Single-Cycle Nonlinear Optics
E. Goulielmakis,1*
M. Schultze,1
M. Hofstetter,2
V. S. Yakovlev,2
J. Gagnon,1
M. Uiberacker,2
A. L. Aquila,3
E. M. Gullikson,3
D. T. Attwood,3
R. Kienberger,1
F. Krausz,1,2*
U. Kleineberg2*
Nonlinear optics plays a central role in the advancement of optical science and laser-based technologies. We report on the confinement of the nonlinear interaction of light with matter to a single wave cycle and demonstrate its utility for time-resolved and strong-field science. The electric field of 3.3-femtosecond, 0.72-micron laser pulses with a controlled and measured waveform ionizes atoms near the crests of the central wave cycle, with ionization being virtually switched off outside this interval. Isolated sub-100-attosecond pulses of extreme ultraviolet light (photon energy 
80 electron volts), containing 0.5 nanojoule of energy, emerge from the interaction with a conversion efficiency of 10–6. These tools enable the study of the precision control of electron motion with light fields and electron-electron interactions with a resolution approaching the atomic unit of time (24 attoseconds).
1 Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany.
2 Department für Physik, Ludwig-Maximilians-Universität, Am Coulombwall 1, D-85748 Garching.
3 Center for X-Ray Optics, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
* To whom correspondence should be addressed. E-mail: elgo{at}mpq.mpg.de (E.G.); krausz{at}lmu.de (F.K.); ulf.kleineberg{at}physik.uni-muenchen.de (U.K.)
