Content uploaded by Marko Swoboda
Author content
All content in this area was uploaded by Marko Swoboda on Dec 16, 2013
Content may be subject to copyright.
Content uploaded by Johan Mauritsson
Author content
All content in this area was uploaded by Johan Mauritsson on Jul 18, 2013
Content may be subject to copyright.
Available via license: CC BY 3.0
Content may be subject to copyright.
Available via license: CC BY 3.0
Content may be subject to copyright.
1
Coherent Electron Scattering Captured by an
Attosecond Quantum Stroboscope
J. Mauritsson
1
, P. Johnsson
1
, E. Gustafsson
1
, M. Swoboda
1
, T. Ruchon
1
, A. L’Huillier
1
& K. J. Schafer
2
1
Department of Physics, Lund University, P. O. Box 118, SE-221 00 Lund, Sweden
2
Department of Physics and Astronomy, Louisiana State University, Baton Rouge,
Louisiana 70803-4001, USA
The basic properties of atoms, molecules and solids are governed by electron
dynamics which take place on extremely short time scales. To measure and control
these dynamics therefore requires ultrafast sources of radiation combined with
efficient detection techniques. The generation of extreme ultraviolet (XUV)
attosecond (1 as = 10
-18
s) pulses
1,2
has, for the first time, made direct
measurements of electron dynamics possible. Nevertheless, while various
applications of attosecond pulses have been demonstrated experimentally
3-5
, no one
has yet captured or controlled the full three dimensional motion of an electron on
an attosecond time scale. Here we demonstrate an attosecond quantum
stroboscope capable of guiding and imaging electron motion on a sub-femtosecond
(1 fs = 10
-15
s) time scale. It is based on a sequence of identical attosecond pulses
6
which are synchronized with a guiding laser field. The pulse to pulse separation in
the train is tailored to exactly match an optical cycle of the laser field and the
electron momentum distributions are detected with a velocity map imaging
spectrometer (VMIS)
7,8
. This technique has enabled us to guide ionized electrons
back to their parent ion and image the scattering event. We envision that coherent
electron scattering from atoms, molecules and surfaces captured by the attosecond
quantum stroboscope will complement more traditional scattering techniques
9-11
since it provides high temporal as well as spatial resolution.
Pioneering experiments with femtosecond infrared (IR) laser fields have
demonstrated that temporally localized electron wave packets (EWPs) can be used to
study molecular structures and dynamics
12-14
. In these experiments the EWPs are
generated through tunnel ionization twice per optical cycle near the peaks in the laser’s
oscillating electric field. They are subsequently accelerated by the same laser field and
may be driven back to their parent ion for further interaction. If, for example, aligned
molecules are used as targets their orbitals can be characterized from the resulting
harmonic emission. The basic sequence of events, which is the essence of strong field
physics, is very versatile and leads to many different phenomena
15,16
. The only control
knob in these experiments, however, is typically the laser intensity, which must be quite
high in order that there be a reasonable probability of tunneling through the Coulomb
barrier. Further control of the electron dynamics requires that the creation and
acceleration of the EWPs are decoupled; and this is not possible using tunneling
ionization since the same laser field governs both events. Decoupling can be achieved
using XUV attosecond pulses to create temporally localized EWPs through single
photon ionization at a well defined phase of a synchronized IR field. These attosecond
EWPs are distinctly different from tunnel ionization EWPs: they are born at the centre
2
of the potential well with a non-zero velocity and their subsequent dynamics can be
controlled by choosing the phase and amplitude of a synchronized IR field
appropriately. In particular, the laser field needed to drive these EWPs back to the
potential is usually far weaker than the laser field needed to form tunnel EWPs, leading
to much less distortion of the electronic or nuclear properties to be studied.
Decoupling laser-driven dynamics from ionization is at the heart of the attosecond
quantum stroboscope, a device to guide and image electron motion on a sub-
femtosecond time scale, which is illustrated in Fig. 1a, b. The stroboscope technique is
based on a sequence of identical attosecond pulses that are used to release electrons into
a moderately strong laser field exactly once per laser cycle. Just as a conventional
stroboscope can be used to freeze the beating of a hummingbird’s wings, revealing
details that would normally be blurred, we use the quantum stroboscope to record the
electron momentum distribution from a single ionization event, free from interference
effects due to multiple ionization events. Operationally, the quantum stroboscope works
because ionized electrons receive a momentum impulse from the IR field along its
polarization direction (the vertical in Fig. 1). Since this impulse depends on the
magnitude and direction of the laser field at the moment of ionization
17-19
, each phase of
the oscillating laser field yields a unique final momentum distribution. If ionization
occurs over the whole IR cycle, or even at as few as two times during the cycle, the
distribution will be smeared out and show interference fringes that depend on the
different ionization times
20
. When the attosecond pulse periodicity matches the optical
cycle, the XUV pulses create identical EWPs that add up coherently, with the result that
the properties of an individual EWP can be studied stroboscopically. In addition, the
temporal localization of the EWPs within the optical period of the IR field allows for
precise guiding of the wave packets after their birth.
