Calculations using the time-dependent Schrödinger equation (here showing the probable position of the remaining electron after photoemission of an electron from a helium atom) served as a benchmark against which to measure the accuracy of the research team’s experiments. [Image: M. Ossiander (TUM) / M. Schultze (MPQ)]
The photoelectric effect—photoemission of electrons upon absorption of a photon of sufficient energy—constitutes a pillar of quantum mechanics and the foundation for a wide range of practical technologies. It also happens at unspeakably rapid rates, on the order of 5×10–18 seconds, or 5 attoseconds. A team of scientists from five European institutions has now used advanced attosecond laser sources to investigate the dynamics of helium photoionization—with measurements that have reportedly pushed accuracy and precision into the sub-attosecond, or zeptosecond, realm (Nat. Phys., doi: 10.1038/nphys3941).
The “many-body problem at the heart of chemistry”
For nearly a century after Einstein explained the photoelectric effect in a landmark paper marking the birth of modern quantum mechanics, photoionization has generally been modeled as an instantaneous, single-particle process. With the emergence of attosecond light sources and time-resolved spectroscopy, however, it has become clear in the past six years that photoemission actually involves a tiny time delay, ranging from 5 to 15 attoseconds.
The reason for the time delay lies in the fact that, in atomic species other than hydrogen, electrons don’t travel alone. In situations where only a single electron is photoionized, the instantaneous, single-particle approximation works reasonably well. But things become decidedly more complicated when a high-energy photon simultaneously photoionizes one electron and kicks another bound electron into a higher energy state. Then, the dynamics depend not only on calculating the kinetic energy transferred from the photon to the ionized electron, but on correlations between the photoionized electron and the excited bound electron or electrons left behind.
The impact of electron correlation on photoionization might seem like a problem of mainly academic interest. But finding solutions could have significant implications for fields from chemistry to condensed-matter physics. Indeed, electron correlation has been described as “the many-body problem at the heart of chemistry.”
Attosecond streak camera
To dig deeper into that problem, researchers led by OSA Member Martin Schultze of the Max Planck Institute of Quantum Optics (MPQ) and Ludwig Maximilians University (LMU), Garching, Germany, used an emerging technique, the attosecond streak camera, to probe the photoionization dynamics of helium. The team zeroed in on helium because it’s the only multi-electron system that allows an exact solution of the time-dependent Schrödinger equation—and, thus, that would let the team’s experimental observations be validated against robust quantum-mechanical theory.
The attosecond streak camera works by using an ultrashort pulse from a pump beam to ionize the electron, in the presence of a second laser electric probe field. The probe field modifies the photoelectron’s kinetic energy in ways that can be inferred from the arrival-time difference between the pump and probe pulses, allowing electronic processes to be tracked with attosecond resolution.
850-zeptosecond precision
To create the high-energy pump pulse, the MQP-led team’s setup used frequency upconversion of near-infrared laser pulses to generate extreme-ultraviolet (EUV) attosecond bursts, and used a series of dielectric and metallic band-pass mirrors and partly transmitting thin foils to select isolated, near-Fourier-limited attosecond pulses. The researchers aimed this stream of sharp attosecond pulses at a jet of helium atoms, in the presence of a second, collinear “streaking” laser probe field.
They then used a dispersion-free interferometer setup to scan the relative time delay between the attosecond and laser-probe pulses, obtaining data for attosecond pulses centered around a number of different photon energies. Multiple runs at each photon energy value allowed the researchers to obtain standard-error values for the technique ranging from 1.6 attoseconds to as low as a previously unheard-of 0.85 attoseconds—850 zeptoseconds.
An “absolute zero” of photoionization time
With that level of precision in the bag, the team next had to see how well the results actually agreed with quantum-mechanical theory. To do so, the researchers calculated the expected time delay using the time-dependent two-electron Schrodinger equation, factoring in all relevant interparticle interactions and electron correlations at various photon energy values. The experimental results agreed handsomely with the theory, within the sub-attosecond experimental standard error.
According to Schultze, the validation of these methods with helium, with this level of accuracy and precision, provides “a tremendously reliable basis for future experiments,” including those involving atoms that don’t have the advantage of an exact quantum-mechanical solution. Indeed, the team suggests in the study that helium can serve as a sort of tracer in experiments dealing with more complex systems, allowing determination of “an absolute zero of time” for photoionization in those experiments.
In addition to Schultze at MPQ and LMU, contributors to the study included lead author (and OSA Student Member) Marcus Ossiander of the Technical University of Munich (TMU); other scientists at MPQ, LMU, and TMU; and colleagues from Austria’s Vienna University of Technology and Spain’s Universidad Autónoma de Madrid.