P.B. Corkum and Zenghu Chang
Electron tunneling from molecular O2. The wave packet that tunnels is a filter version of the momentum wavefunction of the bound orbital. As it propagates, it expands. Re-collision drives this almost plane electron wave against the ion core from which it left only about 1 fs ago. There, it diffracts.
Tunneling, which is confined to the field crests, provides another measurement method.
• The dynamics of a strongly driven two-surface system has strobed by tunneling, revealing an unexpected spatial structure of the dynamics.
• Hole dynamics in xenon have been time-resolved.
Already the attosecond streak camera measurements are frequently applied to collision problems. For example, the dynamics of double ionization have been measured in a variety of rare gas atoms and for aligned N2 for different molecular alignments.
Imaging molecular structures and dynamics
So far, we have seen that attosecond technology relies on advanced laser science but has a unique flavor. Perhaps its greatest uniqueness comes from the interplay between collision physics and optical physics. Collision physics has a long tradition of measuring molecular structure. The re-collision electron can be used in a similar fashion, giving optics access to the electron wavelength (1-5 Å). Every step of the strong field ionization processes has imaging potential. Together they provide an array of methods to observe both the electrons and nuclei in molecules.
Laser STM
Structural information is impressed on the electron right from the beginning—tunneling. The figure above illustrates how tunneling from the molecule carries information on the orbital. An electron wavefunction interacts with the spatial filter of the tunnel in much the same way that a mode of an optical beam interacts with a spatial filter a node on. Not only symmetry (the position of nodes), but more detailed information about a mode (orbital) is transferred through the filter (tunnel) as we scan the beam across the filter (rotate the molecule).
The analogy with scanning tunneling microscopy (STM), used for surface science, is also very good. In a laser STM for molecules, rotating the molecule is the analogue of scanning the tip in a conventional STM.
Laser-induced electron diffraction
If the tunneling electron emerges from a single orbital, it is perfectly coherent. When it recollides, it diffracts from its parent ion. Although there are a range of collision energies and the collision occurs in the presence of the laser electric field, this diffraction pattern can be read. It gives structural information about the ion from which it originated.
Orbital tomography
In optics, interferometry allows us to fully characterize the interfering waves. This should be equally true for the electron interferometer created by the laser field. The attosecond or high harmonic pulse, produced during re-collision, encodes the interference. Recording the spectrum as a function of molecular alignment, one obtains all the information needed to reconstruct the orbital.
Laser-induced electron holography
Gabor, who discovered holography, initially dreamed of using electrons, not light. As you have seen, there are many ways that interference between a reference wave and a scattered wave can arise in strong field and attosecond technology. For example, holographic information is present in all re-collision experiments because parts of the ionizing electron wave packet escape directly to the detector, while parts re-scatter and can gain the same momentum.
Holographic information is also present when two identical attosecond XUV pulses create two photoelectron replica wave packets in the presence of the phased infrared field. All that is needed is for one replica to escape directly to the detector while the infrared field forces others to re-collide and elastically scatter. The interference between the two wave packets contains holographic information. It seems clear that Gabor’s original dream is alive and well in attosecond technology.
Looking forward
We have discussed how sub-cycle science was developed from studies of the highly nonlinear interaction between light and matter. In fact, it is the high nonlinearity that allows the laser cycle to be sub-divided. Re-collision is one form of highly nonlinear interaction. With re-collision and using atoms or molecules, it is probably possible to produce pulses with bandwidth to reaching pulse duration of about 25 as—one atomic unit of time. For many applications, a transform-limited pulse is not needed. Transform-limited measurement is possible as long as the chirp is known.
Re-collision is not the only highly nonlinear process to exploit. Many other such interactions await us, so there is no obvious lower limit to the pulse duration since there is no obvious limit to high-order nonlinear light-matter interactions. In addition, there is no fundamental reason why time is a unique variable. Almost certainly, related ideas can be extended to space—that is, to nano- as well as atto-optics.
In fact, molecular structure can already be measured optically, so one form of sub-nanometer optics is demonstrated. Furthermore, many of the attosecond science ideas should translate into other media—anyplace where highly nonlinear interactions are possible. In other words, there is a broad vista for extreme nonlinear optics, just as there was a broad vista for low-order nonlinear optics in 1960.
Finally, there are still other routes to attosecond science. We have discussed how, aside from the transition moment, attosecond optical pulses are replicas of re-collision electron pulses. Linacs and other electron accelerators also create intense electron beams. These electron pulses can be compressed to the attosecond time scale. It seems inevitable that attosecond free electron lasers will ultimately be constructed, introducing a complementary technology. Already there is progress. Optical and synchrotron technology are becoming entwined, further extending the reach of both.
The authors jointly acknowledge U.S. Army Research Office support under grant number W911NF-07-1-0475.
P.B. Corkum is with the Joint Laboratory for Attosecond Science at the University of Ottawa/National Research Council, Ottawa, Canada. Zenghu Chang, the chair of the newly established “Optical Attoscience Technical Group” of OSA, is with the department of physics, Kansas State University, Manhattan, Kan., U.S.A.
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