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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.

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 single-pass high-harmonic generation (HHG) with amplified driving laser pulses at a repetition rate of 20.8 MHz. An Yb:YAG Innoslab amplifier system provides 35 fs pulses with 20 W average power at 1030 nm after external pulse compression. Following tight focusing into a xenon gas jet, we observe the generation of high-harmonic radiation of up to the seventeenth order. Our results show that state-of-the-art amplifier systems have become a promising alternative to cavity-assisted HHG for applications that require high repetition rates, such as frequency comb spectroscopy in the extreme UV.

We report the use of a specially designed tapered photonic crystal fiber to produce a broadband optical spectrum covering the visible spectral range. The pump source is a frequency doubled Yb fiber laser operating at a repetition rate of 14 GHz and emitting sub-5 pJ pulses. We experimentally determine the optimum core diameter and achieve a 235 nm broad spectrum. Numerical simulations are used to identify the underlying mechanisms and explain spectral features. The high repetition rate makes this system a promising candidate for precision calibration of astronomical spectrographs., (© 2011 Optical Society of America)

We apply spatially and spectrally resolved interferometry to measure the complex ratio between the field circulating inside a high-finesse femtosecond enhancement cavity and the seeding field. Our simple and highly sensitive method enables the measurement of single-round-trip group delay dispersion of a fully loaded cavity at resonance for the first time. Group delay dispersion can be determined with a reproducibility better than 1 fs2 allowing the investigation of nonlinear processes triggered by the high intracavity power. The required data acquisition time is less than 1 s.

We report on injection locking of optically excited mechanical oscillations of a single, trapped ion. The injection locking dynamics are studied by analyzing the oscillator spectrum with a spatially selective Fourier transform technique and the oscillator phase with stroboscopic imaging. In both cases we find excellent agreement with theory inside and outside the locking range. We attain injection locking with forces as low as 5(1)×10{-24}  N so this system appears promising for the detection of ultraweak oscillating forces.

A passive optical resonator is used to enhance the power of a pulsed 78 MHz repetition rate Yb laser providing 200 fs pulses. We find limitations relating to the achievable time-averaged and peak power, which we distinguish by varying the duration of the input pulses. An intracavity average power of 18 kW is generated with close to Fourier-limited pulses of 10 W average power. Beyond this power level, intensity-related effects lead to resonator instabilities, which can be removed by chirping the seed laser pulses. By extending the pulse duration in this way to 2 ps, we could obtain 72 kW of intracavity circulating power with 50 W of input power.

Measuring the hydrogen-deuterium isotope shift via two-photon spectroscopy of the 1S-2S transition, we obtain 670,994,334,606(15) Hz. This is a 10-times improvement over the previous best measurement [A. Huber, Phys. Rev. Lett. 80, 468 (1998)] confirming its frequency value. A calculation of the difference of the mean square charge radii of deuterium and hydrogen results in d - p =3.82007(65)  fm2, a more than twofold improvement compared to the former value.

We have explored the performance of 2 "dark fibers" of a commercial telecommunication fiber link for a remote comparison of optical clocks. These fibers establish a network in Germany that will eventually link optical frequency standards at PTB with those at the Institute of Quantum Optics (IQ) at the Leibniz University of Hanover, and the Max Planck Institutes in Erlangen (MPL) and Garching (MPQ). We demonstrate for the first time that within several minutes a phase coherent comparison of clock lasers at the few 10(-15) level can also be accomplished when the lasers are more than 100 km apart. Based on the performance of the fiber link to the IQ, we estimate the expected stability for the link from PTB to MPQ via MPL that bridges a distance of approximately 900 km.

By frequency quadrupling a picosecond pulse train from a Ti:sapphire laser at 820 nm we generate a frequency comb at 205 nm with nearly bandwidth-limited pulses. The nonlinear frequency conversion is accomplished by two successive frequency doubling stages that take place in resonant cavities that are matched to the pulse repetition rate of 82 MHz. This allows for an overall efficiency of 4.5 % and produces an output power of up to 70 mW for a few minutes and 25 mW with continuous operation for hours. Such a deep UV frequency comb may be employed for direct frequency comb spectroscopy in cases where it is less efficient to convert to these short wavelengths with continuous wave lasers.

