Benchmark Calculations for Multi-Photon Ionization of the … · 2012. 9. 5. · Theoretical...

XSEDE-12, Chicago, July 16-20, 2012 Benchmark Calculations for Multi-Photon Ionization of the Hydrogen Molecules . . . Laser Radiation - p. 1/32

Benchmark Calculations for Multi-Photon Ionization of theHydrogen Molecule and the Hydrogen Molecular Ion by

Short-Pulse Intense Laser Radiation

XSEDE-12, ChicagoXiaoxu Guan and Klaus Bartschat

Department of Physics and Astronomy, Drake University, Des Moines, IA

Barry SchneiderOffice of Cyberinfrastructure, National Science Foundations, Arlington, VA

supported by the NSF under PHY-1068140 and XSEDE under PHY-090031

•Overview

Introduction

Motivation

Theoretical Approaches

Double Ionization

One-photon DI at 75 eV

Two-photon DI at 30 eV

Double-slit Interference in H+

2

Progress Toward Moving Nuclei

Summary and Future Plans


Overview

• Introduction to the Interaction of Ultrafast Intense LaserPulses with Matter (Atoms, Molecules, Clusters, Solids,Plasma, etc.)

•Overview

Introduction

Motivation


Double Ionization




2




Overview


• Motivation for Exploring Laser-Driven H2 and H+2

Molecules.

•Overview

Introduction

Motivation


Double Ionization




2




Overview



Molecules.• Algorithms and Computational Details (H2MOL code).

◦ Solving a Four-Body Coulomb Problem (H2) in aTemporal Intense Laser Field

◦ Spatial Discretization of the Problem (FE-DVR)◦ Extraction of Physical Quantities

•Overview

Introduction

Motivation


Double Ionization




2




Overview






• Some Results : Integral Cross Sections and AngularDistributions.◦ One- and Two-photon Double Ionization of H2

◦ Interference Effect of H+2 in X-ray Free Electron Lasers

(FELs)

•Overview

Introduction

Motivation


Double Ionization




2




Overview








(FELs)• Progress Toward Moving Nuclei.

•Overview

Introduction

Motivation


Double Ionization




2




Overview








(FELs)• Progress Toward Moving Nuclei.• Summary and Future Plans

•Overview

Introduction

•Physics at the attosecond

frontier•Ultrafast and Intense Laser

Pulses

Motivation


Double Ionization




2




Physics at the attosecond frontier

females spend a lot of time — tend to overlapwith shipping lanes, and because the energydemands of motherhood exacerbate the ill-effects of any serious injury.

Because there are so few right whales left in the North Atlantic, the US NationalMarine Fisheries Service (NMFS) has alreadyadopted a policy that emphasizes the value of each whale3. Consequently, although the NMFS has not attributed any special significance to mature females, they have interpreted the US Endangered Species Actof 1973 to mean that efforts must be taken to prevent any human-related whale deaths.Indeed, the NMFS initiated an extensivewhale-tracking programme in 1996 to mini-mize such deaths by keeping ships away from sites of whale sightings4. But becausemore than 60% of North Atlantic rightwhales have scars from entanglement in fishing gear, such as lobster pots and sinkgillnets (Fig. 2), environmental groups such as the Sierra Club in Massachusetts arguethat simply alerting ships to the presence of whales does not provide adequate pro-tection5. Moreover, the US Humane Society is currently suing the NMFS over its failure to address entanglement-related deaths, andhas won an initial favourable ruling becausethe NMFS’s current plan to minimize whaledeaths is inadequately specified.

In short, Fujiwara and Caswell’s study1

provides both hope and despair. A popula-tion that was thought by many to be doomedbecause of terribly low numbers can probablybe saved. But the fact that just a few human-induced deaths could tip the balance towardsthe population’s demise exposes a familiarstory: a government agency is charged withcapitulating to a powerful industry, butclaims to be doing all it can. Throughout the world, harvest of endangered species,whether accidental or deliberate, is permittedbecause the measures needed to prevent such deaths — such as closing down lobsterfisheries — are seen as too draconian6. Butaccording to environmental groups such asthe Sierra Club, these extreme measures arenot necessary5. They suggest instead thattechnical improvements in fishery opera-tions may be sufficient, for example usinglighter lines that break more easily whenwhales become entangled.

