# Challenges and opportunities in attosecond and XFEL science

Eva Lindroth, Francesca Calegari, Linda Young, M. Harmand, Nirit Dudovich, Nora Berrah, Olga Smirnova

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Eva Lindroth, Francesca Calegari, Linda Young, M. Harmand, Nirit Dudovich, et al.. Challenges and opportunities in attosecond and XFEL science. Nature Reviews Physics, 2019, 1 (2), pp.107-111. 10.1038/s42254-019-0023-9. insu-02270672

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# Challenges and opportunities in attosecond and XFEL science

Eva Lindroth, Francesca Calegari, Linda Young, Marion Harmand, Nirit Dudovich, Nora Berrah and Olga Smirnova

Seven scientists share their views on some of the latest developments in attosecond science and X-ray free electron lasers (XFELs) and highlight exciting new directions.

**Q** *Time for excursions into the time domain*

**Eva Lindroth.** The possibility to generate light pulses with a duration of fewer than a hundred attoseconds has opened new perspectives for studying the electron dynamics in atoms and molecules and promises a deeper understanding of ionization and charge transfer processes, with implications also for chemistry. One of the most interesting applications of attosecond technology is the possibility to measure the phase of quantum mechanical wave packets and thus completely characterize them. The derivative of this phase with respect to energy gives the group the delay acquired by the electronic wave packet when it propagates through an atomic potential. During the past few years, the study of the delay in photoionization has emerged as a prominent example of what can be achieved in the time domain, with highlights such as the temporal reconstruction of the build-up of an autoionizing resonance¹.

Experimentally measured delays include not only the physically interesting photoionization delay but also contributions from the ionizing field and from the measurement process. This is a challenge, but it can be circumvented by exploiting relative delays to remove the effect from the light field. A number of different approaches have already been successfully used in this direction. The measurement-induced contribution may be corrected for theoretically, at least in the general case, as it depends on the long-range potential and not on the

details of the multi-body environment. In systems that lack a long-range potential, such as negative ions, measurement-induced contributions vanish completely for more energetic photoelectrons. It is thus possible to imagine strategies to control the measurement effects with a combination of theoretical and experimental efforts.

The possibility of using a stopwatch for events on the atomic scale can be used to address questions around charge transfer and ionization in a variety of systems from isolated atoms to solids. But it is also possible to address fundamental questions concerning time and time-order in quantum mechanics. A still-debated point is whether and when, from a fundamental point of view, it is possible to say that one quantum mechanical event occurs before another. Ionization from inner orbitals provides a suitable test case. After such an event, the relaxation processes typically involve the ejection of a secondary electron in an Auger process. It is well known from frequency domain studies that when a slow photoelectron is followed by a fast Auger electron this gives rise to specific spectral features called post-collisional effects. In a classical picture, the situation corresponds to the Auger electron overtaking the photoelectron, meaning that the potential landscape through which the two electrons are moving suddenly changes. How is this temporal interplay between the electrons manifested in the ionization delay and can delay measurement be used to study the time-development of entanglement and its connection to the emergence of time-order?

**Q** *Attosecond technology for imaging the electron timescale in photochemistry*

**Francesca Calegari.** Watching a chemical reaction in progress has long been a dream of chemists. In 1999, Ahmed Zewail was awarded a Nobel Prize for the real-time investigation of the formation and breaking of chemical bonds, heralding the beginnings of femtochemistry. Several years later, the advent of attosecond technology dramatically improved the resolution of time-resolved measurements, ultimately allowing direct access to the electronic timescale in matter.

