Theoretical and experimental Theoretical and experimental progress towards HHG and progress towards HHG and

quantum tomography of quantum tomography of excited states of moleculesexcited states of molecules

Grad Grad student:student:

Li FangLi Fang

FundingFunding::NSF-AMONSF-AMO

July 14, 2009July 14, 20091818thth International Laser Physics Workshop International Laser Physics Workshop

Barcelona, SpainBarcelona, Spain

George N. GibsonGeorge N. GibsonUniversity of ConnecticutUniversity of Connecticut

Department of Physics, andDepartment of Physics, and

The Institute of Photonic The Institute of Photonic SciencesSciences

with Jens Biegertwith Jens Biegert

IntroductionIntroduction Interested in QT of excited states of Interested in QT of excited states of

molecules – can watch bonds break or molecules – can watch bonds break or evolve in time.evolve in time.

Problems with Quantum Problems with Quantum TomographyTomography

Inner-orbital ionization, or role of Inner-orbital ionization, or role of HOMO-1HOMO-1

Greater variety of orbital symmetriesGreater variety of orbital symmetries – can they be reconstructed? – can they be reconstructed?

g u u g g g

Evidence for inner-orbital Evidence for inner-orbital ionization has been around ionization has been around

for awhilefor awhile Generally hard to detect in ion TOF.Generally hard to detect in ion TOF. Electron spectroscopy on NElectron spectroscopy on N22.. All charge-asymmetric channelsAll charge-asymmetric channels New data on populating A-state in INew data on populating A-state in I22

++

Ionization of B-state to (2,0) Ionization of B-state to (2,0) asymmetric state – even excited asymmetric state – even excited states experience inner-orbital states experience inner-orbital ionization!ionization!

Photo-Photo-electronelectron

SpectroscoSpectrosco

pypyX-state: 4 X-state: 4 photonsphotons

A and B states: A and B states: 5 photons5 photons

[PRL [PRL 6767, 1230 (1991)], 1230 (1991)]

Charge asymmetric Charge asymmetric dissociationdissociation

II224+4+ → I → I2+2+ + I + I2+2+ or I or I3+3+ + I + I1+1+

The branching ratio to the asymmetric The branching ratio to the asymmetric channel can be 20%.channel can be 20%. [PRA [PRA 5858, , 4723, (1998)]4723, (1998)]

II22 potential potential energy energy curvescurvesAsymmetric

channels probably populated through inner-orbital ionization.

II2+2+ pump-probe data pump-probe data

(2,0) vibrational signal(2,0) vibrational signal Amplitude of vibrations so large that Amplitude of vibrations so large that

we can measure changes in KER, we can measure changes in KER, besides the signal strength.besides the signal strength.

[PRA, [PRA, 7575, 063410 (2007)], 063410 (2007)]

Know final state – want to identify Know final state – want to identify intermediate state.intermediate state.

II22 potential potential energy energy curvescurves

What about the What about the dynamics?dynamics? How is the A-state populated?How is the A-state populated?

II22 I I22++ (I (I22

++)* - resonant excitation?)* - resonant excitation?

II22 (I (I22++)* directly – innershell ionization?)* directly – innershell ionization?

No resonant transition from X to A state No resonant transition from X to A state in Iin I22

++..

From polarization From polarization studiesstudies

The A state is only produced with the The A state is only produced with the field field perpendicular to the molecular perpendicular to the molecular axisaxis. This is opposite to most other . This is opposite to most other examples of strong field ionization in examples of strong field ionization in molecules.molecules.

The A state only The A state only ionizes to the (2,0)ionizes to the (2,0) state!?state!?Usually, there is a branching ratio Usually, there is a branching ratio between the (1,1) and (2,0) states, but between the (1,1) and (2,0) states, but what is the orbital structure of (2,0)?what is the orbital structure of (2,0)?

Ionization of A to (2,0) stronger with Ionization of A to (2,0) stronger with parallel polarization.parallel polarization.

Implications for HHG Implications for HHG and QTand QT

We can readily see ionization We can readily see ionization from orbitals besides the HOMO.from orbitals besides the HOMO.

Admixture of HOMO-1 depends Admixture of HOMO-1 depends on angle.on angle.

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.

I2+ spectrum: vibrations in signal strength and kinetic energy release (KER) for different pump pulse wavelength [517nm, 560 nm and 600 nm]

Can ionize from the B state to the (2,0) asymmetric state.

What about orbital What about orbital reconstruction?reconstruction?[PRA [PRA 7878, 033423 (2008)], 033423 (2008)]

Assume that the 3-step model for HHG Assume that the 3-step model for HHG gives us exactly what we want:gives us exactly what we want:

tiacc etVtdtA )()()(

tixiktii

eei ebeeat )(

),( PWaccA

);,();,(

)(

yxyxVdxdye ixik

ei

e

This has the right form for a Radon transformation,allowing tomographic reconstruction.

However, we don’t want:However, we don’t want:

So, we consider the length and velocity gauges:So, we consider the length and velocity gauges:

tilen ettdtA )()()( 2 r

),( PWlenA

);,(

)( 2

yxrdxdye ixik

ei

e

);,();,( yxyxV i

),( PWvelA

);,(

)(

yxdxdye ixik

ei

e

tivel ettdtA )()()(

Length vs. velocity formsLength vs. velocity forms

Using the length form, we recover:Using the length form, we recover:this is useful, because we know this is useful, because we know rr..

Similarly, in the velocity form, we Similarly, in the velocity form, we recover:recover:

This is actually easier to deal with, This is actually easier to deal with, since there is no division by zero, since there is no division by zero, and generally gives better results.and generally gives better results.

);,( yxr i

);,( yxi

Assume two forms are equal:Assume two forms are equal:

Calculate right-hand side and perform Calculate right-hand side and perform inverse Radon transformation to inverse Radon transformation to recover .recover .

);,();,(

);,(~

22 )2/(1

yxyxVdxdye

yxredxdy

ixik

k

ixik

e

ie

e

);,();,(

);,(~

2/1

2

yxyxVdxdye

yxedxdy

ixik

k

ixik

e

ie

e

),(~ yxi

11gg ground state ground state

Radon xforms – parallel Radon xforms – parallel 1s1sgg

Pseudo-radon: accelerationProper-radon: acceleration

Proper-radon: velocityProper-radon: length

11uu – excited state – excited state

Radon xforms – parallel Radon xforms – parallel 1s1suu

Pseudo-radon: accelerationProper-radon: acceleration

Proper-radon: velocityProper-radon: length

Radon xforms – perp. Radon xforms – perp. 1s1suu

Pseudo-radon: accelerationProper-radon: acceleration

Proper-radon: velocityProper-radon: length

11uu – excited state – excited state

11gg – excited state – excited state

ConclusionsConclusions

Velocity form may be better for Velocity form may be better for actual reconstruction of orbitalsactual reconstruction of orbitals

Some symmetries are very hard to Some symmetries are very hard to reconstruct, especially reconstruct, especially gg..

Perpendicular polarization in the Perpendicular polarization in the molecular frame gives the best molecular frame gives the best results.results.

Coordinate systemCoordinate system

Ionization geometryIonization geometry

Ionization geometryIonization geometry