Population biology and demographicstudies can predict how much better a population would fare if certain numbers of individuals were spared. Unfortunately, it is uncommon in conservation biology6 toget the kind of clarity provided by Fujiwaraand Caswell’s analysis. Conservation oftenmeans protecting individual animals fromdeath caused by human activities. Fujiwaraand Caswell have shown us the importanceof highlighting what might at first glanceseem like insignificant numbers of deaths.Their approach promises to be useful foreverything from grizzly bears to spotted

owls to sockeye salmon — species for whichsimilar mark–recapture data are availableand which have in some places dwindled to such low numbers that saving individuallives could matter.Peter Kareiva is at The Nature Conservancy,217 Pine Street, Seattle, Washington 98101, USA.e-mail: [email protected]. Fujiwara, M. & Caswell, H. Nature 414, 537–541 (2001).2. Hain, J. H. W. USGS Technical Note;

http://biology.usgs.gov/s+t/SNT/noframe/mr183.htm3. Waring, G. T. et al. NOAA Technical Memorandum NMFS-NE-

153 (1999); http://www.nefsc.nmfs.gov/psb/sar1999.pdf 4. http://whale.wheelock.edu/whalenet-stuff/reportsRW_NE5. McCaffrey, J. The Massachusetts Sierran Online 6 (2001);

http://www.sierraclubmass.org/news/news0301/endangered_species.htm

6. Paine, R. T. Report of the Recovery Science Review PanelAugust 27–29, 2001;http://www.nwfsc.noaa.gov/cbd/trt/rsrp.htm

7. http://www.nmfs.noaa.gov/prot_res/PR2/Stock_Assessment_Program

news and views

494 NATURE VOL 414 29 NOVEMBER 2001 www.nature.com

As every photographer knows, a flash oflight can stop the action. Just as a fastflash lamp can freeze the image of a

bullet in mid-flight, so short laser pulses canbe used to probe fast molecular motion. It isno surprise, then, that laser scientists havebeen pushing for ever-shorter pulses of lightin order to follow ever-more rapid processes.The quest has taken us from the first sub-picosecond (1 picosecond is 10–12 s) pulses,more than a generation ago, to the develop-ment of femtosecond optics (1 femtosecondis 10–15 s). These time periods are hard toimagine, but a femtosecond is to a minutewhat a minute is to the age of the Universe.

Femtosecond pulses led to femtochem-istry, the experimental study of fast chemicalreactions and molecular dynamics. Even thefastest molecular vibrations appear com-

pletely still when probed with a pulse lastinga few femtoseconds. Now, we are entering the era of attosecond pulses (1 attosecond is 10–18 s). On page 509 of this issue Hentschelet al. describe1 the generation and use ofpulses lasting 650 attoseconds, in what mightbe the dawn of attophysics — the study of dynamics on timescales fast enough to follow electronic motion within atoms.

The road from picosecond to femto-second light pulses has seen laser technologyevolve towards lasers that emit light withgreater ‘spectral’ width — that is, covering a wider range of wavelengths. A short pulseresults when all the spectral components in the light beam interfere in a way that adds up to a single burst of light. The dura-tion of this pulse is inversely proportional to the spectral width — so a wider spectral

Laser science

Physics at the attosecond frontierYaron SilberbergUltrashort laser pulses allow physicists and chemists to watch fastmolecular motion as it happens. But many fundamental atomic processesare even faster and require the shortest pulses ever created.

Figure 1 Generating and using attosecond laser pulses. In their experiment, Hentschel et al.1 shine anultrashort visible light pulse on a gas of neon atoms to produce higher frequency ‘harmonic’radiation (rainbow-coloured pulses) at ultraviolet and X-ray wavelengths. The visible and harmonicpulses pass together through a zirconium filter, which reduces the train of harmonic pulses to a singleattosecond pulse (1 attosecond is 10 18 s). Both the attosecond pulse and the optical beam are focusedonto the krypton target where they accomplish the very first attosecond measurement. The authorsmonitor the attosecond dynamics of photoelectrons emitted by the krypton gas by varying the delaybetween the attosecond and visible pulses.

