Intense LASER interactions with H2+ and D2+:A Computational Project Ted Cackowski

Project DescriptionAssisting the multiple-body-mechanics group at KSU with calculations of H2+/D2+ behavior under the influence of a short, yet intense laser pulse.

MotivationTo explore the validity of the Axial Recoil ApproximationExploring the quantum mechanics of H2+/D2+ in a time-varying electric field under various experimental conditionsExploring the quantum dynamics there afterward

Modes of OperationSchrdinger's Equation

and the associated quantum mechanicsFortran 90/95

Process Overview

Physical Situation

Scales of Physical InterestLaser Intensity: ~1E14 watts/cm2Pulse Length: ~7E -15 s (femtoseconds)Frequency: 790E-9 m (nanometers)H2/D2 Nuclear Separation: ~3E-10 m (angstroms)

Diatomic HydrogenTwo protons, two electronsBorn-Oppenheimer ApproximationFirst Electrons, then Nuclei

Figure 1

H2+ MoleculeThere are two separate pulses.Ionizing pulse gives us our computational starting pointFranck-Condon Approximation

Figure 2

Note on CompletenessThe Overlap Integral

Where, |FCV|2 are bound/unbound probabilitiesUnavoidable dissociation by ionizationControlled dissociation

MechanicsThe second pulse is the dissociating pulse.We now have the Hamiltonian of interestDipole Approximation

Linear MethodsWe expand Yinitial onto an orthonormal basisOverlap integral / Fouriers trickWe then generate the matrix H as in

Propagate the vector through time using an arsenal of numerical techniques

Data ProductionAfter producing a nuclear wave function associated with a particular dissociation channel, any physical observable can be predicted.Density Plots are probability density plots (*)

Channels

Notable Observables Angular distribution of dissociationas it depends on:Pulse DurationPulse Intensity Carrier Envelope Phase (CEP)

My WorkComputational OversightTwo Fortran ProgramsFirst: Calculate the evolution of the wave function when the Electric field is non-negligibleSecond: Calculate the evolution of the wave function when the Electric field is negligibleProduce measurable numbers

Afore Mentioned Figure

Chart7

4.1422509671

1.2452270279

0.200758006

Pulse Length (Femtoseconds)

Percent Change in

Alignment VS. Pulse DurationFor H2+, CEP Zero, 1E13

Sheet1

MoleculeFWHMIntensityAll TimeCEP(Pi)InitialFinalChange

H2+55.00E+1324500.543309960.60298110.9828724657

5.00E+1320000.54330418510.60265710.9244170198

6.00E+1320000.55387961310.61978611.8990454483

7.00E+1320000.56587947080.63428512.0883567518

8.00E+1320000.5781466730.64993912.4176667137

9.00E+1320000.58934964420.66591912.9921781672

1.00E+14200000.72409736640.80093110.6109533236

1.00E+1424500.598992060.6764112.9247022072

0.25FUTURE WORK

0.5FUTURE WORK

0.75FUTURE WORK

1FUTURE WORK

1.25FUTURE WORK

1.5FUTURE WORK

1.75FUTURE WORK

71.00E+1420000FUTURE WORK

0.25FUTURE WORK

0.5FUTURE WORK

0.75FUTURE WORK

1FUTURE WORK

1.25FUTURE WORK

1.5FUTURE WORK

1.75FUTURE WORK

101.00E+1320000.52321799740.5448914.1422509671

5.00E+1320000.64464414020.71107710.3053538687

5.00E+1340000.64464414020.71107710.3053538687

6.00E+1320000.66603451090.73673210.6146885718

7.00E+1320000.68466848720.75821910.7425000833

8.00E+1320000.70057501970.7758810.7490244761

9.00E+1320000.71357862140.78948210.6370028992

1.00E+1420000.72409736650.80093110.6109533111

451.00E+1320000.63963212790.6475971.2452270279

1351.00E+1320000.68101181430.6823790.200758006

D2+51.00E+14200000.52475105660.60546815.3819496603

0.250.58739704350.6439389.6256794404

0.50.58880563540.6449329.532239707

0.750.59498241220.6504899.3291140433

10.59267184270.6488179.473228401

1.250.59047628680.6468739.5510547027

1.50.58697296430.6434849.6275363875

1.750.59227892390.6472239.2767231579

71.00E+14200000.62461832730.69707511.6001515672

0.250

0.50

0.750.62489009340.69721711.5743404078

10.62535363320.69766111.5626363906

1.250.62409046170.69663711.6243626141

1.50.62305234090.69572511.6639733701

1.750.62387447140.69636211.6189284797

101.00E+1420000.68032699530.75999911.7108398261

Sheet1

Intensity (Watts/(cm^2))

Percent Change in

Alignment VS. Electric Field StrengthFor H2+, 5fs, CEP Zero

Sheet2

Intensity (Watts/(cm^2))

Percent change in

Alignment VS. Electric Field StrengthFor H2+, 10fs, CEP Zero

Sheet3

Pulse Length (Femtoseconds)

