The Dynamics Of Molecules In Intense Ultrashort Laser Fields: Measurements of Ultrashort, Intense Laser-induced Fragmentation of The Simplest Molecular Ion (H2

+ )

Necati Kaya

H2+ the most elementary molecule in

nature

Theoretically, H2+ 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.

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.

Why H2+ ?

0 4 8 12 16

-15

-10

-5

0

5

10

1/R

2pu

H+ + H+

H(2l) + H+

E (

eV)

R (a.u.)

H(1s) + H+

1sg

H2+

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:

Potential Energy Curves of the photon dressed states

In this regime molecule-light system is usually described by potential curves "dressed" with photons or with so-called light-induced potential curves.

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

(Sayler, 2008)

Hamiltonian H can be written as:

dipole moment of the molecule

Molecular reduced mass

Electricfield due to the lasernuclear kinetic energy

potential due to the laser fieldthe sum of the electronic kinetic energy and Coulomb interaction of all particles

Floquet picture

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

DP2

DP1

EL1

EL2A2

A1

A4 A5 A6

Ion Source

SM

A3Ion gate

FC

MCP

DP3A4 IA

Delay-Line Anode

lens

H2+ Beam

(7 keV) FC

V

H+

H

t1

t2

Laser Beam800 nm, ~1014 W/cm2 @ 50fs

(x1, y1)

(x2, y2)

Microchannel Plate

Time- and Position-Sensitive Detector

E E

z

Voltage

Y. Lee MS Thesis ,2006

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)

Intermediate electrode Uzw: Voltage on the intermediate electrode (0-100V)

Izw: current from the intermediate electrode (-300-0-+300mA)

Extractor electrode Ua: positive acceleration voltage to extract the positive ions Ua =12kV Is: current from extractor electrode Is =0.100mA

Small electromagnet Imag: current through the electromagnet to create

a magnetic field for ionization efficiency (0.0-2.5A adjustable)

e-

Anode

H2

H2+

 

~300-600V~100V

12kV

Voltage

Distance

Ion source

Einzel Lens Dimensions (End cylinders at ground)

D = 1.86 auL = 2.44 auG = 0.184 auS = 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

The vibrational energy v=9 is approximately 1200 cm−1 ( 0.3 eV), with the vibrational ∼period of 29fs. (Pavivic 2004)

Typical Energy & Times Scale•e- 10 eV ~ 100 as•Vibration 0.1 eV ~ 10 fs•Rotation 0.001 eV ~ 1 ps

14fs

29fs

Adiabatic climbing of vibrational ladders of H2+

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.

1. The pump-laser pulse ionizes the neutral H2 molecule, launching a nuclear vibrational wave packet in the H2+ ion.

2. 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.

3. Finally, the vibrational state is probed destructively by dissociation or Coulomb explosion in the probe-laser pulse.

a control-laser pulse for the lowest 5 vib. levels of H2+800 nm, 1014 W/cm2 @ 6fs

Laser-controlled vibrational heating and cooling of oriented H2+ molecules (Niederhausen et al 2012)

(Niederhausen et al 2012)