In its infancy, most attosecond science was devoted to the investigation of fundamental phenomena in atoms and small molecules, for which increasingly accurate theoretical models have been developed. However, real progress occurs when a field is pushed towards new challenges. I believe this is exactly what happened to attosecond science after two theoretical works suggested that the sudden ionization of a large molecule could induce attosecond charge flow along the molecular backbone²,³. These works triggered the investigation of more complex targets. Scientists immediately realized that attosecond technology could be used to track this ultrafast charge motion, known as charge migration, and ultimately control the outcome of a chemical reaction by acting at the electronic timescale. In the past few years, several attempts have been made to capture charge migration in biochemically relevant molecules, such as aromatic amino acids, with preliminary but encouraging results. Much effort has also been dedicated to improving the theoretical modelling to understand the basics of this process.

Today, there remain challenges that make it difficult to predict the full potential of attochemistry. First, the role of complex non-adiabatic couplings between the electronic and nuclear degrees of freedom still needs to be clarified. There are a few theoretical predictions that suggest that nuclear motion could ‘kill’ electronic coherences, even in the first few femtoseconds after light absorption. This could strongly limit our ability to drive coherent electronic motion and thereby control the reactivity of a system. Second,
it is still unknown how the environment
affects the dynamics initiated in the
molecule. Until now, experiments have
generally been carried out in isolated
molecules in the gas phase. However, a
more realistic environment needs to be
considered, as most bio-relevant molecules
are typically found, for instance, in water.
Third, a strong technological effort is
required to improve the signal-to-noise ratio
of attosecond time-resolved experiments in
biomolecules. The relatively low conversion
efficiency of the attosecond pulse generation
process, especially at high photon energies,
combined with the extremely low density
of the complex molecular target, make the
ongoing experiments challenging. In this
context, tremendous progress could be
made by replacing table-top attosecond
sources with free-electron lasers (FELs).
However, whether FELs will soon be ready
to deliver attosecond light pulses with
reproducible time profile and intensity is yet
to be demonstrated.

I cannot predict whether there will be a
bright future for attochemistry, but to me
one thing is clear: imaging and controlling
the chemical reactivity of a molecule on the
electronic timescale will open up new and
important perspectives into photochemistry
and photobiology, with tremendous
prospects for understanding fundamental
problems across physics, chemistry
and biology.

<figure><img src="image_2.png" /></figure>

3D *dynamic imaging of complex*
*systems with XFELs*

**Linda Young.** In 2009, the world's first hard XFEL provided a 10-billion-fold gain in X-ray peak brightness. This fuelled the avidly pursued, but still elusive, dream of single-shot imaging of non-crystalline samples at near-atomic resolution. The overarching concept of 'diffract-before-destroy' imaging is that a powerful burst of ultrafast X-rays can produce a coherent diffraction pattern of a nanoscale object — before the object explodes owing to Coulomb repulsion caused by a massive parallel ionization of the atoms in the sample. A collection of snapshots of identical objects in random orientations then provides information from which a 3D structure can be retrieved.

Underlying the development of such
3D imaging is an understanding of the
fundamental interactions of X-rays
with matter at extreme intensities, up to
10²⁰ W cm⁻². Since 2009, much has been
learnt about ultrafast, ultra-intense X-ray
interactions, using atoms, molecules and

rare gas clusters as targets. For instance,
the sequential multiphoton absorption
dominates, and nonlinear field-driven
phenomena that characterize intense optical
laser interactions are of minor importance.
Now, theoretical modelling can point to
optimal X-ray laser parameters for ultrafast
atomistic imaging and warn about 'hot
spots' for damage. This knowledge base
for flash imaging of molecular structures
has been built with the first generation of
XFELs, which operate near 100 Hz primarily
with stochastically varying self-amplified
spontaneous-emission pulses. These
powerful but crude pulses have enabled
the successful and popular application of
serial femtosecond crystallography for
biomolecule structure determination,
as in this application the details of the
temporal pulse structure are of relatively
minor importance. However, with the next
generation of high-repetition-rate XFELs
one can envisage improved X-ray temporal
profiles, stability and synchronization
with external laser pulses, in addition to
multicolour, multipulse X-ray pump-
probe modalities using sub-femtosecond
pulses. I believe that the improved X-ray
characteristics can lead to a new era of
X-ray quantum control empowered by the
ability to capture all ejecta, photons, ions
and electrons from individual interaction
events, accumulate this information over
many events and, subsequently, extract
insights on the 3D dynamic behaviour
of complex systems at the atomic and
electronic scale.