In a first experimental demonstration of the quantum stroboscope we use pulses
with a 300 as duration and a central energy of 24 eV to ionize argon in the presence of a
guiding IR laser field with an intensity of W/cm
2
. The attosecond pulse train
(APT) was generated from a two colour laser field consisting of the IR field and its
second harmonic to ensure that the XUV pulses were separated by one full optical
cycle
6
. Four stroboscopic images taken at different XUV-IR delays are presented in Fig.
1 (c). The clear up/down-asymmetry in the momentum distributions confirms that each
image corresponds to ionization at one particular phase of the IR field, so that the total
momentum is shifted up or down in the direction of polarization of the IR field. These
results illustrate two essential aspects of stroboscopic imaging. First, we can freeze the
periodically varying momentum distribution at a single phase of the IR field, and then
capture the entire time-dependent distribution by varying the XUV-IR delay. Second,
the measured signal is larger than what we would measure with a single pulse. In a
quantum stroboscope this effect is enhanced because a train of N pulses yields fringes
that are N
2
times brighter than the signal from an isolated pulse, owing to the coherence
of the process (
12
105⋅
10
≈
N in our experiment). This has allowed us to obtain full three
dimensional images of an attosecond EWP for the first time. An additional feature is
that the position of the stationary interference fringes depends only on the IR intensity.
The quantum stroboscope is therefore self-calibrating since the only unknown
parameter, the IR intensity, can be read directly from the interference pattern.
3
In the experimental results presented in Fig. 1 coherent electron scattering was not
observed since the intensity of the guiding laser field was not high enough to direct the
EWPs back to the ion core. To estimate the field intensity needed for coherent electron
scattering, simple classical arguments can be used. The momentum at time t of an
electron born in the field )sin()(
0
tEtE
ω
= at time t
0
with initial momentum p
0
is equal
to
[
)cos()cos(),(
0
0
00
tt
eE
pttp
ωω
ω
−+=
]
. (1)
It is the sum of a drift momentum (which is a combination of the initial
momentum obtained from the XUV ionization and of that gained in the laser field) and
an oscillating term describing wiggle motion in the field. Introducing the wiggle energy
and the initial kinetic energy , where I
p
is
the ionization energy, the condition for the final (drift) momentum to be zero or
opposite to the initial momentum can be formulated as
22
0
2
4/
ω
mEeU
p
=
PXUV
IEmpW −== 2/
2
0´
12/
~
≤=
p
UW
γ
. When 1
~
=
γ
,
the momentum transferred by the field to the electrons is such that only electrons that
are born exactly at times when
E(t)=0 will return to the ion since the net transfer of
momentum from the laser field is maximized for these times. For smaller
γ
~
-values the
momentum transfer is larger, and returns are possible also for other initial times. We can
tune the interaction (the energy of the returning electrons, the number of times they pass
the core and the field strength at the moment of re-collision) by varying the delay
between the attosecond pulse and the laser field. For an 800 nm laser wavelength, 1
~
=
γ
can be obtained by using, for example, W/cm
2
and W=1.2 eV. This intensity
is an order of magnitude smaller than that needed for tunnel ionization.
13
101⋅=I
To understand what we can expect from experiments that guide ionized electrons
to rescatter off the ion core, we have performed a series of calculations in helium by
numerically integrating the time-dependent Schrödinger equation (TDSE). The
momentum distributions obtained at the XUV-IR delay leading to maximum
momentum transfer from the guiding field to the electrons are shown in Fig. 2 for four
different IR intensities. The white circle in each panel denotes the range of momenta
expected if there is no rescattering from the ion. We clearly see the onset of scattering
for
γ
~
values near one ( 2.1
~
≈
γ
). At this intensity the low energy fraction of the EWPs
has scattered off the atomic potential while the high energy portion remains unaffected.
With decreasing
γ
~
values a larger portion of the EWP scatters off the potential, which
increases the scattering signal.