Percent Change in

Alignment VS. Pulse DurationFor H2+, CEP Zero, 1E13

Chart3

10.9244170198

11.8990454483

12.0883567518

12.4176667137

12.9921781672

10.6109533236

Intensity (Watts/(cm^2))

Percent Change in

Alignment VS. Electric Field StrengthFor H2+, 5fs, CEP Zero

Sheet1

MoleculeFWHMIntensityAll TimeCEP(Pi)InitialFinalChange

H2+55.00E+1324500.543309960.60298110.9828724657

5.00E+1320000.54330418510.60265710.9244170198

6.00E+1320000.55387961310.61978611.8990454483

7.00E+1320000.56587947080.63428512.0883567518

8.00E+1320000.5781466730.64993912.4176667137

9.00E+1320000.58934964420.66591912.9921781672

1.00E+14200000.72409736640.80093110.6109533236

1.00E+1424500.598992060.6764112.9247022072

0.25FUTURE WORK

0.5FUTURE WORK

0.75FUTURE WORK

1FUTURE WORK

1.25FUTURE WORK

1.5FUTURE WORK

1.75FUTURE WORK

71.00E+1420000FUTURE WORK

0.25FUTURE WORK

0.5FUTURE WORK

0.75FUTURE WORK

1FUTURE WORK

1.25FUTURE WORK

1.5FUTURE WORK

1.75FUTURE WORK

101.00E+1320000.52321799740.5448914.1422509671

5.00E+1320000.64464414020.71107710.3053538687

5.00E+1340000.64464414020.71107710.3053538687

6.00E+1320000.66603451090.73673210.6146885718

7.00E+1320000.68466848720.75821910.7425000833

8.00E+1320000.70057501970.7758810.7490244761

9.00E+1320000.71357862140.78948210.6370028992

1.00E+1420000.72409736650.80093110.6109533111

451.00E+1320000.63963212790.6475971.2452270279

1351.00E+1320000.68101181430.6823790.200758006

D2+51.00E+14200000.52475105660.60546815.3819496603

0.250.58739704350.6439389.6256794404

0.50.58880563540.6449329.532239707

0.750.59498241220.6504899.3291140433

10.59267184270.6488179.473228401

1.250.59047628680.6468739.5510547027

1.50.58697296430.6434849.6275363875

1.750.59227892390.6472239.2767231579

71.00E+14200000.62461832730.69707511.6001515672

0.250

0.50

0.750.62489009340.69721711.5743404078

10.62535363320.69766111.5626363906

1.250.62409046170.69663711.6243626141

1.50.62305234090.69572511.6639733701

1.750.62387447140.69636211.6189284797

101.00E+1420000.68032699530.75999911.7108398261

Sheet1

Intensity (Watts/(cm^2))

Percent Change in

Alignment VS. Electric Field StrengthFor H2+, 5fs, CEP Zero

Sheet2

Sheet3

Chart5

10.3053538687

10.6146885718

10.7425000833

10.7490244761

10.6370028992

10.6109533111

Intensity (Watts/(cm^2))

Percent change in

Alignment VS. Electric Field StrengthFor H2+, 10fs, CEP Zero

Sheet1

MoleculeFWHMIntensityAll TimeCEP(Pi)InitialFinalChange

H2+55.00E+1324500.543309960.60298110.9828724657

5.00E+1320000.54330418510.60265710.9244170198

6.00E+1320000.55387961310.61978611.8990454483

7.00E+1320000.56587947080.63428512.0883567518

8.00E+1320000.5781466730.64993912.4176667137

9.00E+1320000.58934964420.66591912.9921781672

1.00E+14200000.72409736640.80093110.6109533236

1.00E+1424500.598992060.6764112.9247022072

0.25FUTURE WORK

0.5FUTURE WORK

0.75FUTURE WORK

1FUTURE WORK

1.25FUTURE WORK

1.5FUTURE WORK

1.75FUTURE WORK

71.00E+1420000FUTURE WORK

0.25FUTURE WORK

0.5FUTURE WORK

0.75FUTURE WORK

1FUTURE WORK

1.25FUTURE WORK

1.5FUTURE WORK

1.75FUTURE WORK

101.00E+1320000.52321799740.5448914.1422509671

5.00E+1320000.64464414020.71107710.3053538687

5.00E+1340000.64464414020.71107710.3053538687

6.00E+1320000.66603451090.73673210.6146885718

7.00E+1320000.68466848720.75821910.7425000833

8.00E+1320000.70057501970.7758810.7490244761

9.00E+1320000.71357862140.78948210.6370028992

1.00E+1420000.72409736650.80093110.6109533111

451.00E+1320000.63963212790.6475971.2452270279

1351.00E+1320000.68101181430.6823790.200758006

D2+51.00E+14200000.52475105660.60546815.3819496603

0.250.58739704350.6439389.6256794404

0.50.58880563540.6449329.532239707

0.750.59498241220.6504899.3291140433

10.59267184270.6488179.473228401

1.250.59047628680.6468739.5510547027

1.50.58697296430.6434849.6275363875

1.750.59227892390.6472239.2767231579

71.00E+14200000.62461832730.69707511.6001515672

0.250

0.50

0.750.62489009340.69721711.5743404078

10.62535363320.69766111.5626363906

1.250.62409046170.69663711.6243626141

1.50.62305234090.69572511.6639733701

1.750.62387447140.69636211.6189284797

101.00E+1420000.68032699530.75999911.7108398261

Sheet1

Intensity (Watts/(cm^2))

