Attosecond real-time observation of
electron tunnelling in atoms
M. Uiberacker1,2, Th. Uphues3, M. Schultze2, A. J. Verhoef2,4, V. Yakovlev1, M. F. Kling5, J. Rauschenberger1,2,
N. M. Kabachnik3,6, H. Schro ¨der2, M. Lezius2, K. L. Kompa2, H.-G. Muller5, M. J. J. Vrakking5, S. Hendel3,
U. Kleineberg1, U. Heinzmann3, M. Drescher7& F. Krausz1,2,4
via tunnelling through the binding potential that is suppressed by the light field near the peaks of its oscillations. Here we
report the real-time observation of this most elementary step in strong-field interactions: light-induced electron tunnelling.
technique, attosecond tunnelling, for probing short-lived, transient states of atoms or molecules with high temporal
resolution. The utility of attosecond tunnelling is demonstrated by capturing multi-electron excitation (shake-up) and
relaxation (cascaded Auger decay) processes with subfemtosecond resolution.
volts per angstrom have become routinely available. They rival the
fields acting on valence electrons in atomic systems, allowing their
release from atoms, molecules and solids. These advances sparked a
revolution in studying the interaction of electrons with light. The
primary step in strong-field interactions is the liberation of electrons
from their atomic bound state. The revolutionary theory of Keldysh1
and subsequent work2–6suggested that a valence electron may escape
bytunnelling through its atomic binding potential suppressed bythe
light field (Fig. 1a). If the dimensionless parameter:
e j jE0
is less than one, under the assumption of "vL=Wbionization is
oscillation cycle of the light field (Fig. 1b). Here E0and vLstand for
the amplitude and angular frequency of the oscillations of the laser
electric field EL(t)5E0e(t)cos(vLt1Q), with e(t) being the ampli-
tude envelope function, and e, m and Wbthe charge, mass and bind-
ing energy of the electron. Recent studies6suggest that tunnelling
remains thedominantionization mechanism even for csubstantially
exceeding one, that is, under conditions when the potential barrier
formed by the atomic binding potential and the ionizing light field
varies during tunnelling (non-adiabatic regime).
In this work we report what we believe is the first real-time obser-
vation of light-induced electron tunnelling. The observation of ion-
ization occurring in subfemtosecond steps spaced by the half laser
agreement with analytic and numerical calculations. Our approach
both adiabatic and nonadiabatic tunnelling, as well as barrier-
suppression ionization—and allows us to test models of these pro-
cesses for the first time.
Once the process of field ionization is fully understood, the tech-
nique of attosecond tunnelling will provide direct time-domain
insight into a wide range of multi-electron dynamics and electron–
electron interactions, ultimately with a resolution approaching
the atomic unit of time (,24as). We demonstrate this potential by
Attosecond probing of electron dynamics
Figure 2 illustrates different options for attosecond sampling of elec-
tronic motion in atoms or molecules. A subfemtosecond extreme
ultraviolet (XUV) pulse triggers the motion by exciting a valence
or core electron (Fig. 2a, b). The unfolding excitation and relaxation
processes (Fig. 2) could, in principle, be probed by a delayed replica
of the pulse. However, the low flux of currently available subfemto-
second XUV pulses and the low two-photon transition probabilities
in the XUV and X-ray regimes have thwarted this straightforward
extension of conventional pump–probe techniques into the XUV–
X-ray spectral range.
A few-cycle wave of visible or near-infrared (NIR) light with con-
trolled waveform7in combination with a highly nonlinear process
may replace the subfemtosecond pulse either in probing or starting
ing8,9: the strong-field interaction of a few-cycle light wave with free
electrons released by a subfemtosecond XUV excitation pulse results
in broadening and shifting of their final momentum distribution.
