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.

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.

We report on an absolute frequency measurement of the hydrogen 1S-2S two-photon transition in a cold atomic beam with an accuracy of 1.8 parts in 10(14). Our experimental result of 2 466 061 413 187 103(46) Hz has been obtained by phase coherent comparison of the hydrogen transition frequency with an atomic cesium fountain clock. Both frequencies are linked with a comb of laser frequencies emitted by a mode locked laser.

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 199 Hg ϩ 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 ϫ 10 Ϫ15 is measured in 1 second of averaging-a value substantially better than that of the world's best microwave atomic clocks.

We describe a possible new technique for precise wavelength calibration of high‐resolution astronomical spectrographs using femtosecond‐pulsed mode‐locked lasers controlled by stable oscillators such as atomic clocks. Such ‘frequency combs’ provide a series of narrow modes which are uniformly spaced according to the laser's pulse repetition rate and whose absolute frequencies are known a priori with relative precision better than 10−12. Simulations of frequency comb spectra show that the photon‐limited wavelength calibration precision achievable with existing echelle spectrographs should be ∼1 cm s−1 when integrated over a 4000 Å range. Moreover, comb spectra may be used to accurately characterize distortions of the wavelength scale introduced by the spectrograph and detector system. The simulations show that frequency combs with pulse repetition rates of 5–30 GHz are required, given the typical resolving power of existing and possible future echelle spectrographs. Achieving such high repetition rates, together with the desire to produce all comb modes with uniform intensity over the entire optical range, represents the only significant challenges in the design of a practical system. Frequency comb systems may remove wavelength calibration uncertainties from all practical spectroscopic experiments, even those combining data from different telescopes over many decades.

We have measured the absolute optical frequency of the cesium D 1 line at 335 THz (895 nm). This frequency provides an important link for a new determination of the fine structure constant a. The D 1 line has been compared with the fourth harmonic of a methane stabilized He-Ne laser at 88.4 THz (3.39 mm). To measure the frequency mismatch of 18.39 THz between 4 3 88.4 THz 354 THz and the D 1 line a frequency comb spanning around 244 000 modes of a Kerr-lens mode-locked laser was used. We find 1 167 688 (81) kHz for the hyperfine splitting of the 6P 1͞2 state and 335 116 048 807 (41) kHz for the hyperfine centroid from which we derive a 21 137.035 992 4͑41͒.

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Using a coherent nonlinear optical technique, slipping of the carrier through the envelope of 6-fs light wave packets emitted from a mode-locked-oscillator/pulse-compressor system has been measured, permitting the generation of intense, few-cycle light with precisely reproducible electric and magnetic fields. These pulses open the way to controlling the evolution of strong-field interactions on the time scale of the light oscillation cycle and are indispensable to reproducible attosecond x-ray pulse generation.