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New Light Sources
New light sources of very high intensity and short duration allow us to carry out
time resolved studies of atomic and molecular dynamics
Femtosecond Lasers
Attosecond Lasers
1
Characterized by a duration of a few to hundreds of
femtoseconds (10-15 s).
The peak intensity is high and the electric field of the
laser is comparable to the electric field that a bound
electron experiences from the nucleus.
Compared to a laser field of long duration one needs
an additional parameter, the carrier-envelope phase difference (CEPD), to characterize a few-cycle femtosecond
pulse (see figure 1).
0.8
Normalized electric field
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0
Near-infrared (NIR), 1200-800 nm.
1013-1016W/cm2.
High-order harmonic generation,
tomography,
coherent control, ablation,
time-resolved chemical reactions.
2.5
5
7 .5
Realized by exploiting high-order harmonic generation (HHG) from atoms.
Typical pulse length is hundreds of attoseconds (10-18 s).
The intensity is low because of the low
efficiency of the HHG process.
A tool for time-resolved studies of electron dynamics in atoms, molecules and
solids.
Wavelength:
Intensity:
Applications:
Fig. 1: Two few-cycle femtosecond pulses.
The CEPD is the phase shift between the
carrier-wave and the envelope of the
pulse.
UV-XUV, 10-1 nm.
Low.
Attoscience, biophysical and biomedical investigations,
surgery.
Wavelength:
Intensity:
Applications:
Fig. 2: The HHG three-step
model. Ionization at time t’ followed by propagation and recombination at time t. Different
ionization instants lead to radiation at different frequencies.
The basic principle of coherent control is to use laser
sources to manipulate physical and chemical processes.
One example of coherent control is laser induced
alignment and orientation of molecules where the rotational motion is manipulated by one or more laser
pulses of picoseconds (10-12s) or subpicoseconds duration to make the molecule point in a certain direction in
space.
Another example of coherent control is the use of
the asymmetry of the electric field of a few-cycle femtosecond pulse to control the electron distribution in the
dissociative ionization of molecules (see figure 3).
Molecular-Orbital Tomography
Fig. 3: Measured asymmetry of the D+ fragment in dissociative ionization of D2 molecules as a function of
energy and CEPD [M. F. Kling et al. ,Science 2007]. The asymmetry in the signal is ascribed to a localization of
the electron around one of the two nuclei in the singly ionized D2+ prior to dissociation, and the figure
clearly demonstrates control of this localization as a function of the CEPD phase.
Time-Resolved Studies of Nuclear Motion
in Molecules
y(Å)
Molecule
Laser
Time
y(Å)
Electron
x(Å)
Fig. 4: (Top) The reconstructed N2 molecular-orbital in an experiment [Itatani et al., Nature 2004].
(Bottom) The theoretically calculated N2 molecular orbital.
Harmonic intensity
Attoscience
Ioniz a tion yie ld (a rbitra ry units )
a)
–1.0
380 as
–0.5
0.0
0.5
1.0
Delay time, ∆ t (fs)
b)
V
+V
Coulomb
Potential
The characteristic time scale
for electron motion in atoms
and molecules is typically a few
hundred attoseconds.
Attosecond pulses extracted from the HHG process
can be used to conduct time resolved measurements of this
fast electron motion.
Fast rearrangement of the
electron is a fundamental part
of a vast number of processes
such as photosynthesis and
vision.
Several pioneering attoscience experiments are currently
conducted.
VCoulomb
E−field
Electron
tunneling
Distance
Tunable from microwaves to x-rays.
Up to 1022 W/cm2.
Fast ignition of fusion, particle
physics, biophysical and
biomedical investigations and
surgery.
Coherent Control
High-Order Harmonic Generation
The HHG spectrum contains information about the orbital, since it is generated
when the electron recombines with the ion
under emission of a harmonic photon.
The idea in molecular-orbital tomography is to use this information to reconstruct the molecular-orbital.