<figure><img src="image_3.png" /></figure>

Exploring the time dependence of phase
stability

**Marion Harmand.** Understanding how matter behaves under the most extreme conditions is very challenging. It is of great importance for the study of planetary interiors or to unravel the processes taking place during accretion, giant and high-velocity impacts of astrophysical bodies. Laser compression is a unique tool that enables us to obtain pressures and temperatures far above the current limits of diamond anvil cell technology (several megabar and thousands Kelvin). It consists in generating compression waves in a material from the rapidly expanding plasma created on its surface upon irradiation with a pulsed laser beam. However, the ultrafast timescales involved in laser compression (picosecond and nanosecond timescales) combined with a limited number of ultrafast diagnostics has so far prevented full characterization of

the material sample under these extreme
conditions, in particular its structural
physical properties. Furthermore, the very
short timescale of the measurements has
always cast some doubt on the relevance
of the technique for the long timescales in
planetary science.

XFEL facilities brought a new range of
ultrafast X-ray diagnostics for time-resolved
experiments. X-ray pulses can be combined
with optical laser compression in pump-
probe schemes: a pump optical laser creates a
shock wave going through the sample, which
is probed after a controlled time delay with an
XFEL probe. Therefore it is now possible to
study matter under laser compression on the
picosecond timescale. The high brilliance of
XFELs enables high-quality X-ray diffraction,
scattering and absorption spectroscopy with
laser compression. In this way, it is possible to
investigate ultrafast changes under conditions
beyond the limits of static compression (with
diamond anvil cell technology), and study
electronic and atomic structures in systems
whose intrinsic interplay gives rise to exotic
states of matter, such as anomalous melting
or metastable phases. Furthermore, in recent
laser compression experiments the higher
repetition rate allows statistically significant
amounts of data to be acquired for the
first time.

XFELs are now changing our perception
of laser compression physics by providing
access to ultrafast dynamics and out-
of-equilibrium processes, and by offering
new opportunities to relate measurements
of such extreme conditions to the
properties of matter in planetary interiors.
However, for the analogy to work, one
needs to understand how to relate ultrafast
experimental timescales to planetary
timescales, through the concept of stability.
Traditional studies using static compression
are implicitly based on the concept of phase
stability, assuming a free energy minimum
to derive the phase diagrams and physical
properties. However, dynamic compression
experiments coupling XFELs and high-
energy lasers call for a different paradigm.
How can we explore phase stability or
instability by accessing temporal behaviour
and dynamics? What information can be
extracted from the temporal behaviour and
out-of-equilibrium processes? How shall we
define our experimental protocols to adapt
to this new paradigm and think about the
notion of stability in a physical system under
extreme perturbations?

In this context, I think it is of the utmost
importance to redefine the notion of
temporal stability relative to the energetic
stability of a system. In practice, I identify
three important aspects to be considered experimentally. First, we need to explore the nature of the accessible phase transition and associated limitations when using laser compression by varying the accessible sample parameters, such as preferred crystal orientations and grain sizes, and modifying the compression schemes. Second, we need to define experimental protocols to disentangle the ultrafast changes in the thermodynamic conditions from the phase transition processes and kinetics. Third, we need to explore the probabilities related to the observation of the onset of a phase transition and its stability. In other words, look into the changes that would occur in a system evolving towards a phase before it fully reaches that phase. These ideas will certainly require close collaboration between theorists, modellers and experimentalists.