To experimentally access the regime of coherent electron scattering we change the
target gas to helium, so that W=1.2 eV, and we increase the IR intensity to
W/cm
2
. Four experimental momentum distributions recorded at different XUV-IR
delays are presented in Fig. 3. When the XUV-IR timing is set to maximize the
momentum transfer from the IR field in the upwards (panel 1) or downwards (panel 3)
directions we see a clear signature of re-scattering, manifested by a significant increase
of low-energy electrons in the direction opposite to the momentum transfer from the IR
13
102.1 ⋅=I
4
field
21
. The experimental results are compared with theoretical calculations in Figure 4
and the agreement is excellent with all the substructures well reproduced. We believe
that this is the first evidence for coherent electron scattering of attosecond EWPs
created by single photon ionization.
In this letter we have demonstrated an attosecond quantum stroboscope capable of
imaging the electron momentum distribution resulting from a single ionization event.
We have also used it to guide ionized electrons back to their parent ions and to image
the coherent electron scattering. The basic technique we have demonstrated is very
versatile and may be altered in a number of potentially useful ways. For example, the
guiding field could be a replica of the two-colour driving field we used to make the
attosecond pulses. This would provide additional control over the return time and
energy of the electrons. Using a longer wavelength driving laser would lengthen the
time between attosecond pulses, allowing more time for internal dynamics initiated by
the launch of the EWP to develop before being probed by the returning electron. We
envision that controlled, coherent scattering such as we have demonstrated will enable
time resolved measurements with very high spatial resolution in atoms and molecules or
at surfaces.
1. Paul, P. M., et al. Observation of a train of attosecond pulses from high harmonic generation. Science
292, 1689-1692 (2001).
2. Hentschel, M. et al. Attosecond metrology. Nature 414, 509-513 (2001).
3. Drescher, M. et al. Time-resolved atomic inner-shell spectroscopy. Nature 419, 803-807 (2002).
4. Kienberger, R. et al. Atomic transient recorder, Nature 427, 817-821 (2004).
5. Goulielmakis, E. et al. Direct Measurement of Light Waves, Science, 305, 1267-1269 (2004).
6. Mauritsson, J. et al. Attosecond Pulse Trains Generated Using Two Color Laser Fields, Phys. Rev. Lett.
97, 013001 (2006).
7. Vrakking, M. J. J. An iterative procedure for the inversion of two-dimensional ion/photoelectron
imaging experiments, Rev. Sci. Instrum. 72, 4084-4089 (2001).
8. Eppink, A. T. J. B. & Parker D. H., Velocity map imaging of ions and electrons using electrostatic
lenses. Application in photoelectron and photofragment ion imaging of molecular oxygen, Rev. Sci. Instr.,
68, 3477-3484 (1997).
9. Miao, J. Charalambous, P. Kirz, J. & Sayre, D. Extending the methodology of X-ray crystallography to
allow imaging of micrometre-sized non-crystalline specimens, Nature 400, 342 (1999).
10. Chapman, H. N. et al. Femtosecond diffractive imaging with a soft-X-ray free-electron laser, Nature
Physics 2, 839-843 (2006).
11. Wu, J., Weierstall, U. & Spence J. C. H., Diffractive electron imaging of nanoparticles on a substrate,
Nature Materials 4, 912 (2005).
12. Niikura, H. et al. Sub-laser-cycle electron pulses for probing molecular dynamics. Nature 417,
917–922 (2002).
13. Itatani, J. et al., Tomographic imaging of molecular orbitals, Nature 432, 867-872 (2004).
14. Kanai T., Minemoto S. & Sakai H., Quantum interference during high-order harmonic generation
from aligned molecules, Nature 435, 470-474 (2005).
15. Schafer, K. J. et al. Above threshold ionization beyond the high harmonic cutoff. Phys. Rev. Lett. 70,
1599-1602 (1993).
5
16. Corkuum, P. B. Plasma perspective on strong-field multiphoton ionization. Phys. Rev. Lett. 70, 1994-
1997 (1993).
17. Itatani, J. et al. Attosecond streak camera. Phys. Rev. Lett. 88, 173903 (2002).
18. Kienberger, R. et al. Steering attosecond electron wave packets with light. Science 297, 1144-1148
(2002).
19. Johnsson, P. et al., Attosecond electron wave packet dynamics in strong laser fields, Phys. Rev. Lett.
95, 013001 (2005).
20. Remetter, T. et al., Nature Physics 2, 323 (2006).
21. We note that there is an up/down asymmetry even for the XUV-IR delays where no net momentum is
transferred to the electrons. We attribute this asymmetry partially to a small frequency modulation on the
attosecond pulses and partially to the distortion of the atomic potential.