Percent Change in

Alignment VS. Electric Field StrengthFor H2+, 5fs, CEP Zero

Sheet2

Intensity (Watts/(cm^2))

Percent change in

Alignment VS. Electric Field StrengthFor H2+, 10fs, CEP Zero

Sheet3

Chart9

15.3819496603

9.6256794404

9.532239707

9.3291140433

9.473228401

9.5510547027

9.6275363875

9.2767231579

CEP ( Pi )

Percent change in

Alignment VS. Carrier Envelope PhaseFor D2+, 5fs, 1E14

Sheet1

MoleculeFWHMIntensityAll TimeCEP(Pi)InitialFinalChange

H2+55.00E+1324500.543309960.60298110.9828724657

5.00E+1320000.54330418510.60265710.9244170198

6.00E+1320000.55387961310.61978611.8990454483

7.00E+1320000.56587947080.63428512.0883567518

8.00E+1320000.5781466730.64993912.4176667137

9.00E+1320000.58934964420.66591912.9921781672

1.00E+14200000.72409736640.80093110.6109533236

1.00E+1424500.598992060.6764112.9247022072

0.25FUTURE WORK

0.5FUTURE WORK

0.75FUTURE WORK

1FUTURE WORK

1.25FUTURE WORK

1.5FUTURE WORK

1.75FUTURE WORK

71.00E+1420000FUTURE WORK

0.25FUTURE WORK

0.5FUTURE WORK

0.75FUTURE WORK

1FUTURE WORK

1.25FUTURE WORK

1.5FUTURE WORK

1.75FUTURE WORK

101.00E+1320000.52321799740.5448914.1422509671

5.00E+1320000.64464414020.71107710.3053538687

5.00E+1340000.64464414020.71107710.3053538687

6.00E+1320000.66603451090.73673210.6146885718

7.00E+1320000.68466848720.75821910.7425000833

8.00E+1320000.70057501970.7758810.7490244761

9.00E+1320000.71357862140.78948210.6370028992

1.00E+1420000.72409736650.80093110.6109533111

451.00E+1320000.63963212790.6475971.2452270279

1351.00E+1320000.68101181430.6823790.200758006

D2+51.00E+14200000.52475105660.60546815.3819496603

0.250.58739704350.6439389.6256794404

0.50.58880563540.6449329.532239707

0.750.59498241220.6504899.3291140433

10.59267184270.6488179.473228401

1.250.59047628680.6468739.5510547027

1.50.58697296430.6434849.6275363875

1.750.59227892390.6472239.2767231579

71.00E+14200000.62461832730.69707511.6001515672

0.250

0.50

0.750.62489009340.69721711.5743404078

10.62535363320.69766111.5626363906

1.250.62409046170.69663711.6243626141

1.50.62305234090.69572511.6639733701

1.750.62387447140.69636211.6189284797

101.00E+1420000.68032699530.75999911.7108398261

Sheet1

0

0

0

0

0

0

Intensity (Watts/(cm^2))

Percent Change in

Alignment VS. Electric Field StrengthFor H2+, 5fs, CEP Zero

Sheet2

0

0

0

0

0

0

Intensity (Watts/(cm^2))

Percent change in

Alignment VS. Electric Field StrengthFor H2+, 10fs, CEP Zero

Sheet3

0

0

0

Pulse Length (Femtoseconds)

Percent Change in

Alignment VS. Pulse DurationFor H2+, CEP Zero, 1E13

0

0

0

0

0

0

0

0

CEP ( Pi )

Percent change in

Alignment VS. Electric Field StrengthFor D2+, 5fs, 1E14

ConclusionsRotational inertia plays an important rolePulse intensity is criticalFurther analysis will be required for pulse length and CEP

Future WorkSimulate H2+ under various CEP initial conditionsConfidence TestingData Interpretation Connect with JRM affiliates

Special Group ThanksDr. EsryFatima AnisYujun WangJianjun HuaErin Lynch

Special REU ThanksDr. WeaverDr. CorwinParticipantsJane Peterson

BibliographyFigure 1 from Max Planck institute for Quantum Optics website

Figure 2 from Wikipedia, Frank-Condonhttp://images.google.com/imgres?imgurl=http://www.mpq.mpg.de/~haensch/grafik/3DdistributionD.gif&imgrefurl=http://www.mpq.mpg.de/~haensch/htm/Research.htm&h=290&w=420&sz=24&hl=en&start=0&um=1&tbnid=rOBflIUYzSm7xM:&tbnh=86&tbnw=125&prev=/images%3Fq%3DH2%252B%26svnum%3D10%26um%3D1%26hl%3Den%26sa%3DN