<figure><img src="image_4.png" /></figure>

### High-harmonic generation interferometry

**Nirit Dudovich.** Attosecond science enables the observation of multi-electron dynamics in atoms, molecules and solids. One of the most exciting advances in this field is high harmonic generation (HHG) spectroscopy. It combines sub-angstrom spatial resolution with attosecond temporal resolution, making it possible to dynamically resolve the structure of electronic wavefunctions as they evolve. HHG spectroscopy exploits a built-in pump-probe process: driven by the strong laser field, the liberated electron wavepacket returns to the parent ion and probes the hole through radiative recombination. In turn, this leads to the emission of higher-order harmonics of the driving laser field. The emitted attosecond burst of light takes a snapshot of the system, probing the evolving wavefunction, in an attosecond movie in which each harmonic order serves as one frame.

During the past two decades, HHG spectroscopy has been successfully applied to resolve fundamental strong-field phenomena such as field-induced tunnelling in atoms, hole dynamics or charge migration in molecules and field-induced currents in solids. However, whereas HHG spectroscopy holds great promise for both the measurement and control of matter, the understanding of the processes involved and the implementation of the technique still pose significant challenges. The extreme nonlinear nature of the strong-field interaction offers numerous channels — strongly coupled by the laser field — in which electronic dynamics can evolve.

One of the most important aspects of HHG spectroscopy lies in its coherent nature. The strong-field interaction directly transfers the coherence of the laser field into the coherent properties of the electronic wavefunction and then, upon re-collision, into the optical properties of the emitted harmonics. The coherence is encoded in the amplitudes, phases and polarization state of the harmonics and is key to reconstructing the internal dynamics. But resolving the internal coherence is one of the primary challenges in HHG spectroscopy. As in many other branches of physics, the presence of coherence is determined through interferometry. Synchronizing several fields produces the interferometric measurement during the strong-field interaction itself. By using a combination of strong and weak driving laser fields, one can perturb the interaction on sub-optical-cycle timescales. This perturbation induces a temporal interferometer whose two arms are represented by two attosecond bursts originating from consecutive laser half-cycles. The control of the two-colour delay manipulates the relative phase between the two arms and enables resolution of the coherent properties of the electronic wavefunction, represented by each arm. This scheme was applied to resolve field-induced tunnel ionization in atoms, multichannel dynamics in molecules or interband dynamics in solid state systems.

A more advanced scheme combines attosecond extreme ultraviolet (XUV) pulses with a strong infrared field. In this scheme the initial excitation is induced by an attosecond XUV pulse, rather than field-induced tunnelling. The integration of attosecond pulses with re-collision combines the simplicity of single XUV photon excitation with the accuracy provided by the re-collision process. In this case one creates an internal interferometer whose arms are the single photoionization channel and the re-collision path. This scheme enables direct control over the interferometer, whose beam splitter, in this case, the photoionization, can be fully tuned both in time and in energy.

Finally, the HHG coherence can be directly resolved via an all-optical approach. In this case, the internal interferometer, induced by multiple quantum path interference, is replaced by an external optical one. Optical extreme ultraviolet interferometry has been realized by inducing two or more phase-locked HHG sources. This scheme has been applied to reveal re-collision dynamics, the contribution of multiple molecular orbitals or as a

direct measurement of the spectral phase associated with photoionization.

Inducing strong-field interferometers increases the dimensionality of both the measurement and the control of attosecond-scale processes. Multidimensional HHG spectroscopy has the potential to isolate the numerous degrees of freedom involved in many strong-field phenomena, thus revealing their underlying mechanisms. The role of coherence in systems with more complex coupled electronic and nuclear dynamics and the possibility to laser-control these dynamics on the sub-cycle timescale set some of the most important challenges of the field.

<figure><img src="image_5.png" /></figure>

### Towards attosecond XFELs

**Nora Berrah.** XFELs⁴ have unprecedented brightness and short pulses of the order of a few femtoseconds. XFELs are relatively new tools but they have already enabled new science opportunities in physical chemistry and biology; in the study of nonlinear processes in atoms, molecules and solids; and in understanding ultrafast molecular dynamics.

