Intense LASER interactions with H 2 + and D 2 + : A Computational Project

Intense LASER interactions with H2

+ and D2+:

A Computational Project

Ted Cackowski

Project Description

Assisting the multiple-body-mechanics group at KSU with calculations of H2

+/D2+

behavior under the influence of a short, yet intense laser pulse.

Motivation

To explore the validity of the Axial Recoil Approximation Exploring the quantum mechanics of

H2+/D2

+ in a time-varying electric field under various experimental conditions

Exploring the quantum dynamics there afterward

Modes of Operation

Schrödinger's Equation

and the associated quantum mechanics Fortran 90/95

Process Overview

Physical Situation

Scales of Physical Interest

Laser Intensity: ~1E14 watts/cm2

Pulse Length: ~7E -15 s (femtoseconds) Frequency: 790E-9 m (nanometers) H2/D2 Nuclear Separation:

~3E-10 m (angstroms)

Diatomic Hydrogen

Two protons, two electrons Born-Oppenheimer Approximation

First Electrons, then Nuclei

Figure 1

H2+ Molecule

There are two separate pulses. Ionizing pulse gives us our

computational starting point Franck-Condon Approximation

Figure 2

Note on Completeness

The Overlap Integral

Where, |FCV|2 are bound/unbound probabilities Unavoidable dissociation by ionization Controlled dissociation

Mechanics

The second pulse is the dissociating pulse.

We now have the Hamiltonian of interest Dipole Approximation

Linear Methods

We expand initialonto an orthonormal basis Overlap integral / Fourier’s trick

We then generate the matrix H as in

Propagate the vector through time using an arsenal of numerical techniques

Data Production

After producing a nuclear wave function associated with a particular dissociation channel, any physical observable can be predicted.

“Density Plots” are probability density plots (Ψ*Ψ)

Channels

Notable Observables

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

My Work

Computational Oversight Two Fortran Programs

First: Calculate the evolution of the wave function when the Electric field is non-negligible

Second: Calculate the evolution of the wave function when the Electric field is negligible

Produce measurable numbers

Afore Mentioned Figure

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

0

1

2

3

4

5

0 50 100 150

Pulse Length (Femtoseconds)

Per

cent

Cha

nge

in

<Cos

(thet

a)**

2>

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

1010.5

1111.5

1212.5

1313.5

4.00E+13

5.00E+13

6.00E+13

7.00E+13

8.00E+13

9.00E+13

1.00E+14

1.10E+14

Intensity (Watts/(cm^2))

Per

cent

Cha

nge

in

<Cos

(thet

a)**

2>

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

10.25

10.5

10.75

11

4.00E+13

5.00E+13

6.00E+13

7.00E+13

8.00E+13

9.00E+13

1.00E+14

1.10E+14

Intensity (Watts/(cm^2))

Per

cent

cha

nge

in

<Cos

(thet

a)**

2>

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

89

10111213141516

0 0.5 1 1.5 2

CEP ( Pi )

Per

cent

cha

nge

in

<Cos

(thet

a)**

2>

Conclusions

Rotational inertia plays an important role Pulse intensity is critical Further analysis will be required for

pulse length and CEP

Future Work

Simulate H2+ under various CEP initial

conditions Confidence Testing Data Interpretation Connect with JRM affiliates

Special Group Thanks

Dr. Esry Fatima Anis Yujun Wang Jianjun Hua Erin Lynch

Special REU Thanks

Dr. Weaver Dr. Corwin Participants Jane Peterson

Bibliography

Figure 1 from Max Planck institute for Quantum Optics website

Figure 2 from Wikipedia, “Frank-Condon”

http://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