Tube ofneon gas

Filter

TimeTime

Kryptontarget

Delay andfocusing

Visible lightfield

Generatedharmonics

Singleattosecondpulse

Time-delayedpulse

Generating and using attosecond laserpulse. In their experiments, Hentschelet al. shine an ultrashort visible lightpulse on a gas of neon atoms to producehigher frequency ‘harmonic’ radiation(rainbow coloured pulses) at ultravioletand X-ray wavelengths. The visibleand harmonics pass together through azirconium filter, which reduces the train ofharmonic pulses to a single attosecond

pulse (1 attosecond is 10−18s). Boththe attosecond pulse and the opticalbeam are focused onto the krypton targetwhere they accomplish the very firstattosecond measurement. The authorsmonitor the attosecond dynamics ofphotoelectrons emitted by the kryptongas by varying the delay between theattosecond and visible pulses.

Yaron Silberberg,Nature 414, 494 (2001)

•Overview

Introduction



Pulses

Motivation


Double Ionization




2




Ultrafast and Intense Laser Pulses

• Interaction of ultrafast intense laser pulse with atoms, molecules, clusters,solids, plasma, etc.

• Photon energy: from X-ray (a few hundred eV) to Infrared (∼ 1 eV) laser.• Peak intensity: from 1013 W/cm2 to 1020 W/cm2.• Time scale: from ∼ 100 femtosecond (fs) to ∼ 10 attosecond (as)

1 fs = 10−15 s; 1 as = 10−18 s

1fs1s

=8 min

age of our universe

•Overview

Introduction



Pulses

Motivation


Double Ionization




2




Ultrafast and Intense Laser Pulses

• Interaction of ultrafast intense laser pulse with atoms, molecules, clusters,solids, plasma, etc.

• Photon energy: from X-ray (a few hundred eV) to Infrared (∼ 1 eV) laser.• Peak intensity: from 1013 W/cm2 to 1020 W/cm2.• Time scale: from ∼ 100 femtosecond (fs) to ∼ 10 attosecond (as)

1 fs = 10−15 s; 1 as = 10−18 s

1fs1s

=8 min

age of our universe(13.7 billion years)

• Comparison of intense laser (800 nm) with sunlight

Intensity Quiver amplitude Ponderomotive energy

Laser 3.51× 1016 W/cm2 163 Å 2169 eV

Sunlight 0.13 W/cm2 3× 10−7 Å 10−14 eV

• Novel phenomena: HHG, ATI, ATD, LIED, CREI, Molecular bond-softeningand bond-hardening, etc.

•Overview

Introduction

Motivation

•Why Is Our Work

Important?•Multiple Ways for Theory to

Help

•The H+

2and D+

2Molecular

Ions•The D2 Molecule


Double Ionization




2




Why Is Our Work Important?

• Theoretical situation:◦ The current theoretical description of the hydrogen atom

(1 electron) in a laser field is very accurate.◦ Much progress has also been made for He (2 electrons).◦ Molecules are much more difficult, due to additional

degrees of freedom (vibration, rotation).

•Overview

Introduction

Motivation

•Why Is Our Work


Help

•The H+

2and D+

2Molecular



Double Ionization




2







degrees of freedom (vibration, rotation).• Experimental situation:

◦ Experiments on H are very difficult (2 H want to be H2).◦ Experiments on He are also very difficult, due to the high

threshold (≈ 80 eV) for double ionization.◦ As a result, many experiments are being performed on

more complex atoms (Ne, Ar) or molecules (H2, N2).◦ Current strong infra-red (IR) or FELs produce complex

output (pulse shape, frequency spectrum, intensity,focus).

◦ As a result, the interpretation of raw experimental data isvery challenging.

•Overview

Introduction

Motivation

•Why Is Our Work


Help

•The H+

2and D+

2Molecular



Double Ionization




2







degrees of freedom (vibration, rotation).• Experimental situation:

◦ Experiments on H are very difficult (2 H want to be H2).◦ Experiments on He are also very difficult, due to the high

threshold (≈ 80 eV) for double ionization.◦ As a result, many experiments are being performed on

more complex atoms (Ne, Ar) or molecules (H2, N2).◦ Current strong infra-red (IR) or FELs produce complex

output (pulse shape, frequency spectrum, intensity,focus).

◦ As a result, the interpretation of raw experimental data isvery challenging.

• H+2 and H2 look like a possibility for common ground.

