Grad student: Li Fang Funding : NSF-AMO
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Theoretical and experimental Theoretical and experimental progress towards HHG and progress towards HHG and quantum tomography of excited quantum tomography of excited states of molecules states of molecules Grad Grad student: student: Li Fang Li Fang Funding Funding : : NSF-AMO NSF-AMO July 14, 2009 July 14, 2009 18 18 th th International Laser Physics Workshop International Laser Physics Workshop Barcelona, Spain Barcelona, Spain George N. Gibson George N. Gibson University of University of Connecticut Connecticut Department of Physics, Department of Physics, and and The Institute of The Institute of Photonic Sciences Photonic Sciences with Jens Biegert with Jens Biegert
description
Theoretical and experimental progress towards HHG and quantum tomography of excited states of molecules. George N. Gibson University of Connecticut Department of Physics, and The Institute of Photonic Sciences with Jens Biegert. Grad student: Li Fang Funding : NSF-AMO. July 14, 2009 - PowerPoint PPT Presentation
Transcript of Grad student: Li Fang Funding : NSF-AMO
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
