Why I never let go of my Ph.D. thesis research! Rhodes Scholars Symposium University of Illinois, Chicago March 28, 2012 Supported by: National Science Foundation Research Corporation

The story …

The review …

Major result: Inner-shell ionization  Common assumption – only the least bound electron is ionized by tunneling in a strong field and the resulting ion is left in the ground state.  Our (Gibson, Rhodes, et al.) result showed inner-shell ionization and, consequently, excitation of the ion by the strong laser field. In fact, excitation led to fluorescence of a previously unobserved state of N  Results met with some resistance!  I continued to pursue this question in different ways as a postdoc and a professor.

Postdoc work at Bell Labs Could ionize the 1π u and 2σ g electrons, as well.

Dissociation Channels:  N 2  N 2 1+  N 2 2+  N 1+ + N 1+  N 2 3+  N 1+ + N 2+  N 2 4+  N 2+ + N 2+  N 2 5+  N 3+ + N 2+  N 2 6+  N 3+ + N 3+  N 2 7+  N 4+ + N 3+  N 2+ + N 0+ (15.1 eV)  N 3+ + N 1+ (17.8 eV)  N 4+ + N 2+ (30.1 eV)

Conclusions from VUV Spectra Coffee and Gibson, PRA 69 (2004) Nitrogen shows many fluorescence lines generated from direct strong field excitation. In all cases, the excitation involves one or two 2s holes. Some upper states consist of multiply excited states. One is at 25 eV above the ground state. N 2+ : 2s2p 2 – 2p 3. Direct lines identified from N 4+ - a state not seen in ion TOF data, until recently.

Theory of Multiphoton Coupling in Molecules [PRL , PRA ] Atoms do not show signs of multiphoton excitation when exposed to strong laser fields: at intensities high enough to drive multiphoton transitions, the ac Stark shift detunes the laser and ionization sets in. So, what is so special about ionized diatomic molecules? They have an excited state structure that is highly susceptible to multiphoton coupling.

2 electrons in a double well. Ground state is a far off-resonant covalent state. Above this is a pair of strongly coupled ionic states. Only a weak coupling between them.

3-Level Model System This system can be solved exactly for the n-photon Rabi frequency!

N-photon Rabi Frequency: 2-level frequency from Duvall (or Shirley), et al.: In the 3-level system, multiphoton coupling depends on R 23 while the AC Stark shift depends on R 12. In the 2- level system, both effects come from the same coupling.

Perfect Floquet Ladder of States: The pair of ionic states are strongly modulated by the laser field and create a complete Floquet ladder of states – with no ac Stark shift! The ground state couples to this through a 1-photon process which only produces a small Stark shift.

Example: Population transfer in a model system: A 2 4+.

Again, a Floquet Ladder of States: The pair of strongly coupled ionic states is so effective, it can assist a high-order multiphoton transition to a regular covalent state! Verified through a 5- level calculation. Transition requires R 23 to be large.

Can even get adiabatic transfer on a 10-photon transition!

Pump-probe experiments in I 2

Iodine potential curves Many time-resolved pump-probe experiments are possible. Right now, we are specifically interested in the I 2+ + I 0+ states. The (2,0) and (1,1) curves form an excimer-type system in the dication! (2,0) is strictly bound while the (1,1) is at best quasi-bound. Wanted to see if we could populate the (2,0) states.

Populating the (2,0) state:

Simulation: trapped population in the (2,0) potential well The (2,0) potential curve measured from the A state of I 2 + in our previous work: pump-probe delay=180 fs PRA 73, (2006)

Asymmetric channels can show spatial asymmetry in a 1  2  field An asymmetric channel like (2,0) actually consists of two states with gerade and ungerade symmetry. Then one can form: (2,0) R ~ (2,0) g + (2,0) u (2,0) L ~ (2,0) g - (2,0) u where R and L refer to the 2 + ion going to the right or the left. An asymmetric channel like (2,0) actually consists of two states with gerade and ungerade symmetry. Then one can form: (2,0) R ~ (2,0) g + (2,0) u (2,0) L ~ (2,0) g - (2,0) u where R and L refer to the 2 + ion going to the right or the left. Of course, the (2,0) g and (2,0) u states must be populated coherently. Of course, the (2,0) g and (2,0) u states must be populated coherently.

I 2+ TOF Region with 1ω2ω fields

Experimental results

1-D 2-electron model From the asymmetry measurements, we can show that the ionization projects the molecules into the field- induced states. This has not really been considered before and suggests a new form of strong-field control.

Strong laser fields do a lot more than just ionize the least bound electron and leave the ion in its ground state. Diatomic molecules have a structure that is highly susceptible to strong field excitation. High levels of excitation are seen through the dissociation channels and direct fluorescence from the excited molecule. Ionization occurs within the electronic structure induced by the strong laser field. Conclusions