High-energy X-ray photons make it possible to flag element-specific and site-specific physical and chemical processes, which is not possible with optical photons. Time-resolved X-ray scattering techniques make it possible to take snapshots of fundamental processes in solids, films and molecules and to reconstruct images to determine the sample structure. Furthermore, targeting the inner shells in atoms creates localized charge distributions that can be tracked in real time. This ability is useful in spectroscopic studies of photoinduced processes such as photosynthesis and vision, which take place in molecules through coupled nuclear and electronic dynamics on femtosecond and sub-femtosecond timescales. Charge transfer and charge migration also play a decisive role in chemical bond cleavage. In photoinduced processes, a superposition of states evolves on attosecond timescales, leading to electronic motion governed by electron correlations. Such coherent electronic and nuclear dynamics are challenging to capture with ab initio theories, or with attosecond experiments with table-top lasers, which recently started to measure the electronic motion created by photoinduced excitation. These measurements are limited by the low intensity of the attosecond pulses generated by the table-top lasers — which are typically
strong near-infrared fields or a combination of low-intensity attosecond and strong femtosecond pulses — restricting the range of phenomena that can be investigated.

The limitation of low-intensity attosecond pulses will be overcome by attosecond XFELs. The upcoming Linac Coherent Light Source (LCLS-II)<fnref n="5" /> is part of ongoing efforts to reach the attosecond regime and will provide attosecond pulses. The current LCLS has electrons accelerated in copper pipes that operate at room temperature, allowing the generation of 120 × -ray laser pulses per second. The upgraded LCLS-II will add a superconducting accelerator, generating an almost continuous X-ray laser beam. The attosecond pulses are created by manipulating the electron bunch. The LCLS-II facility will, in addition, permit increased access to the FEL, enabling simultaneous experiments during beamtime operation (currently, it is single-user only).

X-ray-based attosecond research will provide amazing opportunities, but not without technical challenges. The self-amplified spontaneous-emission-based FELs, which are built by generating spontaneous lasing by accelerating a high-energy electron beam close to the speed of light, are inherently noisy and present jitter. However, future FELs, including LCLS-II, will use self-seeding and other upgrades to improve the ultrafast pulse profile and generate pulses with high transverse and longitudinal coherence.

<figure><img src="image_6.png" /></figure>

Controlling, shaping and imaging quantum matter with intense light

**Olga Smirnova.** The detection of light shifts of atomic energy levels heralded a new field of shaping matter with light. Light shifts enable optical traps, lattices and tweezers, and the creation of Bose-Einstein condensates and other exotic states of quantum matter. Increasing the intensity of the light fields reveals other facets of this phenomenon: the Autler-Townes splitting of states and, more generally, the appearance of the Floquet ladder, that is, additional light-induced states separated by photon energy. In turn, this has led to new ideas from electromagnetically induced transparency to the Floquet engineering of quantum matter. These concepts involve the response of matter to light on a timescale far longer than a laser cycle, averaging the response over many laser oscillations.

Upon increasing the light intensity further, the utility of the frequency-domain

photon counting picture subsides: too many photons are absorbed or emitted, making photon counting cumbersome. Instead, the time-domain picture becomes particularly insightful as it goes beyond the Floquet ladder by revealing and exploiting the time-domain, sub-laser-cycle response of matter to intense light fields — the mark of strong-field and attosecond physics. Strong-field and attosecond physics bring and exploit truly powerful tools for controlling, shaping and imaging matter with light owing to virtually unlimited opportunities to sculpt individual light oscillations offered by modern technology. These capabilities open several exciting opportunities.

First, in strong light fields, optical transitions are localized near the peaks of the oscillating laser field, a feature encountered in atoms, molecules and solids. This feature enables the exquisite temporal control over electron injection or emission using tailored, multicolour, polarization-controlled laser pulses, in which the phase of each oscillation is locked to the pulse envelope. In solids, this creates opportunities for controlling the excited electronic density in the Brillouin zones. Achieving such control could enable manipulation of currents in solids at sub-laser-cycle timescales, that is, many orders of magnitude faster than possible in conventional electronics.