We demonstrate a method for precision spectroscopy on trapped ions in the limit of unresolved motional sidebands. By sympathetic cooling of a chain of crystallized ions, we suppress adverse temperature variations induced by the spectroscopy laser that usually lead to a distorted line profile and obtain a Voigt profile with negligible distortions. We applied the method to measure the absolute frequency of the astrophysically relevant D2 transition in single 24Mg+ ions and find 1 072 082 934.33(16) MHz, a nearly 400-fold improvement over previous results. Further, we find the excited state lifetime to be 3.84(10) ns.

A direct measurement of the universe's expansion history could be made by observing in real time the evolution of the cosmological redshift of distant objects. However, this would require measurements of Doppler velocity drifts of approximately 1 centimeter per second per year, and astronomical spectrographs have not yet been calibrated to this tolerance. We demonstrated the first use of a laser frequency comb for wavelength calibration of an astronomical telescope. Even with a simple analysis, absolute calibration is achieved with an equivalent Doppler precision of approximately 9 meters per second at approximately 1.5 micrometers-beyond state-of-the-art accuracy. We show that tracking complex, time-varying systematic effects in the spectrograph and detector system is a particular advantage of laser frequency comb calibration. This technique promises an effective means for modeling and removal of such systematic effects to the accuracy required by future experiments to see direct evidence of the universe's putative acceleration.

We generated a series of harmonics in a xenon gas jet inside a cavity seeded by pulses from a Ti:sapphire mode-locked laser with a repetition rate of 10.8 MHz. Harmonics up to 19th order at 43 nm were observed with plateau harmonics at the microW power level. An elaborate dispersion compensation scheme and the use of a moderate repetition rate allowed for this significant improvement in output power of the plateau harmonics of 4 orders of magnitude over previous results. With this power level and repetition rate, high-resolution spectroscopy in the extreme ultraviolet region becomes conceivable. An interesting target would be the 1S-2S transition in hydrogenlike He+ at 60 nm.

We present first experimental results of our investigation of non-collinear high harmonic generation (NCHHG) with a chirped pulse amplification system. Collimated high harmonic radiation of higher than 9th order is observed along the bisector of two fundamental beams crossing in a xenon gas target. The obtained results show that cavity-assisted non-collinear high harmonic generation is a promising candidate for efficient generation and outcoupling of extreme ultraviolet (XUV) radiation.

A femtosecond frequency comb provides a vast number of equidistantly spaced narrow band laser modes that can be simultaneously tuned and frequency calibrated with 15 digit accuracy. Our Vernier spectrometer utilizes all of theses modes in a massively parallel manner to rapidly record both absorption and dispersion spectra with a sensitivity that is provided by a high finesse broadband optical resonator and a resolution that is only limited by the frequency comb line width while keeping the required setup simple.

We report a new absolute frequency measurement of the Cs 6s-8s two-photon transition measured using frequency comb spectroscopy. The fractional frequency uncertainty is 5x10(-11), a factor of 6 better than previous results. The comb is derived from a stabilized picosecond laser and referenced to an octave-spanning femtosecond frequency comb. The relative merits of picosecond-based frequency combs are discussed, and it is shown that the AC Stark shift of the transition is determined by the average rather than the much larger peak intensity.

We demonstrate a new method to simultaneously measure spectrally resolved dispersion and losses (finesse) of a passive optical cavity over the entire bandwidth of an optical frequency comb. To this end, we record and analyze the spectral Moiré pattern between the perfectly equidistant frequency comb emitted from a Ti:Sapphire laser and the longitudinal modes of the passive cavity as a function of the laser's carrier-envelope-offset phase slippage (ø)CE. In the group-delay dispersion measurement of additionally introduced optical elements we verify a 2fs(2) accuracy in a 2THz resolution bandwidth and find good agreement of the measured performance and the target design of a high reflectance dielectric mirror. The sensitivity of the method is essentially equivalent to a cavity ring down technique allowing us also to readily observe signatures of atmospheric gas species.

At present most laser systems for generating phase-stabilized high-energy pulses are chirped pulse amplifier systems that involve the selection and subsequent amplification of pulses from a phase-stabilized seed oscillator. We investigate the effect of the picking process on the carrier envelope phase stability and how the phase noise of the picked pulse sequence can be estimated from the phase noise properties of the seed oscillator. All noise components from the original pulse train above the picking frequency are aliased into the picked pulse train and therefore cannot be neglected.