Recording the streaked spectra of the emitted photo- and Auger
probe allowed us to retrieve the XUV pulse10,11and the laser field12as
well as the inner-atomic relaxation dynamics13with subfemtosecond
Here, we demonstrate that nonlinear interaction of the same light
wave with bound electrons ionizes in subfemtosecond steps and
hence offers a means of probing intra-atomic and intra-molecular
electron dynamics—including when no free electrons are released—
by means of attosecond tunnelling. This approach relies on the fact
that energetic photo-excitation as well as subsequent rearrangement
1Department fu ¨r Physik, Ludwig-Maximilians-Universita ¨t, Am Coulombwall 1,2Max-Planck-Institut fu ¨r Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany.
3Fakulta ¨t fu ¨r Physik, Universita ¨t Bielefeld, Universita ¨tsstrasse 25, D-33615 Bielefeld, Germany.4Technische Universita ¨t Wien, Gusshausstrasse 27, A-1040 Vienna, Austria.5FOM-
Instituut voor Atoom- en Molecuulfysica (AMOLF), Kruislaan 407, 1098 SJ, Amsterdam, The Netherlands.6Institute of Nuclear Physics, Moscow State University, Moscow 119992,
Russia.7Institut fu ¨r Experimentalphysik, Universita ¨t Hamburg, Luruper Chaussee 149, D-22671 Hamburg, Germany.
Vol 446|5 April 2007|doi:10.1038/nature05648
via ‘shake-up’ (Fig. 2d–f)14–16. Here, we use the term ‘shake-up’ in a
broad sense, standing for all possible processes populating excited
ionic states (including instantaneous and non-instantaneous ones),
henceforth referred to as shake-up states (represented by levels 1, 2
and 3 in the example of Fig. 2). These populations can be probed via
optical field ionization by a strong, few-cycle NIR pulse of variable
probe exposure as a function of Dt (Fig. 1d).
Shake-up usually populates several quantum states in the valence
shake-upstates uptoacertainbinding energyfromwhich ionization
states of significantly differing binding energy can be retrieved by
pump–probe scans repeated at different NIR probe intensities and/
or from the temporal separation of the depletion of the states in the
same delay scan, as explained in Fig. 1d and demonstrated in Fig. 4.
The ion yield constitutes an integral signal in a temporal sense, too.
The shake-up states are exposed to the ionizing NIR field from the
beginning of this time interval within the NIR pulse is adjusted with
is scanned from large negative values (NIR probe first) to large pos-
itive values (XUV pump first) the measured ion yield (Fig. 1d) starts
increasing at Dt,0 owing to ionization on the trailing edge of the
NIR pulse and continues to increase with increasing Dt because the
shake-up states are exposed to ever higher NIR probe intensities.
In the absence of Auger decay, shake-up excitation results from
photoionization only (Fig. 2d). The time-dependent ionization
dynamics sketched in Fig. 1d can then be traced by measuring the
yield of doubly charged ions as a function of the delay between the
XUV pump and the sampling NIR light field. The temporal ioniza-
tion gradients sketched in Fig. 1d incorporate the finite duration of
the XUV excitation, a possible delayed response of shake-up and the
tunnelling dynamics. With a sufficiently rapid (=1fs) excitation,
evolution of shake-up (in the presence of a strong optical field) and
light-induced tunnelling. In what follows, first we prove this concept
cycle NIR probe pulses (Fig. 3) and measuring the yield of the prod-
uct of the pump–probe exposure, Ne21, versus Dt (Fig. 4). Then we
extend the approach to probing electrons shaken up in xenon atoms
during Auger decay. Our primary observables in this case are higher
charged states, XeN1(for N.2). Measuring their yield versus Dt
displays the course of an Auger cascade.
Delay time, ∆t
∆t (> 0)
W1 and W2
W1 and W2
Depletion of states
with binding energy
Figure 1 | Strong-field ionization and pump-probe setting for its real-time
observation. a, Exposing an atom to a strong NIR laser field will result in a
modified potential (solid curve) composed of the Coulomb potential
(dashedcurve)andthe time-dependent effectivepotential ofthelaser pulse.
