Quantum Optics and Laser Science Group Blackett Laboratory, Imperial College London

1
Quantum Optics and Laser Science Group Blackett
Laboratory, Imperial College London
Imaging Molecular Structure and Dynamics using
Laser Driven Recollisions

• Introduction to high harmonic generation (HHG)
• Imaging molecular structure through HHG
• two-centre interference and mapping electronic
  structure in
• polyatomic molecules.
• 3. Probing of proton dynamics in molecules using
  chirp
• encoded electron recollision.

S.Baker, J.Robinson, R.Torres, N.Kajumba, M. Lein
(Kassel) , C.Chirila (Kassel), Jonathan Underwood
(UCL), C.Haworth, R. De Nalda, E. Springate,
L.Chipperfield, P. L. Knight, J.W.G.Tisch and J.
P. Marangos (Imperial College) R.Velotta,
C.Altucci (Naples), C. Vozzi, G. Sansone, S.
Stagira, M.Nisoli (Politecnico of Milan), E.Turcu
and W.Bryan (RAL), Heidi Bandulet, David
Villeneuve (ALLS/NRC)
2
High harmonic generation occurs on a sub-optical
cycle timescale
? Recollisional model of HHG e.g. Corkum PRL
(1993), Lewenstein et al (1994)
Tunnel ionisation
Acceleration in the laser field
Recombination to ground state
Bound electron
HHG signal arises from coherent addition of
contributions from atoms/molecules in the
sample. For these contributions to add
constructively initial and final states must be
the same, giving the process a unique specificity.
3
Temporal chirp of harmonic spectrum
Ionisation can occur for a range of times around
the peak of the electric field. Parts of the
electron wavepacket born at different times
follow different trajectories, and gain varying
amounts of energy from the field.
Laser electric field
Time
4
Temporal chirp of electron wavepacket
long trajectories
short trajectories
Harmonic cut-off
5
Harmonic Dipole Amplitude and Phase Depends upon
Molecular Alignment
Harmonic dipole phase and amplitude calculated by
numerical treatment with TDSE for harmonic in
H2 as a function of orientation for 31st
harmonic
Two centre interference is shown to be
responsible for dip and phase modulation (Lein et
al, PRL 88-183903 (2002) and PRA 66-023805 (2002))
Experimental evidence for anisotropic dipole
phase from earlier experiments of HHG in
adiabatically aligned CS2 (Velotta et al, PRL
87-183901 (2001))
6
The dipole amplitude is determined by the
relative phase of the recolliding electron wave
at the two centres.
PRA 66-023805 (2002)
This process has recently been observed in HHG
from CO2 in the group of Hirofumi Sakai (Tokyo)
Nature 435, 470 (2005)
7
The HHG process can be transparently formulated
in the strong field approximation
Amplitude of HHG process determined by (c.f
Lewenstein et al 1994)
Tunnel ionization from the molecular bound-state
Propagation in the laser field
Recombination back into molecular bound-state.
The last factor plays a critical role in new
methods to use HHG to image molecular structure
in aligned molecular samples e.g. Tomographic
reconstruction (Itatani et al Nature (2004)) or
recombination step interference signatures
studied by our group (Lein et al PRL (2002),
Vozzi et al PRL (2005)) and Kanai et al Nature
(2005).
8
Fixing molecules in space Non-adiabatic
alignment

• Intense ultrashort (t lt Trot) laser field (I0 gt
  1012 W/cm2) and coherent
• excitation of rotational levels.

a
Polarizability anisotropy Da a - a?
a?
H B J2 - 1/4 E2 (Da cos2q a?)
J Mgtin
9
Non-adiabatic alignment of molecules allows
molecular structure to be extracted from HHG
measurements
10
At the peak of the rotational revival a robust
minimum is observed in the HHG due to the
destructive interference between 2-centres
Our work goes further than that of Sakai in that
we have measured HHG to significantly higher
recollision momenta (up to 49th rather than 31st
harmonic)
Published in Physical Review Letters 95 153902
(2005)
11
Can HHG from polyatomic molecules be mapped to
electronic structure via SFA? We have
investigated HHG from a series of aligned organic
molecules acetylene, ethylene, allene, at ASTRA
CLF-RAL
12
HHG in Aligned Organic Molecules

• Observe HHG spectra in small organic molecules
  with a p-bonding HOMO structure.
• Measure HHG spectra as a function of alignment.
• Seek signatures of the molecular structure
  through the HHG spectra.