•Overview

Introduction

Motivation

•Why Is Our Work


Help

•The H+

2and D+

2Molecular



Double Ionization




2




Multiple Ways for Theory to Help

• Provide benchmark results to check experiment (e.g.,characterization of the laser) in cases where theory shouldbe reliable. (Unfortunately, some published results are notcorrect or differences are misinterpreted → examples.)

•Overview

Introduction

Motivation

•Why Is Our Work


Help

•The H+

2and D+

2Molecular



Double Ionization




2






• Predict the interesting part of the parameter space toinvestigate.

•Overview

Introduction

Motivation

•Why Is Our Work


Help

•The H+

2and D+

2Molecular



Double Ionization




2







• Guide experiment by suggesting new effects to study(alignment dependence in molecules, interference due tomultiple nuclei, effect of nuclear motion, ... → examples).

•Overview

Introduction

Motivation

•Why Is Our Work


Help

•The H+

2and D+

2Molecular



Double Ionization




2







• Guide experiment by suggesting new effects to study(alignment dependence in molecules, interference due tomultiple nuclei, effect of nuclear motion, ... → examples).

• Develop schemes for quantum dynamic imaging andquantum control.

•Overview

Introduction

Motivation

•Why Is Our Work


Help

•The H+

2and D+

2Molecular



Double Ionization




2




The H+2 and D+

2 Molecular IonsDissociative Ionization in H+

2 and D+2 (Expt.)

0 1.0 2.0 3.0 4.0 eV

Energy distribution of theneutral and charged frag-ments from the dissociationand Coulomb explosion ofH+

2 . Laser pulse was fo-cused to peak intensity of10

15 W/cm2 with time dura-tion of 130 fs at 785 nm.

Fragmentation from the Coulomb explosion of D+

2 at different pulseduration (τ ) and peak intensity (I).

—D. Pavicic et al., Phys. Rev. Lett. 94, 163002 (2005)

•Overview

Introduction

Motivation

•Why Is Our Work


Help

•The H+

2and D+

2Molecular



Double Ionization




2




The D2 Molecule

Double Photoionization in D2 (expt. & model calc.)

—Y.H. Jiang et al., Phys. Rev. 81, 021401(R) (2010)

•Overview

Introduction

Motivation


•Theoretical Approaches –

H2

(Algorithms and

Computational Details)•Theoretical Approaches

•Theoretical Approaches



Double Ionization




2




Theoretical Approaches – H2

(Algorithms and Computational Details)• Two-electron motion in two-center potential.

•Overview

Introduction

Motivation



H2

(Algorithms and





Double Ionization




2





(Algorithms and Computational Details)• Two-electron motion in two-center potential.• Fixed-nuclei approximation (FNA, i.e., the internuclear

separation R is fixed); Req = 1.4 bohr (about 0.07 nm).

•Overview

Introduction

Motivation



H2

(Algorithms and





Double Ionization




2






separation R is fixed); Req = 1.4 bohr (about 0.07 nm).• Two-center prolate spheroidal coordinates.

•Overview

Introduction

Motivation



H2

(Algorithms and





Double Ionization




2






separation R is fixed); Req = 1.4 bohr (about 0.07 nm).• Two-center prolate spheroidal coordinates.• Finite-Element Discrete Variable Representation (FE-DVR).• Field-free Hamiltonian (ξq, ηq, ϕq, q = 1, 2)

Hq =−2

R2(ξ2q − η2q )

[

∂

∂ξq(ξ2q − 1)

∂

∂ξq+

∂

∂ηq(1− η2q )

∂

∂ηq

+1

(ξ2q − 1)

∂2

∂ϕ2q

+1

(1− η2q )

∂2

∂ϕ2q

]

−4ξq

R(ξ2q − η2q ).

• Time-dependent Schrödinger equation (TDSE):

i∂

∂tΨ(1, 2, t) =

[

H1 +H2 +1

r12+E(t) · (r1 + r2)

]

Ψ(1, 2, t).

•Overview

Introduction

Motivation



H2

(Algorithms and





Double Ionization




2





• How do we discretize the wave function?◦ We expand the wave function for the H2 molecule in the

body-frame as

Ψ(1, 2, t) =∑

m1m2

Πm1m2(ξ1, η1, ξ2, η2, t)Φm1m2

(ϕ1, ϕ2).

Here Φm1m2(ϕ1, ϕ2) = ei(m1ϕ1+m2ϕ2)/(2π) is the angular

function, where m1 and m2 denote the magneticquantum numbers of the two electrons along themolecular axis.