The laser is polarized along the x direction and Wbis the binding energy of
the electron. At sufficiently high laser field strengths the atomic binding
potential is suppressed to a small barrier in the x or –x direction for the
maxima and minima of the laser electric field, respectively, allowing optical
tunnelling to become the dominant ionization mechanism. b, The highly
nonlinear dependence of the tunnelling rate on the width of the potential
barrier confines ionization to time intervals of very short duration near the
field oscillation maxima. In the electric field of a few-cycle NIR laser pulse
(thin line) ionizationis predicted to be restrictedto several subfemtosecond
intervals (thick line). c, Concept for tracing optical-field ionization: a
which a time-delayed NIR few-cycle probe pulse liberates electrons to
peak of the XUV pulse envelope precedes that of the NIR pulse. d, Yield of
doubly charged ions versus delay Dt between the XUV pump and the NIR
probe, as predicted qualitatively for the case of electrons being prepared in
two shake-up states of significantly differing binding energy (W1and
W2?W1) for liberationviastrong-fieldionization (see textfor discussion).
The state of low binding energy is depleted at low intensities, where multi-
dynamics is absent. By contrast, the state of high binding energy is emptied
Probing by attosecond
Figure 2 | Probing electron dynamics in atoms, molecules or solids with
motion by inducing valence (process a) or core photoelectron emission
(process b). The temporal evolution of photo- and Auger electron emission
pulse or the sampling NIR field and trace inner-shell relaxation dynamics.
XUV photoexcitation as well as subsequent Auger decay processes are
usually accompanied by shake-up of another electron to a previously
unoccupied level (processes d, e and f). In this case the liberated electrons
will be ejected at a reduced kinetic energy compared to the cases without
bound electrons (represented by curved black arrows to levels 1, 2 and 3).
For sufficiently strong probing laser fields, the shake-up electrons can be
liberated by tunnellingionization. The temporal evolution of the tunnelling
current will provide information about the inner-atomic electron dynamics
that populates and/or depopulates the interrogated shake-up states and the
duration of the process that have populated the levels on atto- and
increased by attosecond tunnelling, while it remains unchanged in the case
of attosecond streaking. The observable for streaking is the momentum
distribution of liberated electrons, whereas in tunnelling it is the number of
ions in different charge states.
NATURE|Vol 446|5 April 2007
For a detailed description of the attosecond pump–probe apparatus,
see the Supplementary Information. Briefly, the XUV pump origi-
nates from high-harmonic generation in a neon gas jet exposed to
300-mJ, 750-nm waveform-controlled laser pulses with a duration of
polarized XUV and NIR light beams are passed through several
filters and reflected by a concentric double-mirror arrangement
(Mo/Si multilayer: , 9eV bandwidth at photon energy of 91eV).
fields, isolates a single or twin XUV pulse (depending on the carrier-
envelope phase of the laser pulse) of tX<250 as duration11by filter-
ing the cut-off part of the harmonic emission spectrum and focuses
both beams into a jet of atoms under scrutiny. The absolute delay
of better than 60.5fs; for details see Supplementary Information.
Ions created in the common focus of the two beams are detected
by a time-of-flight ion spectrometer (reflectron) that combines
particles within a micrometre-scale detection volume17–19. The
target and background pressures were ,1022and ,1028mbar,
Shake-up and tunnelling
To probe shake-up and light-induced electron tunneling, we ionized
level structure and transitions relevant to our experiments. The core
absent20. The threshold energies for single and double ionization
from the outer shell of Ne are 21.56 and 62.53eV, respectively21.
The XUV photons produced Ne11and Ne21ions with a ratio of
XUV + IR (∆t > 0): 93.3%
Figure 3 | Energy levels and transitions in Ne11and Ne21ions relevant to
this study. The plotted levels represent energies required to ionize and
possibly excite a neutral atom from its ground state. Absorption of photons
of about 91-eV energy can produce singly or doubly charged ions with
probabilities of 95.2% and 4.8%, respectively. Owing to shake-up a small
fraction of the singly-charged ions is produced in 2p22nl configurations,
where the probabilities of different channels are known from electron
spectroscopy (see Supplementary Information). Each of these
configurations, represented by a green box, consists of 2p22(3P)nl,
the XUV pulse (Dt.0) can remove electrons from these shake-up states,
thus increasing the probability of double ionization to 6.7%. Depending on
states. On its own, the laser pulse produces only singly charged ions (in
configuration 2p21) above the detection limit.
