residual rms phase noise (integrated between 20 Hz and 5 MHz) of the stabilized oscillator is found to be below 160 mrad with each pump laser, corresponding to less than 1/40 of an optical cycle. Differences in performance vary slightly. In particular, our results indicate that the latest generation of multi-mode pump lasers can be used for applications where precise phase control of the oscillator is strictly required.

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.

We have realized a hybrid optomechanical system by coupling ultracold atoms to a micromechanical membrane. The atoms are trapped in an optical lattice, which is formed by retroreflection of a laser beam from the membrane surface. In this setup, the lattice laser light mediates an optomechanical coupling between membrane vibrations and atomic center-of-mass motion. We observe both the effect of the membrane vibrations onto the atoms as well as the backaction of the atomic motion onto the membrane. By coupling the membrane to laser-cooled atoms, we engineer the dissipation rate of the membrane. Our observations agree quantitatively with a simple model.

We have measured the 1S-2S transition frequency in atomic hydrogen via two-photon spectroscopy on a 5.8 K atomic beam. We obtain f(1S-2S) = 2,466,061,413,187,035 (10)  Hz for the hyperfine centroid, in agreement with, but 3.3 times better than the previous result [M. Fischer et al., Phys. Rev. Lett. 92, 230802 (2004)]. The improvement to a fractional frequency uncertainty of 4.2 × 10(-15) arises mainly from an improved stability of the spectroscopy laser, and a better determination of the main systematic uncertainties, namely, the second order Doppler and ac and dc Stark shifts. The probe laser frequency was phase coherently linked to the mobile cesium fountain clock FOM via a frequency comb.

We report on a low-noise diode laser oscillator at 972 nm actively stabilized to an ultrastable vibrationally and thermally compensated reference cavity. To increase the fraction of laser power in the carrier we designed a 20 cm long external cavity diode laser with an intracavity electro-optical modulator. The fractional power in the carrier reaches 99.9%, which corresponds to an rms phase noise of φ(rms)2=1 mrad2 in 10 MHz bandwidth. Using this oscillator, we recorded 1S-2S spectra in atomic hydrogen and have not observed any significant loss of the excitation efficiency due to phase noise multiplication in the three consecutive two-photon processes.