For decades, x-ray and electron diffraction have resolved the atomic-scale details of matter. Extending such techniques to the ultrafast time scales at which chemical reactions occur is a more recent achievement.1 Thanks to recent advances in accelerator technology this past decade, x rays from free-electron lasers can now probe the structural dynamics of molecules at femtosecond resolution (see Physics Today, April 2011, page 13, and for background on FELs the article by William Colson, Erik Johnson, Michael Kelley, and Alan Schwettman, Physics Today, January 2002, page 35). And for the past few years, a handful of groups have been working to extend electron sources to that time regime as well—no big-machine physics required. The essential ingredients can all fit on a tabletop.
Unlike photons from a laser, though, electrons emitted from a photocathode don’t usually hang together well: Thermal drift and Coulomb repulsion spread them apart. And the resulting transverse momentum spread—or, more precisely, its inverse multiplied by Planck’s constant, a figure of merit known as the transverse coherence length—determines the sharpness of the Bragg peaks in any electron diffraction experiment.
In 2005 Jom Luiten and his colleagues from Eindhoven University of Technology in the Netherlands proposed a bold scheme to ameliorate the spreading without resorting to apertures, which sacrifice the brightness of a beam. The idea, which his and other groups later implemented, was to liberate bunches of electrons not from a photocathode but from a cloud of laser-cooled atoms held in a magneto-optical trap.2 According to simulations, the atoms, when excited just above their ionization threshold, would emit electrons at temperatures as cold as 10 K. The coherence length, which scales inversely with the square root of temperature at low charge densities, would thus be more than an order of magnitude greater than that of electrons released at thousands of kelvin, the temperature typical of a photocathode.
After nearly a decade of exploring the properties of their ultracold electron source, the Eindhoven researchers have now put it to work: By adding magnetic lenses they projected a 100-Hz pulsed electron beam onto a thin graphite flake. The resulting diffraction patterns offer a proof-of-principle demonstration,3 “an important technical step in our field,” says the University of Melbourne’s Robert Scholten. “Diffraction is ordinarily put in the service of revealing details about a poorly understood sample. But that procedure is here turned on its head: Diffraction patterns of a well-known crystal may reveal insights for optimizing a new and unusual source.”
Spots and sizes
Preparing the electron beam is a multistep process. The Eindhoven researchers first load some 100 million rubidium atoms into the cold trap, shown in figure 1. To strip out electrons, they overlap two coincident laser beams—a red pulse that excites the atoms from a 5s to 5p hyperfine state and a 100-fs blue pulse that ionizes those excited atoms. The ionizing pulse imprints the electron bunch with its ultrashort duration and is tunable around a central wavelength. A local electrostatic field then accelerates the bunch downstream toward the graphite, about a meter away, as illustrated in figure 2a.
Figure 1. A magneto-optical trap (center) holds an ultracold gas of rubidium atoms that are ionized to generate a 100-fs pulse of electrons. Those electrons are then accelerated and travel to the right in a diffraction experiment. Doctoral students Martin van Mourik (left) and Peter Pasmans (right) adjust the setup. Cooling and trapping laser beams pass from an optical table (foreground) through the quarter-wave plate in Pasmans’s hand, and ionization laser pulses are reflected into the trap after passing through the upward-directed black pipe. (Image courtesy of Bart van Overbeeke Fotografie.)
Figure 1. A magneto-optical trap (center) holds an ultracold gas of rubidium atoms that are ionized to generate a 100-fs pulse of electrons. Those electrons are then accelerated and travel to the right in a diffraction experiment. Doctoral students Martin van Mourik (left) and Peter Pasmans (right) adjust the setup. Cooling and trapping laser beams pass from an optical table (foreground) through the quarter-wave plate in Pasmans’s hand, and ionization laser pulses are reflected into the trap after passing through the upward-directed black pipe. (Image courtesy of Bart van Overbeeke Fotografie.)
