Electrons probe ultrafast dynamics
Laser-controlled electrons, traditionally used to generate ultrafast optical pulses, can themselves be used to probe dynamics on this time scale.
FIGURE 1. David Villeneuve of the National Research Council of Canada explores the subfemtosecond realm using a system containing cutting-edge optics and an ordinary Ti:sapphire laser.
The challenge of consistently generating and measuring very short optical pulses of 5 fs or less has been intensely pursued in ultrafast spectroscopy. The motion of atoms within molecules is on the timescale of 10 fs. Probing with these few-femtosecond pulses allows "snapshots" of how molecules are contorted during chemical reactions. Femtosecond laser sources have resulted in substantial spin-off research in chemical physics, molecular biology, and materials science.
Beyond the realm of femtosecond lasers, electron motion takes place on an even shorter timescale of attoseconds (1 as = 10-18 s)—the classical orbital time for an electron in the ground state of hydrogen is 24 as. Spectroscopic access to this frontier timescale would allow one to see how an atom reconfigures its own electrons.
In the past four years, much progress has been made in trying to break this pulse-duration barrier. At first, trains of subfemtosecond pulses were reported.1 Then single subfemtosecond pulses were achieved.2 The most recent feat was a collaborative effort in Vienna, Austria, where 650-as pulses were generated to resolve the excitation dynamics of strongly bound electrons.3 Because the duration of any pulse cannot be smaller than the oscillation period of the electromagnetic waves within it, these cutting-edge pulses are necessarily in the extreme-ultraviolet (EUV) or x-ray wavelengths.
The high way
The leading approach to achieve these subfemtosecond pulses is high-harmonic generation (HHG). Although popularly used, HHG is not yet fully understood, and manufacturing HHG materials in response to desired specific inputs or outputs can be hit-or-miss. It is also an inefficient process and produces pulses that tend to be difficult to focus and interact weakly.
High-harmonic generation involves exposing atomic media to a femtosecond laser of field strength comparable to the nuclear electron-binding field (on the order of 1014 W/cm2). The probability of ionization is high enough that it is virtually a certainty. In the first quarter of the laser cycle, the ionized electron is freed by tunneling through the combined potential barriers of the laser and ionic fields, and accelerated away from the ion. In the next quarter cycle, when the laser field reverses, the electron is accelerated back. Because of the probabilistic nature of the trajectory reversal, there is, at first, a 50% probability of recollision followed by an attenuating series of probabilities.
The ensuing recollision has three possible outcomes: elastic scattering, inelastic scattering (excitation of the ion), and recombination (HHG). The latter requires the highest recollision energies and involves the ion recapturing the ionized electron and emitting a high-energy photon. A gestalt nonlinear effect of many atoms cooperatively responding to this laser-induced ionization is the emission of photon frequencies that are many high-order multiples of the driving-laser frequency. Typically these emissions are in the EUV to x-ray wavelengths. The duration of the electron-ion recollision largely determines the duration of the resultant high-harmonic pulses produced, potentially in the attosecond regime. Bursts of high-order harmonics of subfemtosecond duration can be generated from femtosecond optical pulses of 50-fs or longer duration.
It has been recently demonstrated, however, that the recollision electrons involved in HHG can themselves be used to as ultrafast probes. Hiromichi Niikura, Paul Corkum, and David Villeneuve at the National Research Council of Canada in Ottawa have successfully used inelastic scattering of these electrons to observe the vibration of a hydrogen molecule with a precision of under 1 fs.5 Only an ordinary 50-fs Ti:sapphire laser of 800-nm wavelength was used to create these recollision electrons (see Fig. 1).
In the experiment, the laser pulse singly ionized hydrogen molecules, triggering the molecule into a higher vibrational energy state and simultaneously freeing the electron that subsequently recollided with the parent ion. Since the vibration period of this state was known, this started a molecular "clock" against which to measure the time of electron-ion recollision. Inelastic scattering of the electrons upon recollision stopped the clock by further triggering the molecule into higher vibrational energy states, all of which lead to dissociation. To read the clock at the time of recollision, the kinetic energy distribution of the protons was analyzed (see Fig. 2).