Precision spectroscopy of the simple hydrogen atom has inspired dramatic advances in optical frequency metrology: femtosecond laser optical frequency comb synthesizers have revolutionized the precise measurement of optical frequencies, and they provide a reliable clock mechanism for optical atomic clocks. Precision spectroscopy of the hydrogen 1S-2S two-photon resonance has reached an accuracy of 1.4 parts in 10(14), and considerable future improvements are envisioned. Such laboratory experiments are setting new limits for possible slow variations of the fine structure constant alpha and the magnetic moment of the caesium nucleus mu(Cs) in units of the Bohr magneton mu(B).

Since 1998, the interaction of precision spectroscopy and ultrafast laser science has led to several notable accomplishments. Femtosecond laser optical frequency 'combs' (evenly spaced spectral lines) have revolutionized the measurement of optical frequencies and enabled optical atomic clocks. The same comb techniques have been used to control the waveform of ultrafast laser pulses, which permitted the generation of single attosecond pulses, and have been used in a recently demonstrated 'oscilloscope' for light waves. Here we demonstrate intra-cavity high harmonic generation in the extreme ultraviolet, which promises to lead to another joint frontier of precision spectroscopy and ultrafast science. We have generated coherent extreme ultraviolet radiation at a repetition frequency of more than 100 MHz, a 1,000-fold improvement over previous experiments. At such a repetition rate, the mode spacing of the frequency comb, which is expected to survive the high harmonic generation process, is large enough for high resolution spectroscopy. Additionally, there may be many other applications of such a quasi-continuous compact and coherent extreme ultraviolet source, including extreme ultraviolet holography, microscopy, nanolithography and X-ray atomic clocks.

A new scheme for stabilizing the carrier-envelope (CE) phase of a few-cycle laser pulse train is demonstrated. Self-phase modulation and difference-frequency generation in a single periodically poled lithium niobate crystal that transmits the main laser beam allows CE phase locking directly in the usable output. The monolithic scheme obviates the need for splitting off a fraction of the laser output for CE phase control, coupling into microstructured fiber, and separation and recombination of spectral components. As a consequence, the output yields 6-fs, 800-nm pulses with an unprecedented degree of short- and long-term reproducibility of the electric field waveform.

We have remeasured the absolute 1S-2S transition frequency nu(H) in atomic hydrogen. A comparison with the result of the previous measurement performed in 1999 sets a limit of (-29+/-57) Hz for the drift of nu(H) with respect to the ground state hyperfine splitting nu(Cs) in 133Cs. Combining this result with the recently published optical transition frequency in 199Hg+ against nu(Cs) and a microwave 87Rb and 133Cs clock comparison, we deduce separate limits on alpha/alpha=(-0.9+/-2.9) x 10(-15) yr(-1) and the fractional time variation of the ratio of Rb and Cs nuclear magnetic moments mu(Rb)/mu(Cs) equal to (-0.5+/-1.7) x 10(-15) yr(-1). The latter provides information on the temporal behavior of the constant of strong interaction.

We demonstrate that multiphoton-induced photoelectron emission from a gold surface caused by low-energy (unamplified) 4-fs, 750-nm laser pulses is sensitive to the timing of electric field oscillations with respect to the pulse peak. This observation confirms recent theoretical predictions and opens the door to measuring the absolute value of the carrier-envelope phase difference of few-cycle light pulses with a solid-state detector.

We demonstrate a simple optical clockwork mechanism based on the broadened frequency comb of a femtosecond laser and on difference-frequency generation (DFG) in a nonlinear crystal. The DFG comb possesses a vanishing carrier envelope offset frequency that permits the construction of a simple and thus potentially more stable optical clockwork. In addition it offers the possibility of extending the frequency comb into the infrared spectral region. The overall accuracy and stability of the DFG comb relative to the initial frequency comb were measured to be 6.6 x 10(-21) and 10(-18) tau(-1), respectively, where tau is the averaging time in seconds. Assuming that sum- and difference-frequency generation are independent processes, our measurements suggest a <10(-20) accuracy for them.