Ionization yield (arbitrary units)
Ionization yield (arbitrary units)
Delay time, ∆t (fs)
Delay time, ∆t (fs)
Figure 4 | Ne21ion yield versus delay between the subfemtoscond XUV
pump and the few-cycle NIR probe: experiment and modelling. The peak
intensity of the NIR probe was (761)31013Wcm22. a, The experimental
data were acquired from six delay scans repeated under the same
experimental conditions. The signal was accumulated for 3s at each delay
setting. The squares and the error bars show the average and the standard
the average of five adjacent data points; the thin grey line shows the same as
the thick line but recorded with NIR probe pulses of random carrier-
envelope phase. In the inset, squares, triangles, and circles depict an
ionization step extracted from three different measurements normalized
to give the same change in the ionization yield. The solid line shows an
error-function fit to the data yielding a rise time of 380as (full-width at
half-maximum, FWHM, of the gaussian function derived from the error
function). The zero of delay is set arbitrarily to the centre of the tunnelling
process. b, Simulation of the pump–probe experiment based on the
nonadiabatic theory of tunnel ionization6. The thin coloured lines show the
calculated fractional ionization yields contributed by electrons liberated
from different shake-up states. The thick blue line depicts the overall
ionization rate obtained by totalling the fractional rates (and by adding the
were carried out for a gaussian 250-as XUV pulse and a gaussian 5.5-fs laser
pulse with a peak intensity of 731013Wcm22. The black solid curve
represents the absolute value of the laser field. For discussion of the results,
NATURE|Vol 446|5 April 2007
(19.760.5):1 (with ,2,500Ne11ions created per second), in good
number n: 3 or4;quantumorbit l: s, p ord)configurations23(Fig.3).
Double ionization by the NIR field was not observed at the intens-
ity level chosen. The XUV-generated Ne21yield was therefore not
affected by the NIR probe for Dt=2tL but was significantly
enhanced by the laser field for Dt approaching zero and becoming
positive. The NIR-induced Ne21yield enhancement amounted to
(4064)% of the XUV-produced Ne21yield at a NIR peak intensity
of (761)31013Wcm22. The absence of this enhancement for
excited by the XUV pulse as sketched in Fig. 2d. The laser-induced
Ne11ions. This implies that a substantial fraction of the population
of the 2p22nl shake-up satellites must have been depleted by field
Figure4ashows thenumberofNe21ionsdetectedas afunction of
the prediction of the Yudin–Ivanov theory6(lines) with the experi-
mental data (squares). In our modelling the shake-up states were
populated instantly during XUV photoionization (for more details,
see Supplementary Information). The calculations are in reasonable
agreement with our measurements and reveal how the different
shake-up states are depleted sequentially by laser-field ionization.
of the 2p224p state (relative population ,12%) and the 2p223d state
(,10%) at NIR intensity levels reached some 10 and 6fs after the
peak of the NIR probe (Dt,210 and 26fs), respectively. A more
dramatic increase in the Ne21yield is observed as the delay
populated 2p223p (,50%) and 2p223s (,25%) states. In spite of
their relatively high binding energy (,10 and 13eV, respectively),
these states are also depleted before zero delay, that is, by the field
oscillation cycles comprised in the trailing edge of the pulse, leaving
no room for increasing the Ne21yield with increasing Dt beyond 0.
This main contribution to the Ne21yield emerges within approxi-
the Ne21yield. This conclusion is also supported by the disappear-
ance of the steps in a pump–probe scan performed with a randomly
varying carrier-envelope phase of the NIR probe pulses (grey line in
states) is depleted at NIR intensities corresponding to a Keldysh
parameter c of the order of three. Hence, our experiment verifies
not only the existence of light-field-induced tunnelling, as predicted
by Keldysh some four decades ago1, but also confirms the dominant
ing 1, as predicted recently by Yudin and Ivanov6. This conclusion
is also backed by numerical solutions of the time-dependent
Schro ¨dinger equation (see Supplementary Information).
