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.

Optical frequency metrology

Ultrafast lasers, which generate optical pulses in the picosecond and femtosecond range, have progressed over the past decade from complicated and specialized laboratory systems to compact, reliable instruments. Semiconductor lasers for optical pumping and fast optical saturable absorbers, based on either semiconductor devices or the optical nonlinear Kerr effect, have dramatically improved these lasers and opened up new frontiers for applications with extremely short temporal resolution (much smaller than 10 fs), extremely high peak optical intensities (greater than 10 TW/cm2) and extremely fast pulse repetition rates (greater than 100 GHz).

Recent developments in compact ultrafast lasers

Summary form only given. Fundamental processes in atoms, molecules, as well as condensed matter are triggered or mediated by the motion of electrons inside or between atoms. Electronic dynamics on atomic length scales tends to unfold within tens to thousands of attoseconds (1 attosecond [as] = 10-18 s). Recent breakthroughs in laser science are now opening the door to watching and controlling these hitherto inaccessible microscopic dynamics. The key to accessing the attosecond time domain is the control of the electric field of (visible) light, which varies its strength and direction within less than a femtosecond (1 femtosecond = 1000 attoseconds). Atoms exposed to a few oscillations cycles of intense laser light are able to emit a single extreme ultraviolet (XUV) burst lasting less than one femtosecond. Full control of the evolution of the electromagnetic field in laser pulses comprising a few wave cycles have recently allowed the reproducible generation and measurement of isolated sub-femtosecond XUV pulses, demonstrating the control of microscopic processes (electron motion and photon emission) on an attosecond time scale. These tools have enabled us to visualize the oscillating electric field of visible light with an attosecond "oscilloscope", to control single-electron and probe multi-electron dynamics in atoms, molecules and solids. Recent experiments hold promise for the development of an attosecond X-ray source, which may pave the way towards 4D electron imaging with sub-atomic resolution in space and time.

Attosecond Physics

The advent of ultraintense laser pulses generated by the technique of chirped pulse amplification (CPA) along with the development of high-fluence laser materials has opened up an entirely new field of optics. The electromagnetic field intensities produced by these techniques, in excess of ${10}^{18}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$, lead to relativistic electron motion in the laser field. The CPA method is reviewed and the future growth of laser technique is discussed, including the prospect of generating the ultimate power of a zettawatt. A number of consequences of relativistic-strength optical fields are surveyed. In contrast to the nonrelativistic regime, these laser fields are capable of moving matter more effectively, including motion in the direction of laser propagation. One of the consequences of this is wakefield generation, a relativistic version of optical rectification, in which longitudinal field effects could be as large as the transverse ones. In addition to this, other effects may occur, including relativistic focusing, relativistic transparency, nonlinear modulation and multiple harmonic generation, and strong coupling to matter and other fields (such as high-frequency radiation). A proper utilization of these phenomena and effects leads to the new technology of relativistic engineering, in which light-matter interactions in the relativistic regime drives the development of laser-driven accelerator science. A number of significant applications are reviewed, including the fast ignition of an inertially confined fusion target by short-pulsed laser energy and potential sources of energetic particles (electrons, protons, other ions, positrons, pions, etc.). The coupling of an intense laser field to matter also has implications for the study of the highest energies in astrophysics, such as ultrahigh-energy cosmic rays, with energies in excess of ${10}^{20}\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The laser fields can be so intense as to make the accelerating field large enough for general relativistic effects (via the equivalence principle) to be examined in the laboratory. It will also enable one to access the nonlinear regime of quantum electrodynamics, where the effects of radiative damping are no longer negligible. Furthermore, when the fields are close to the Schwinger value, the vacuum can behave like a nonlinear medium in much the same way as ordinary dielectric matter expanded to laser radiation in the early days of laser research.

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Optics in the relativistic regime

We generated single-cycle isolated attosecond pulses around ∼36 electron volts using phase-stabilized 5-femtosecond driving pulses with a modulated polarization state. Using a complete temporal characterization technique, we demonstrated the compression of the generated pulses for as low as 130 attoseconds, corresponding to less than 1.2 optical cycles. Numerical simulations of the generation process show that the carrier-envelope phase of the attosecond pulses is stable. The availability of single-cycle isolated attosecond pulses opens the way to a new regime in ultrafast physics, in which the strong-field electron dynamics in atoms and molecules is driven by the electric field of the attosecond pulses rather than by their intensity profile.

https://science.sciencemag.org/content/sci/314/5798/443.full.pdf

Isolated Single-Cycle Attosecond Pulses

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.

Attosecond control of electronic processes by intense light fields

Several methods of carrier-envelope-phase stabilization of amplified ultrashort laser pulses are presented. Full temporal characterization of the resultant intense few-cycle light waveforms, reproducible with every laser shot, was achieved by combining conventional pulse characterization techniques with observing the signature of soft-X-ray emission.

Phase-controlled amplification of few-cycle laser pulses

We report measurements of the response of a Kerr-lens mode-locked Ti:sapphire frequency comb to pump power modulation. For each setting of the laser, the comb expands and contracts about a particular fixed point in frequency. We measured this fixed point and found that it is within 8% of our frequency comb’s center. In addition, we found that as we shift the comb’s center frequency, the fixed point follows to some extent. It follows that modulating the pump power mostly affects the comb’s group velocity, i.e., the repetition rate.

Frequency dependence of the fixed point in a fluctuating frequency comb

Nature 421, 611–615 (2003). In Fig. 2c of this Letter, the units of time on the x axis should be seconds, not femtoseconds.

/pdf/erratum-attosecond-control-of-electronic-processes-by-xnd664h2u4.pdf

erratum: Attosecond control of electronic processes by intense light fields

Modulating the pump power of a mode-locked laser causes the frequency comb to expand and contract about a fixed point in frequency. We report the first measurement of this fixed point in a tunable laser.

Ch. Gohle

Papers

Attosecond control of electronic processes by intense light fields

Phase-controlled amplification of few-cycle laser pulses

Frequency dependence of the fixed point in a fluctuating frequency comb

erratum: Attosecond control of electronic processes by intense light fields

Frequency dependence of the fixed point in a fluctuating frequency comb