The amplitude and frequency of laser light can be routinely measured and controlled on a femtosecond (10(-15) s) timescale. However, in pulses comprising just a few wave cycles, the amplitude envelope and carrier frequency are not sufficient to characterize and control laser radiation, because evolution of the light field is also influenced by a shift of the carrier wave with respect to the pulse peak. This so-called carrier-envelope phase has been predicted and observed to affect strong-field phenomena, but random shot-to-shot shifts have prevented the reproducible guiding of atomic processes using the electric field of light. Here we report the generation of intense, few-cycle laser pulses with a stable carrier envelope phase that permit the triggering and steering of microscopic motion with an ultimate precision limited only by quantum mechanical uncertainty. Using these reproducible light waveforms, we create light-induced atomic currents in ionized matter; the motion of the electronic wave packets can be controlled on timescales shorter than 250 attoseconds (250 x 10(-18) s). This enables us to control the attosecond temporal structure of coherent soft X-ray emission produced by the atomic currents--these X-ray photons provide a sensitive and intuitive tool for determining the carrier-envelope phase.

Extremely narrow optical resonances in cold atoms or single trapped ions can be measured with high resolution. A laser locked to such a narrow optical resonance could serve as a highly stable oscillator for an all-optical atomic clock. However, until recently there was no reliable clockwork mechanism that could count optical frequencies of hundreds of terahertz. Techniques using femtosecond-laser frequency combs, developed within the past few years, have solved this problem. The ability to count optical oscillations of more than 1015 cycles per second facilitates high-precision optical spectroscopy, and has led to the construction of an all-optical atomic clock that is expected eventually to outperform today's state-of-the-art caesium clocks.

We have created a broad spectrum spanning more than an optical octave by launching femtosecond pulses from a battery operated Cr:LiSAF laser into a photonic crystal fiber. Despite the massive broadening in the fiber, the comb structure of the spectrum is preserved, and this frequency comb is perfectly suited for applications in optical frequency metrology.

Microwave atomic clocks have been the de facto standards for precision time and frequency metrology over the past 50 years, finding widespread use in basic scientific studies, communications, and navigation. However, with its higher operating frequency, an atomic clock based on an optical transition can be much more stable. We demonstrate an all-optical atomic clock referenced to the 1.064-petahertz transition of a single trapped 199Hg+ ion. A clockwork based on a mode-locked femtosecond laser provides output pulses at a 1-gigahertz rate that are phase-coherently locked to the optical frequency. By comparison to a laser-cooled calcium optical standard, an upper limit for the fractional frequency instability of 7 x 10(-15) is measured in 1 second of averaging-a value substantially better than that of the world's best microwave atomic clocks.

The frequency comb created by a femtosecond mode-locked laser and a microstructured fiber is used to phase coherently measure the frequencies of both the Hg+ and Ca optical standards with respect to the SI second. We find the transition frequencies to be f(Hg) = 1 064 721 609 899 143(10) Hz and f(Ca) = 455 986 240 494 158(26) Hz, respectively. In addition to the unprecedented precision demonstrated here, this work is the precursor to all-optical atomic clocks based on the Hg+ and Ca standards. Furthermore, when combined with previous measurements, we find no time variations of these atomic frequencies within the uncertainties of the absolute value of( partial differential f(Ca)/ partial differential t)/f(Ca) < or =8 x 10(-14) yr(-1) and the absolute value of(partial differential f(Hg)/ partial differential t)/f(Hg) < or =30 x 10(-14) yr(-1).

The absolute frequency of the In(+) 5s(2) (1)S(0)5s5p (3)P(0) clock transition at 237 nm was measured with an accuracy of 1.8 parts in 10(13). Using a phase-coherent frequency chain, we compared the (1)S(0)(3)P(0) transition with a methane-stabilized HeNe laser at 3.39 microm, which was calibrated against an atomic cesium fountain clock. A frequency gap of 37 THz at the fourth harmonic of the HeNe standard was bridged by a frequency comb generated by a mode-locked femtosecond laser. The frequency of the In(+) clock transition was found to be 1,267,402,452,899.92 (0.23) kHz, the accuracy being limited by the uncertainty of the HeNe laser reference. This result represents an improvement in accuracy of more than 2 orders of magnitude over previous measurements of the line and now stands as what is to our knowledge the most accurate measurement of an optical transition in a single ion.s.

We have used the frequency comb generated by a femtosecond mode-locked laser and broadened to more than an optical octave in a photonic crystal fiber to realize a frequency chain that links a 10 MHz radio frequency reference phase-coherently in one step to the optical region. By comparison with a similar frequency chain we set an upper limit for the uncertainty of this new approach to 5. 1x10(-16). This opens the door for measurement and synthesis of virtually any optical frequency and is ready to revolutionize frequency metrology.