The steepness of the ionization steps and the dips preceding them
in the measured data are not well reproduced by our model, which
neglects the influence of electron–electron interactions and that of
the strong NIR field on the XUV-induced transitions populating the
shake-up states. Recent work24and our TDSE simulations (see Sup-
plementary Information) indicate that the influence of the strong
laser field on the XUV excitation process may (at least partially) be
responsible for this discrepancy.
We feel that these experiments afford profound insight into fun-
damental electronic processes such as tunnelling and shake-up by
contrasting theoretical models with time-domain data. To exploit
this potential both (1) accurate models of shake-up in the presence
of a strong laser field need to be developed and (2) the temporal
resolution needs to be improved by using shorter XUV pulses25
and improving the signal-to-noise ratio as well as the accuracy of
determining the zero of delay. These advances will allow determina-
tion of the attosecond temporal evolution of the light-field-induced
tunnelling current and they will provide deep insight into the nature
of the electron–electron interactions responsible for shake-up.
Once models for shake-up and tunnelling have been tested and
verified with attosecond precision, the technique of attosecond tun-
nelling will provide direct time-domain insight into a wide range of
multi-electron dynamics inside atoms and molecules by probing the
transient population of excited valence states while these dynamics
are unfolding. With improved signal-to-noise and XUV pulse dura-
tion, the temporal resolution may potentially approach the atomic
unit of time (,24as). At present, the observed rise time of the Ne21
yield of less than 400as (which sets a corresponding upper limit on
the time it takes the excited electronic states to become populated
the temporal resolution of our pump–probe approach. In the next
section we demonstrate its applicability to probing intra-atomic
multi-electron dynamics in real time.
XUV mirror reflectivity
5p–4 nl n′l′
Figure 5 | Energy levels and transitions in xenon ions relevant to the
excitation energy of 90eV from ref. 30. The XUV light preferably ionizes
from the 4d21shell, creating an inner-shell vacancy. A subsequent Auger
process (green arrows labelled A1) will follow with 99% probability26and is
predominantly decaying to Xe21in configuration 5p22. Some of the
populated states, a and b (presumably 5s215p227p states28,31) can further
decay to Xe31via a second Auger process (green arrow labelled A2), leading
to triply charged ions. The A1 process also populates states below the
as 5p23nl configurations. The laser pulse can ionize these states (red arrow
labelled NIR-I). Furthermore, a series of 4d21shake-up satellites in Xe11is
also populated—with a small probability—by the XUV pulse. The inset
shows the possible configurations29together with the XUV mirror
reflectivity determining the XUV excitation spectrum. The satellites mainly
decay to the a, b, c states, with a small fraction of the Xe21population
ending up in 5p24nln9l9 configurations. These states are short-lived and
decay via the A2 process. Before this occurs, the nln9l9 electrons can be
liberated by the laser field to yield Xe41in the 5p24state(red arrow labelled
NATURE|Vol 446|5 April 2007
As a first application of the technique of attosecond tunnelling, we
captured Auger cascade xenon atoms following excitation by a sub-
femtosecond XUV pulse. Figure 5 sketches the relevant energy levels
and transitions. Energy-resolved synchrotron measurements have
revealed that (1) the 91-eV XUV pulse will preferably liberate elec-
trons from the 4d orbital22, (2) the vacancy decays by subsequent
single (A1 in Fig. 5) and cascaded (A1 and A2 in Fig. 5) Auger
processes, leading to Xe21and Xe31, respectively26, and (3) the life-
times of the 4d3/2and 4d5/2holes are 6.360.2 and 5.960.2fs,
respectively27. These time-integral measurements have hitherto been
able to set only a lower limit of 23fs for the time constant of A2 (ref.