Extend the methods of ultra-fast molecular
imaging to more complex systems.
13
The molecules
Acetylene (CH?CH) - Linear Symmetric top -
Triple bond - IP 11.4 eV
14
Calculations use the SFA (Lewenstein model)
15
Acetylene
16
Allene
17

• Summary of aligned organic molecule HHG studies
• The measurements of HH emission as a function of
  the alignment angle show a behaviour which is
  characteristic of the bonding p structure in the
  HOMO orbital of the molecules. Extra features are
  observed in Allene.
• A calculation using SFA reproduces the general
  features. The angular distribution of the aligned
  sample must be taken into account in order to
  compare the calculations quantitatively with the
  experimental results.
• HHG from aligned organic molecules is directly
  related to electronic structure through the SFA.

Torres et al Physical Review Letters 98, 203007
(2007)
18
HHG from molecules can also be used to see fast
nuclear dynamics in the molecular ion
19
For the short trajectories selected in this
experiment there is a well defined time to
frequency encoding during the 0.6-1.6fs
recollision interval
Chirp Encoded Electron Recollisions
20
Exploiting the temporal chirp of an harmonic
spectrum
Lein showed Phys. Rev. Lett., 94, 053004
(2005). that harmonic signal includes
contribution from nuclear part of
wavefunction Dipole moment responsible for HHG
given by
where C(t) is the nuclear correlation function
Wavefunction describing nuclear wavepacket
21
Exploiting the temporal chirp of an harmonic
spectrum

• 2 predictions
• Stronger harmonic signal in a heavy isotope
• Ratio between signals D2H2 increases with
  harmonic order

Phys. Rev. Lett., 94, 053004 (2005)
Strong order-to-order variation due to
interference between short and long trajectories.
22
This measurement uses our high intensity
few-cycle laser system to drive HHG in the
molecules
Requires short (lt10fs) pulses to avoid
disturbance of molecule prior to ionisation. In
particular ionization occurs only in the
few-cycles 2x1014 Wcm-2.
1 kHz, 7-8 fs, 0.25 mJ.
23
Experimental approach
Focus 9 mm before jet to isolate short
trajectories. Intensity delivered at interaction
region 2 x 1014 Wcm-2 shot-to-shot fluctuation
lt3, monitored between data runs. Apply correct
gas jet backing pressures to ensure equal gas
densities at the interaction region.
2 Hz pulsed valve
Microchannel Plate Imaging Detector
Off-Axis Parabolic Mirror
Soft X-ray Flat-Field Grating
24
Experiment Confirms These Predictions
Calculated value of ratio from C(?)
25
And the proton dynamics can be reconstructed from
the H2/D2 ratio
The nuclear motion reconstructed from the
experimental data by multiple runs of a genetic
algorithm (red curves) converges closely to the
exact result (blue curves) calculated using the
exact Born-Oppenheimer potentials for H2 and
D2.
This method has determined ltR(t)gt with 100
attosecond / 0.1 Angstrom resolution Probing
Attosecond Dynamics with Chirp Encoded
Recollisions PACER
26
The nuclear correlation function ratio between
CH4 and CD4 provides the first evidence of an
ultra-fast rearrangement of methane upon
ionisation
Baker et al Science 312, 424 (2006)
27
Recent measurements with 30fs pulses have shown
intensity dependence in the data consistent with
alignment and transient 2-centre interference
intensity 3 x 1014Wcm-2
intensity lt 2 x 1014 Wcm-2
28
Conclusions and further work

• Molecular structure is revealed through
  systematic measurements of HHG in aligned
  molecules
• Proton dynamics can be imaged using inherent
  chirp within the harmonic emission process
• Measurements to track proton dynamics over a
  longer timescale are possible using longer
  wavelengths
• This technique is applicable in principle to
  measurement of electronic dynamics also.