The kinetic energy distribution also allowed the characterization of the electron current density "pulse" experienced by the ion upon recollision. It was shown that the ion experiences unprecedented current densities on the order of 1011 A/cm2 in single-femtosecond pulses (see Fig. 3). Even large accelerators cannot generate these current densities.
FIGURE 3. Calculations show that the current density experienced by a hydrogen ion after ionization approaches 1011 A/cm2. The leading electron pulse marks recollision.
In analogy with conventional pump-probe spectroscopic measurements, dynamics were observed by changing the delay time between pump and probe steps. Changing the laser wavelength did this, even though the delay is based on the laser optical-cycle period. With optical parametric amplifiers, it is relatively easy to tune a 40-fs laser pulse in the range 1 to 2 µm. This gave pump-probe delays of 1.7 to 4.2 fs, much faster than today's fastest visible-wavelength laser. Furthermore, the ultimate duration of the electron probe can be as short as 200 as, and the spatial resolution is not limited by the laser wavelength and is shown to be 5 picometers.
The result created by the researchers at NRC is a new paradigm of ultrafast measurement. Previously it was assumed that pulse durations had to be shorter than the dynamics being measured. By using the new technique of sub-laser-cycle correlation, dynamics on the scale of the laser optical period can now be seen.
Recollision was shown to be solely responsible for the dissociated fragments (as compared to instantaneous ionization) by gradually increasing the elliptical polarization of the laser and comparing the kinetic energy distributions of the fragments. By taking note of which pathways were energetically excitable at which wavelengths, as well as comparing cross sections, dissociation pathways were also differentiated.
The most important potential application of this method is molecular diffraction. Electrons interact with molecules much more strongly than photons. Gas-phase electron diffraction is a well-established method of determining molecular structure, especially for those molecules that cannot easily be crystallized for x-ray diffraction. Ahmed Zewail (the 1999 Nobel Prize winner in chemistry) and his group at the California Institute of Technology (Pasadena, CA) are pursuing time-resolved gas-phase electron diffraction. Using electron pulses with 1-ps duration, they have been successful in seeing changes in molecular structure during chemical reactions. It is challenging to reduce the pulse duration more, however.
The NRC approach uses the recollision electrons to diffract from the very molecule from which the electrons came. Though these enormous current densities will be delivered
in-sample a few femtoseconds after ionization, it will be the neutral molecule imaged; there is not enough time between ionization and recollision probing for the neutral molecule to change. The main limitation is the kinetic energy of the electrons (200 eV, currently) that have a relatively long wavelength. Longer laser wavelengths will be used to substantially increase this.
Subfemtosecond measurement is possible with any pair of charged correlated particles. Electrons are easily controlled because of their low mass. Larger particles can also be controlled, although at higher laser intensities. Each will produce an ultrafast high-intensity charge pulse suitable for probing the dynamics of the collision subject. As long as the laser field can label the relative trajectory of one partner with respect to the other, recollision is unnecessary.
Compared to HHG, recollision electrons are 100% efficiently produced and strongly interact with the probed sample. Best of all, they need not be transported, as they are produced directly in the sample. Recollision electrons can be used as a controllable, coherent, short-duration, short-wavelength beam delivered to the parent ion with subfemtosecond timing precision and with very high current density. It is important to note that only a 50- to 100-fs driving laser is needed to produce these electrons and to have access to measuring this time scale. This is opposite the 30-year trend of higher resolution requiring shorter optical pulses.
- Papadogiannis et al., Phys. Rev. Lett. 22 (November 1999).
- M. Hentschel et al, Nature 414, 509 (2001).
- M. Drescher et al, Nature 419, 803 (2002).
- P. M. Paul et al, Science 292, 1689 (2001).
- Hiromichi Niikura et al., Nature 417, 917 (2002).
ALEX ZIVOJINOVIC is a science writer for The Varsity, University of Toronto, 21 Sussex Avenue, Toronto, Ontario M5S 1J6, Canada; e-mail: firstname.lastname@example.org.