To trace this dynamics in real time, we simultaneously recorded
the number of Xe ions emerging in different charged states as a
function of Dt. At the laser intensity of (761)31013Wcm22used
in this experiment, the XUV-induced Xe11yield is buried in laser-
generated background, preventing delay-dependent effects from
coming to light in the Xe11signal. This is not the case for higher
charged states. With increasing delay, rapid exponential increase was
observed in the Xe31signal near Dt50 (Fig. 6b), concurrent with a
significant decrease of the Xe21yield. The background in the Xe31
signal arises from the A1–A2 Auger cascade discussed above. From
Fig. 5 weinfer that the laser-induced increase in theXe31yield is due
to ionization from the c-states in Xe21, which cannot spontaneously
decay into Xe31. This NIR-probe-induced transition (denoted by
NIR-I in Fig. 5) yields Xe31in configuration 5p23. Because these
in the Xe31signal is the convolution of the A1 decay and the NIR-
induced ionization process. No decrease of the enhanced Xe31yield
was observed up to our maximum delay of 300fs, indicating that the
lifetime of the c states was longer than 1ps.
Charge-states higher than Xe31cannot be created with the XUV
pulse alone, because the XUV photon energy is below the threshold
for Xe41production (,105eV). However, with the probe switched
on, wedid observe Xe41ions for Dt.2tL(Fig. 6a). TheXe41signal
first grows within a few femtoseconds, followed by a longer decay.
The Xe41ions are created by NIR-induced double ionization
(denoted by NIR-DI in Fig. 5) from the intermediate doubly excited
5p24nln9l9 (Fig. 5) and/or singly excited 5s225p21nl (not shown in
Fig. 5) states of Xe21. These states are populated by A1 from the
satellites 4d215p21nl of the 4d21state upon emission of low-energy
electrons28,29and emptied by A2 to states of larger binding energy in
Xe31, which cannot be reached by the NIR probe.
of the Xe41signal in Fig. 6a reveal the evolution of the A1 and A2
Auger decays, respectively. The laser-induced double ionization may
be either sequential or non-sequential (with the second step induced
by recollision of the first electron). In either case, in the first step a
states in the neon experiment must be overcome by tunnel ioniza-
tion. Hence, the probing (ionization) process may be assumed to be
the same as measured in the neon experiment, see Fig. 4a. With this
including the transitions A1 and A2 to the Xe41data shown in Fig. 6
yields decay times of tA156.060.7fs and tA2530.861.4fs for the
A1 and A2 Auger processes, respectively. Both time constants are in
accordance with the results of energy-resolved measurements27.
Conclusions and outlook
We have reported the observation of light-induced electron tunnel-
atomic binding potential within several subfemtosecond time inter-
vals near the oscillation peaks of the ionizing few-cycle near-infrared
laser field. Our results are in good agreement with the predictions of
the theory Keldysh put forward four decades ago. The observed sub-
femtosecond ionization steps provide a powerful means of probing
the transient population of short-lived valence electronic states in
excited atoms or molecules, offering direct, time-domain access to a
wide range of multi-electron dynamics unfolding on an attosecond
to femtosecond timescale. Proof-of-principle attosecond tunnelling
experiments in neon and xenon demonstrate this potential.
Simultaneous implementation of attosecond tunnelling and atto-
second streaking spectroscopy along with scaling of the techniques
to higher photon energies and shorter X-ray pulse durations will
provide unprecedented insight into the transient electronic states
Received 2 November 2006; accepted 26 January 2007.
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Supplementary Information is linked to the online version of the paper at
Acknowledgements We thank A. F. Starace for discussions. We are grateful for
financial support from the Volkswagenstiftung (Germany), the Marie Curie
Research Training Network XTRA, Laserlab Europe, and a Marie Curie
Intra-European Fellowship. F.K. acknowledges support from the FWF (Austria).
The research of M.F.K. and M.J.J.V. is part of the research programme of the
Stichting voor Fundamenteel Onderzoek der Materie, which is financially
supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek.
This research was supported by the cluster of excellence Munich Centre for
Advanced Photonics (www.munich-photonics.de).
Author Information Reprints and permissions information is available at
www.nature.com/reprints. The authors declare no competing financial interests.
Correspondence and requests for materials should be addressed to M.U.
(firstname.lastname@example.org) or F.K. (email@example.com).
NATURE|Vol 446|5 April 2007