Necati Kaya

1. The Dynamics Of Molecules In Intense Ultrashort Laser Fields: Measurements of Ultrashort, Intense Laser-induced Fragmentation of The Simplest Molecular Ion (H2+ ) Necati Kaya

2. Why H2+ ? H2+ • 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.

3. 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

4. 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

5. Potential seen by the  ionizing electron. http://www.mpq.mpg.de/~haensch/h2+/images/Coulomb%20potential.gif

6. Floquet picture (Sayler, 2008) Hamiltonian H can be written as: Electricfield due to the laser nuclear kinetic energy the sum of the electronic kinetic energy and Coulomb interaction of all particles potential due to the laser field Molecular reduced mass dipole moment of the molecule

7. 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.

8. 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)

9. (Pavicic, 2004) • Diabatic Picture • Crossings  Resonant positions • Adiabatic Picture • Coupling  Avoided crossings

10. Experimental Method

11. Voltage V A3 E E DP3 Ion gate SM z FC MCP Ion Source Simplified Diagram of Experimental setup Y. Lee MS Thesis ,2006 A4 A5 DP2 EL2 A2 A4 A6 IA A1 lens Time- and Position-Sensitive Detector EL1 LaserBeam 800 nm, ~1014W/cm2 @ 50fs DP1 H+ (x1, y1) t1 H2+ Beam (7 keV) FC H t2 (x2, y2) Microchannel Plate Delay-Line Anode

12. Intermediate electrode Uzw: Voltage on the intermediate electrode (0-100V) Izw: current from the intermediate electrode (-300-0-+300mA) Ion source Small electromagnetImag: 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 electrodeUa: positive acceleration voltage to extract the positive ions Ua =12kV Is: current from extractor electrode Is =0.100mA Voltage ~100V ~300-600V 12kV Distance

13. Einzel Lens Dimensions (End cylinders at ground) D = 1.86 au L = 2.44 au G = 0.184 au S = 1.72 au

14. 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.

15. Delay-Line Detector

16. 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)

17. 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.

18. 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 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.

19. (Niederhausen et al 2012)