Strongfield physics revealed through timedomain spectroscopy George N

Strong-field physics revealed through time-domain spectroscopy George N. Gibson Grad student: University of Connecticut Department of Physics Li Fang – now at LCLS November 18, 2009 Stevens Institute of Technology Hoboken, New Jersey Funding: NSF-AMO

Motivation Vibrational motion in pump-probe experiments reveals the role of electronically excited intermediate states. n This raises questions about how the intermediate states are populated. Also, we can study how they couple to the final states that we detect. n We observe inner-orbital ionization, which has important consequences for HHG and quantum tomography of molecular orbitals. n

Pump-probe experiment with fixed wavelengths. In these experiments we used a standard Ti: Sapphire laser: 800 nm 23 fs pulse duration 1 k. Hz rep. rate Probe Pump

Pump-probe spectroscopy on Enhanced Excitation Enhanced Ionization at Rc Internuclear separation of dissociating molecule 2+ I 2

Lots of vibrational structure in pump-probe experiments

Vibrational structure Depends on: n wavelength (400 to 800 nm). n relative intensity of pump and probe. n polarization of pump and probe. n dissociation channel. n We learn something different from each signal. n Will try to cover several examples of vibrational excitation.

I 2+ pump-probe data

(2, 0) vibrational signal Amplitude of vibrations so large that we can measure changes in KER, besides the signal strength. n Know final state – want to identify intermediate state. n

I 2 potential energy curves

Simulation of A state

Simulation results From simulations: - Vibrational period - Wavepacket structure - (2, 0) state

What about the dynamics? How is the A-state populated? n I 2+ (I 2+)* - resonant excitation? n I 2 (I 2+)* directly – innershell ionization? n No resonant transition from X to A state in I 2+. n

From polarization studies The A state is only produced with the field perpendicular to the molecular axis. This is opposite to most other examples of strong field ionization in molecules. n The A state only ionizes to the (2, 0) state!? Usually, there is a branching ratio between the (1, 1) and (2, 0) states, but what is the orbital structure of (2, 0)? n Ionization of A to (2, 0) stronger with parallel polarization. n

Implications for HHG and QT We can readily see ionization from orbitals besides the HOMO. n Admixture of HOMO-1 depends on angle. n n Could be a major problem for quantum tomography, although this could explain some anomalous results.

(2, 0) potential curve retrieval It appears that I 22+ has a truly bound potential well, as opposed to the quasi-bound ground state curves. This is an excimer-like system – bound in the excited state, dissociating in the ground state. Perhaps, we can form a UV laser out of this.

Wavelength-dependent pump probe scheme Change inner and outer turning points of the wave packet by tuning the coupling wavelength. Femtosecond laser pulses: Pump pulse: variable wavelength. (517 nm, 560 nm and 600 nm. ) Probe pulse: 800 nm.

Vibrational period (fs) I 2+ spectrum: vibrations in signal strength and kinetic energy release (KER) for different pump pulse wavelength [517 nm, 560 nm and 600 nm] X-B coupling wavelength (nm)

Simulation: trapped population in the (2, 0) potential well pump-probe delay=180 fs The (2, 0) potential curve measured from the A state of I 2+ in our previous work: PRA 73, 023418 (2006)

I 2+ + In+ dissociation channels

Neutral ground state vibrations in I 2 Oscillations in the data appear to come from the X state of neutral I 2. n Measured the vibrational frequency and the revival time. n

Revival structure n Vibrational frequency Measured 211. 0 0. 7 cm-1 Known 215. 1 cm-1 Finite temp 210. 3 cm-1

Raman scattering/Bond softening n Raman transitions are made possible through coupling to an excited electronic state. This coupling also gives rise to bond softening, which is well known to occur in H 2+.

Lochfrass n New mechanism for vibrational excitation: “Lochfrass” R-dependent ionization distorts the ground state wavefunction creating vibrational motion. n Seen by Ergler et al. PRL 97, 103004 (2006) in D 2+.

Lochfrass vs. Bond softening n Can distinguish these two effects through the phase of the signal. LF = n BS = /2. n

Iodine vs. Deuterium Iodine better resolved: 23 fs pulse/155 fs period = 0. 15 (iodine) 7 fs pulse/11 fs period = 0. 64 (deuterium) n Iodine signal huge: n DS/Save = 0. 10 n DS/Save = 0. 60 n

Variations in kinetic energy n Amplitude of the motions is so large we can see variations in KER or <R>.

Temperature effects Deuterium vibrationally cold at room temperature Iodine vibrationally hot at room temperature n Coherent control is supposed to get worse at high temperatures!!! But, we see a huge effect. Intensity dependence also unusual n We fit <R> = DRcos(wt+ ) +Rave As intensity increases, DR increases, Rave decreases. n

Intensity dependence n Also, for Lochfrass signal strength should decrease with increasing intensity, as is seen.

n But, Rave temperature: T decreases while DR

We have an incoherent sea of thermally populated vibrational states in which we ionize a coherent hole: n So, we need a density matrix approach.

Density matrix for a 2 -level model n For a thermal system where p 1(T) and p 2(T) are the Boltzmann factors. This cannot be written as a superposition of state vectors.

Time evolution of r n We can write: n These we can evolve in time.

Coherent interaction – use p/2 pulse for maximum coherence n Off diagonal terms have opposite phases. This means that as the temperature increases, p 1 and p 2 will tend to cancel out and the coherence will decrease.

R-dependent ionization – assume only the right well ionizes. n yf = (yg + ye)/2 n Trace(r) = ½ due to ionization What about excited state? NO TEMPERATURE DEPENDENCE!

Expectation value of R, <R> The expectation values are /2 out of phase for the two interactions as expected.

Comparison of two interactions Coherent interactions: n Off diagonal terms are imaginary. n Off diagonal terms of upper and lower states have opposite signs and tend to cancel out. R-dependent ionization n Off-diagonal terms are real. n No sign change, so population in the upper state not a problem. Motion produced by coherent interactions and Lochfrass are /2 out of phase.

“Real” (many level) molecular system Include electronic coupling to excited state. n Use I(R) based on ADK rates. Probably not a good approximation but it gives R dependence. n Include n = 0 - 14 n

Generalize equations

Same conclusions For bond-softening n Off-diagonal terms are imaginary and opposite in sign to next higher state. r 12(1) -r 12(2) n DR decreases and <n> increases with temperature. For Lochfrass n Off diagonal terms are real and have the same sign. r 12(1) r 12(2) n DR increases and <n> decreases with temperature.

n Excitation from Lochfrass will always yield real off diagonal elements with the same sign for excitation and deexcitation [f(R) is the survival probablility]:

DR and <n>

Density matrix elements

Conclusions Coherent reversible interactions n Off-diagonal elements are imaginary n Excitation from one state to another is out-of-phase with the reverse process leading to a loss of coherence at high temperature n Cooling not possible Irreversible dissipative interactions n Off-diagonal elements are real n Excitation and de-excitation are in phase leading to enhanced coherence at high temperature n Cooling is possible

Conclusions n Excitation of the A-state of I 2+ through inner-orbital ionization n Excitation of the B-state of I 2 to populate the bound region of (2, 0) state of I 22+ n Vibrational excitation through tunneling ionization.

Laser System • Ti: Sapphire 800 nm Oscillator • Multipass Amplifier • 750 J pulses @ 1 KHz • Transform Limited, 25 fs pulses • Can double to 400 nm • Have a pump-probe setup

Ion Time-of-Flight Spectrometer

Phase lag

Ionization geometry

Ionization geometry

I 2+ pump-probe data