Acknowledgments: This research was supported by a Marie Curie Intra-European Fellowship, the Marie
Curie Research Training Networks XTRA, the Marie Curie Early Stage Training Site MAXLAS, the
Integrated Initiative of Infrastructure LASERLAB-EUROPE within the 6th European Community
Framework Programme, the Knut and Alice Wallenberg Foundation, the Crafoord foundation, the
Swedish Research Council and the National Science Foundation.
Author Information The authors declare no competing financial interests. Correspondence and requests
for materials should be addressed to J.M. (johan.mauritsson@fysik.lth.se).
Figure 1: Principle of the attosecond quantum stroboscope. An attosecond pulse train
containing N pulses is used to ionize the target atoms once per cycle of an IR laser field. This
periodicity ensures that the created EWPs are identical and that they add up coherently on the
detector leading to an enhanced signal that is modulated by interferences fringes (a,b). The
bright fringes are increased by a factor N
2
compared to the signal that would be obtained with
only one pulse. The IR field is used to guide the electrons and the momentum transfer can be
controlled by simply varying the XUV-IR delay. When the EWPs are created at the maxima of
the IR electric field (a) the net transfer of momentum is zero and the resulting momentum
distribution is symmetric relative to the plane perpendicular to the laser polarization. When the
EWPs instead are created at the zero-crossings of the IR electric field (b), the momentum
distribution is shifted by the field up- or down-wards along the direction of the laser polarization.
In our experiment, the final momentum distributions of the EWPs are detected using a VMIS.
Experimental results obtained in Ar at four different XUV-IR delays are shown in (c), panels 1-4
correspond to the delays t
0
=-π/2ω, 0, π/2ω, π/ω respectively for an IR intensity of W/cm
2
.
The delay-dependent momentum distribution is imprinted on a set of concentric rings which are
due to the coherent addition of many EWPs. These rings, which are evenly spaced one IR
photon apart in energy, show a decreasing spacing when plotted as a function of momentum.
The positions of the rings do not shift as a function of XUV-IR delay, which shows that we are
imaging a train of identical EWPs spaced one IR cycle apart in time.
12
105⋅
Figure 2: Theoretical illustration of coherent scattering. Theoretical results obtained by
integrating the TDSE are shown for IR intensities ranging from zero to W/cm
2
for the
XUV-IR delay which corresponds to the maximum momentum transfer. The momentum transfer
from the field to the electrons is upward in the figure. The white circles are positioned at the
highest energy electrons in the field free case (panel 1) and shifted by the amount of momentum
added by the IR field in the other panels. If no post-ionization interaction between the electron
and the atom occurs the momentum distributions would remain within the circles. This is the
case in panel 2, in which the IR field is too weak to drive the electron back to the atomic
potential, but not in panel 3 and 4 where electrons appear outside the circles in the downward
direction. Two features are highlighted in panel three, which is calculated at an intermediate
intensity where
13
102⋅
γ
~
= 1.2, by white arrows: I) electrons that have scattered off the core appearing
outside the white circle in the downward direction and II) interference minima in the momentum
6
distribution. The interference minima occur in the region where the rescattered and direct
electrons overlap.
Figure 3: Experimental demonstration of coherent electron scattering. Experimental
results obtained in helium at an intensity of W/cm
2
at the same delays as in Fig. 1 (c)
are shown. The results are distinctively different from those taken in argon (Fig. 1). The
momentum distributions are more peaked along the laser polarization direction, since in helium
the excited EWP is entirely in an m=0 state, whereas in argon there was a mixture of m=0 and
m=1 and the latter has no amplitude along the polarization axis. This is a favourable condition to
observe electron scattering since the electrons along the polarization direction have the highest
probability to scatter off the potential. With this higher intensity more momentum is transferred to
the electrons and in combination with the lower initial energy some electrons return to the
atomic potential for further interaction.
13
102.1 ⋅
Figure 4: Comparison between theory and experiment. We compare the experimental
results (right) with theoretical calculations (left) obtained for the same conditions. The excellent
agreement is the strongest evidence for coherent scattering effects in the experiment. All the
substructures well reproduced except for the innermost peak in the experiment, which most
likely is due to above threshold ionization of residual water in the experimental chamber and
therefore not included in the theoretical results.
Figure 1
Figure 2
No IR field
γ=1.2
~
γ=0.86
~
γ=3.8
~
II
I
Momentum (a. u.)
Momentum (a. u.)
1 0.5 0 -0.5 -1
1
0.5
0
-0.5
-1
Figure 3
Momentum (a. u.)
1
0.5
0
-0.5
-1
Momentum (a. u.)
1 0.5 0 -0.5 -1
Theory Experiment
Figure 4