Measurements of HHG spectra for a
whole range of molecular orientations
probes the Fourier transform of the dipole
operator times the electron orbital, and
from this the wave function is obtained
from an inverse Fourier transform.
Characterized by very energetic and potentially very
intense laser beams.
Lasing medium consists of highly relativistic electrons
in an undulator (magnet array).
A free electron laser is very expensive because
the production of relativistic electrons requires a particle
accelerator.
10
Time (femtoseconds)
When matter interacts with an intense femtosecond laserpulse this may lead to the emision of coherent UV or XUV
radiation.
The production of radiation is understood in terms of a
three-step model:
1. An electron is removed from the atom or molecule by
absorption of k’ laser photons at a time t’ within a subfemtosecond around the peak of the femtosecond laser field.
2. The electron is accelerated in the laser field, initially away
and then back towards the parent ion.
3. The electron recombines with the parent ion under the
absorption of k laser photons at time t within a subfemtosecond interval around the minimum of the laser field. A
photon of frequency k’+k times the laser frequency, a socalled harmonic photon, is emitted.
Because the recombination takes place within a subfemtosecond interval, the harmonic radiation is emitted as a
burst of attosocond duration.
Free Electron Lasers
Frequency
Wavelength:
Intensity:
Applications:
CEPD 0
CEPD π/2
Lundbeck Foundation
Theoretical
Center !!!!!!!!!!!!!! !!!! for
!!!!!!!!!!!!!!!!! !!Quantum
!!! !!System Research
Fig. 5: Uiberacker et al. Nature 2007 used a pumpprobe experiment to study electron tunneling in
neon ions, where the pump is an XUV attosecond
pulse, and the probe is a near-infrared (NIR) femtosecond pulse. The two pulses are displaced by a
variable delay ∆t. The XUV pulse ionizes neon,
leaving neon in a number of excited ionic states.
These states can be probed via tunnel ionization
by the few-cycle NIR femtosecond pulse. Since the
excited states are exposed to the NIR field from the
moment they are made to the end of the NIR pulse,
it is possible to probe different ionic states, by
changing the delay ∆t.
a) Experimental results. The steep part of the curve
correspond to non-adiabatic tunneling ionization.
b) The principle behind laser induced tunneling in
atoms.
Fig. 6: HHG can be used to study nuclear
dynamics, e.g., in H2+. When an electron is
removed from H2, the nuclei start to move
apart due to the larger equlibrium separation in H2+, compared to H2. When the electron returns the recombination process is
dependent on the overlap between the
present nuclear wave function and the
nuclear wave function in H2. If the nuclei
have not moved far the overlap is close to
unity, and a large amount of harmonic radiation is emitted. If, on the other hand, the
nuclei have moved far apart, the overlap of
the nuclear wave functions is small, and
less harmonic radiation is emitted. Using, in
addition, the fact that early returning electrons lead to high-order harmonic generation of low frequencies, while late returning
electrons yield high frequencies one can reconstruct the nuclear motion by comparing results obtained from different isotopes.
For light molecules nuclear dynamics is fast and has to be taken into account even on a femtosecond time
scale.
Simple physical models are necessary since the nuclear motion on top of
the electronic motion would add at
least add three dimensions to the problem if no approximations were made.
A typical simplification of nuclear
motion is to use the Born-Oppenheimer
approximation, which has, e.g., been
successfully employed to describe
double ionization of H2.
Experimentally the motion of nuclei
can be studied with time resolution
using high-order harmonic generation
(See Fig. 6).
The Lundbeck Foundation
Theoretical Center for Quantum System Research (LTC) is
concerned with the theory of
quantum systems at the atomic
level. The center merges research in quantum optics and
information, cold atoms and
matter waves, and atomic and
molecular physics with new
light sources, where immense
experimental progress currently raises high demands on
new theoretical ideas and
analyses.
www.phys.au.dk/ltc