Figure 2. The diffraction experiment. Rubidium atoms in a magneto-optical trap (a) are ionized by two spatially and temporally overlapping laser pulses. A 780-nm pulse (red) excites the electrons and a second pulse (blue) at a wavelength of 480 nm or shorter raises a few hundred of them to the ionization threshold. The electron bunch is then accelerated downstream by a local electric field and focused, as shown by the green path, using magnetic lenses onto a 20-nm-thick graphite flake. (b) A diffraction pattern taken with 10-K electrons illustrates graphite’s hexagonal lattice. Focusing the beam onto the sample enlarges the first-order Bragg peaks for clear comparison of experiments. (Adapted from ref. 3.)
Figure 2. The diffraction experiment. Rubidium atoms in a magneto-optical trap (a) are ionized by two spatially and temporally overlapping laser pulses. A 780-nm pulse (red) excites the electrons and a second pulse (blue) at a wavelength of 480 nm or shorter raises a few hundred of them to the ionization threshold. The electron bunch is then accelerated downstream by a local electric field and focused, as shown by the green path, using magnetic lenses onto a 20-nm-thick graphite flake. (b) A diffraction pattern taken with 10-K electrons illustrates graphite’s hexagonal lattice. Focusing the beam onto the sample enlarges the first-order Bragg peaks for clear comparison of experiments. (Adapted from ref. 3.)
At first glance, one might expect the broad bandwidth of a 100-fs pulse to spoil the coherence because of hot electrons ejected by the shorter wavelengths. But last year Scholten’s and Luiten’s respective groups published independent accounts proving that wasn’t the case.4 The excess kinetic energy does not get redistributed evenly among all degrees of freedom but rather mostly contributes to the electrons’ longitudinal motion. That’s because the trap’s applied electrostatic field, which pulls electrons downstream, also lowers, via the Stark shift, the atoms’ ionization potential in that direction, effectively squeezing liberated electrons transversely at the expense of their longitudinal spread.
The combination of the applied field and the ionization laser pulse determines the kinetic-energy distribution of the released electrons, and thus their effective temperature. By varying the ionizing laser’s wavelength in a series of runs, Luiten and company reduced the electrons’ temperature from 300 K to 10 K. The concomitant narrowing in the width of the diffraction peaks behaved just as they expected.
To resolve molecular structures, the transverse coherence length of diffracting electrons must be larger than a material’s lattice constant. For the diffraction pattern in figure 2b, imaged with 10-K electrons focused to a 100-µm spot size, the researchers estimated the coherence length at no smaller than 15 nm. Reassuringly, that’s high enough for complex macromolecular diffraction, a common goal among many groups.
Toward single-shot imaging
Ultrafast electron beams from hot photocathodes may also possess that large a coherence length. But it comes at the cost of electric current. The most coherent beams come from a point source. But in so confined a space, researchers must turn off the interactions among electrons by photoemitting them one at a time. Accordingly, they resort to a stroboscopic mode that builds up patterns from millions of shots.5
That mode isn’t problematic for processes that are, like phase transitions, reversible and robust through repeated experiments. Capturing irreversible chemical processes, on the other hand, requires packing all those electrons into a single shot. Free-electron lasers are bright enough—nine orders of magnitude brighter than the best synchrotron light sources—to pull that off with x rays. Ultracold electron sources, however, have not yet solved the flux problem. Each ionizing laser pulse in the Eindhoven experiment generates a bunch containing a few hundred electrons. At roughly 40 µm in diameter, the relatively extended size of the laser spot on the atomic cloud is large enough to avoid a “Coulomb explosion” that otherwise would blow apart electrons emitted from a more tightly confined space.
A year before Luiten originally proposed ultracold electron beams, he argued that an electron bunch whose charge density is somehow uniformly distributed in a three-dimensional ellipsoid would make such coulombic expansion reversible. One would simply need the right combination of external electric and magnetic fields to recompress the beam.
The idea was theoretically laid out for photocathode sources, but it applies to cold-atom sources equally well. And in 2011 Scholten’s group demonstrated such dynamic bunch shaping in the context of near-threshold photoionization.6 The trick was to tailor the incident laser pattern with a spatial light modulator to imprint a pattern on the charge distribution. The electron bunch subsequently retained its shape as it travelled away from the gas. Although the imprinted charge distribution wasn’t ellipsoidal—in fact, the imprinting was done in two dimensions—the demonstration represents a promising path toward counteracting space-charge effects and stepping up the brightness of an electron beam.
