The Dynamics Of Molecules In Intense Ultrashort
Laser Fields: Measurements of Ultrashort, Intense
Laser-induced Fragmentation of The Simplest
Molecular Ion (H2+ )
Necati Kaya
Why H2+ ?
H2+
 H2+ the most elementary molecule in
nature
 Theoretically,
is usually treated as a
two-level system, since its ground
1sσg and the first excited state 2pσu are
well separated from next higher states.
10
 This simple molecular structure makes
possible accurate fundamental
quantum mechanical calculations.
 Contrary to its theoretical simplicity,
the preparation of H2+ is not easy and
therefore the experiments on H2+ are
rather rare.
1/R
5
H2+
+
+
H +H
E (eV)
0
+
H(2l) + H
-5
-10
2pu
-15
+
H(1s) + H
1 s g
0
4
8
12
R (a.u.)
16
Photodissociation of H2+
Potential Energy Curves of the two lowest states of
H2+ in a weak field.
Images from http://www.mpq.mpg.de/~haensch/h2+/introduction.htm
At intensities higher than 1012 W/cm2 the coupling between the ground 1sσg and
the first excited state 2pσu becomes very strong. These intensity regimes can be
characterized with the Rabi frequency ωR (see [1,2]), which measures the strength
of the radiative coupling:
In this regime molecule-light system is usually
described by potential curves "dressed" with
photons or with so-called light-induced potential
curves.
Potential Energy Curves of the photon dressed states
Images from http://www.mpq.mpg.de/~haensch/h2+/introduction.htm
Potential seen by the ionizing electron.
http://www.mpq.mpg.de/~haensch/h2+/images/
Coulomb%20potential.gif
Floquet picture
(Sayler, 2008)
Hamiltonian H can be written as:
nuclear kinetic energy
Electricfield due to the laser
potential due to the laser field
Molecular reduced mass
the sum of the electronic
kinetic energy and Coulomb
interaction of all particles
dipole moment of the molecule
 The Floquet picture allows one to envision the effects
of the laser-induced adiabatic coupling of Potantial
Energy Curves, which are obscured in the Vertical
Transition and diabatic Floquet pictures.
 The Floquet theory is a useful tool when dealing with
laser-molecule interactions, which allows one to easily
make qualitative predictions about the behavior of
molecules in a laser field.
 Furthermore, this picture will be referred to in
upcoming discussions of experimental results as a
basis for expectations and results.
 However, one must remember the assumptions made
in generating the Floquet potentials so that the theory
is not over extended.
H2+ adiabatic and diabatic Floquet potential energy curves. (a) Using vertical arrows to represent photon
absorption/emission. (b) Floquet picture with diabatic curves in black and adiabatic curves in color. (c) Adiabatic Floquet
curves at the 1-photon crossing with bond softening and vibrational trapping marked. (d) Adiabatic curves a the 3-photon
crossing with the 1-photon emission crossing circled. Note that the vertical arrows to the right of figures mark the expected
kinetic energy release (KER) for the respective processes. (Sayler, 2008)
(Pavicic, 2004)
• Diabatic Picture
• Crossings  Resonant positions
• Adiabatic Picture
• Coupling  Avoided crossings
Experimental Method
Simplified Diagram of Experimental setup
Y. Lee MS Thesis ,2006
A2 DP2
EL2
A4
A3
A5
A6
IA
Ion gate
SM
DP3
FC
MCP
A1
lens
EL1
Time- and
Position-Sensitive
Detector
Laser Beam
800 nm, ~1014 W/cm2 @ 50fs
DP1
H+
t1
(x1, y1)
FC
t2
(x2, y2)
+ Beam
H2
(7 keV)
H
Microchann
el Plate
V
Voltage
Ion Source
E
E
z
DelayLine
Anode
Ion source
Intermediate electrode Uzw: Voltage on the intermediate electrode (0-100V)
Izw: current from the intermediate electrode (-300-0-+300mA)
Small electromagnet Imag: current through the electromagnet to create
a magnetic field for ionization efficiency (0.0-2.5A adjustable)
Hollow cathode
Uent: Voltage on the cathode
to create and accelerate free
electrons (0 -600V).
Ient: current of electrons from
the cathode (0-100mA
adjustable)
Anode
e-
H2+
H2
Extractor electrode Ua: positive
acceleration voltage to extract the
positive ions Ua =12kV
Is: current from extractor electrode
Is =0.100mA
Voltage
~100V
~300-600V
12kV
Distance
Einzel Lens Dimensions (End cylinders at ground)
D = 1.86 au
L = 2.44 au
G = 0.184 au
S = 1.72 au
Mass selection
After extraction from the ion source, molecular ions are directed into a sector magnet (SM)
through entrance slit A1 (width of 5 mm) by means of a set of horizontal and vertical electrostatic
deflection plates (DP1) and an Einzel lens (EL1) (see exp setup on pg 11). By adjusting the
magnetic field B of the magnet, the molecular ions of mass mm and charge q are deflected by 90◦
to pass through exit slit A2 (width of 5 mm).
The ions selected in this way satisfy the relation
In order to select the desired molecular ion, the current after the mass selection was recorded
as a function of the voltage on the magnet, which is proportional to the magnetic field B.
Delay-Line Detector
Adiabatic climbing of vibrational ladders of H2+
Typical Energy & Times Scale
•e-  10 eV ~ 100 as
•Vibration  0.1 eV ~ 10 fs
•Rotation  0.001 eV ~ 1 ps
29fs
14fs
The vibrational energy v=9 is approximately
1200 cm−1 (∼0.3 eV), with the vibrational
period of 29fs. (Pavivic 2004)
Adiabatic climbing of vibrational ladders using Raman transitions with a chirped pump laser
(Chelkowski and Gibson 1995)
Linkage diagram for
vibrational-ladder
climbing by a pair of
pulses (Raman chirped
adiabatic passage
scheme). Vitanov et. Al.
Annu. Rev. Phys. Chem.
2001.
Laser-controlled vibrational heating and cooling of oriented H2+ molecules
(Niederhausen et al 2012)
a control-laser pulse for the
lowest 5 vib. levels of H2+
800 nm, 1014 W/cm2 @ 6fs
1.
2.
3.
The pump-laser pulse ionizes the neutral H2 molecule, launching a nuclear vibrational wave packet
in the H2+ ion.
A subsequent control pulse modifies the vibrational-state distribution of the ion by inducing
Raman transitions between the 1sσg and 2pσu electronic states at a given delay time.
Finally, the vibrational state is probed destructively by dissociation or Coulomb explosion in the
probe-laser pulse.
(Niederhausen et al 2012)