Second, the sensitivity of the strong-field response to orbital momentum and spin on the sub-laser-cycle timescale, now demonstrated in atoms, is a gateway to sub-laser-cycle imaging of magnetic, chiral and topological phenomena. Thus, strong-field and attosecond physics may offer new tools to explore new phases of materials. Since strong light fields can inject spin-polarized electrons in the atomic and molecular continua, they should be able to do the same for the conduction bands of solids. Controlling the flow of spin in solids at the sub-cycle timescale is a new opportunity for ultrafast spintronics.

Third, very recent work<fnref n="6" /> shows that the sub-cycle strong-field response is sensitive to topological phases of matter, distinguishing between trivial and topological insulators that have identical band structure. This sub-cycle response can be detected via high harmonic spectroscopy whose sensitivity to chiral and correlation-driven electron dynamics has now been well documented in molecules. Application of high harmonic spectroscopy to solids opens a challenging but exciting opportunity for time-resolved imaging of new phases and phase transitions.

An interesting example of shaping matter with intense light is the so-called

Kramers-Henneberger atom, which has been recently observed experimentally<fnref n="1" />. It is an example of strong-field-built electronic structure, in which the electron motion is dominated by the laser field, but the electron is still bound to the atomic core. Applying this concept to solids could lead to new ways of controlling the band structure beyond Floquet engineering, that is, by exploiting the highly non-perturbative interaction with light involving a vast number of low-frequency photons. Furthermore, this could lead to the ambitious goal of creating new phases of matter by reshaping the electronic structure with strong low-frequency laser fields.

Finally, imaging and controlling ultrafast electron dynamics in chiral molecules is an exciting challenge. The aim is to achieve ultimate control over chiral electronic response, that is, to generate such response only in species of desired handedness, while silencing the response of others. To make it happen, a special type of laser electrical field is required. Technically speaking, such laser electrical field should be chiral in the dipole approximation, that is, locally chiral at every point in space. It should also maintain its handedness globally in space, across the whole interaction region. Recent work shows how such fields can be generated by combining several phase-locked and polarization-controlled light pulses, and how highly nonlinear optical responses can be induced only in molecules with desired handedness<fnref n="8" />.

These challenges and opportunities point us to several exciting directions, unified by the desire to reveal new properties of matter associated with highly non-equilibrium ultrafast electronic responses and create new ways of shaping, imaging and controlling matter with light.

Eva Lindroth<fnref n="1" />, Francesca Calegari<fnref n="2" />, Linda Young<fnref n="5" />, Marion Harmand<fnref n="6" />, Nirit Dudovich<fnref n="5" />, Nora Berrah<fnref n="6" />* and Olga Smirnova<fnref n="7" />,<fnref n="8" />

<footnote n="1">¹Department of Physics, Stockholm University, Stockholm, Sweden.</footnote>

<footnote n="2">²Attosecond Science Division at Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany.</footnote>

<footnote n="3">³Argonne National Laboratory and The University of Chicago, Lemont, IL, USA.</footnote>

<footnote n="4">⁴Institut de minéralogie, de physique des matériaux et de cosmochimie, Sorbonne Université, Paris, France.</footnote>

<footnote n="5">⁵Weizmann Institute of Science, Rehovot, Israel.</footnote>

<footnote n="6">⁶Department of Physics, University of Connecticut, Storrs, CT, USA.</footnote>

<footnote n="7">⁷Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, Berlin, Germany.</footnote>

<footnote n="8">⁸Technical University of Berlin, Berlin, Germany.</footnote>

<footnote>*e-mail: nora.berrah@uconn.edu</footnote>

<footnote>https://doi.org/10.1038/s42254-019-0023-9</footnote>
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**Competing interests**

The authors declare no competing interests.

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