◦ Πm1m2(ξ1, η1, ξ2, η2, t) is expanded in a product of

normalized “radial” {fi(ξ)} and “angular” {gk(η)} DVRbases:

Πm1m2(ξ1, η1, ξ2, η2, t) =

∑

ijkℓ

fi(ξ1)fj(ξ2)gk(η1)gℓ(η2)Cm1m2

ijkℓ (t).

•Overview

Introduction

Motivation



H2

(Algorithms and





Double Ionization




2





• How do we discretize the wave function?◦ We expand the wave function for the H2 molecule in the

body-frame as

Ψ(1, 2, t) =∑

m1m2

Πm1m2(ξ1, η1, ξ2, η2, t)Φm1m2

(ϕ1, ϕ2).

Here Φm1m2(ϕ1, ϕ2) = ei(m1ϕ1+m2ϕ2)/(2π) is the angular

function, where m1 and m2 denote the magneticquantum numbers of the two electrons along themolecular axis.

◦ Πm1m2(ξ1, η1, ξ2, η2, t) is expanded in a product of

normalized “radial” {fi(ξ)} and “angular” {gk(η)} DVRbases:

Πm1m2(ξ1, η1, ξ2, η2, t) =

∑

ijkℓ

fi(ξ1)fj(ξ2)gk(η1)gℓ(η2)Cm1m2

ijkℓ (t).

• Solving the TDSE: i∂C(t)/∂t = H(t)C(t).

•Overview

Introduction

Motivation



H2

(Algorithms and





Double Ionization




2





• How do we solve the TDSE?◦ Propagate over the grids from Ψ(t) to Ψ(t+∆t):

Ψ(t+∆t) ≃ e−iH(t)∆tΨ(t).

◦ Short-time Arnoldi-Lanczos propagator◦ Taylor series propagation (n-th order):

Ψ(t+∆t) ≃n∑

k=0

(−i∆t)k

k!H(t)kΨ(t).

◦ Arnoldi-Lanczos propagation:◦ {Ψ(t), HΨ(t), H2Ψ(t), . . . , HnΨ(t)} → the Krylov

subspace.◦ Gram-Schmidt orthogonalization of these n+1 vectors

yields {Q0, Q1, . . . , Qn} → Q (non-square matrix).◦ h = Q†HQ is a tridiagonal matrix of order n+1.

•Overview

Introduction

Motivation



H2

(Algorithms and





Double Ionization




2





• Arnoldi-Lanczos propagation (cont.)◦ Ψ(t+∆t) ≃ Qe−ih∆tQ†Ψ(t).◦ Advantages of Arnoldi-Lanczos propagator:

◦ A unitary propagator accurate up to (∆t)n;◦ n is very small compared to the order of H;◦ Computational overhead is linearly dependent on n;◦ Parallelization through matrix-vector multiplication . . .

Comp. Phys. Commun. 180, 2401 (2009)(Fortran 90 + OpenMP).

Computer Physics Communications 180 (2009) 2401–2409

Contents lists available at ScienceDirect

Computer Physics Communications

www.elsevier.com/locate/cpc

40th Anniversary Issue

ALTDSE: An Arnoldi–Lanczos program to solve the time-dependent

Schrödinger equation✩

Xiaoxu Guan a, C.J. Noble a,1, O. Zatsarinny a, K. Bartschat a,∗, B.I. Schneider b

a Department of Physics and Astronomy, Drake University, Des Moines, IA 50311, USAb Physics Division, National Science Foundation, Arlington, VA 22230, USA

•Overview

Introduction

Motivation



H2

(Algorithms and





Double Ionization




2





• FE-DVR bases (even m, for example):

fi(ξ) = Πn6=i

ξ − ξnξi − ξn

and gk(η) = Πn6=k

η − ηnηk − ηn

ξ

fi(ξ)

139531

1.2

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

η

gk(η)

1.00.50.0-0.5-1.0

1.0

0.5

0.0

-0.5

-1.0

•Overview

Introduction

Motivation



H2

(Algorithms and





Double Ionization




2






fi(ξ) = Πn6=i


and gk(η) = Πn6=k


ξ

fi(ξ)

139531

1.2

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

η

gk(η)

1.00.50.0-0.5-1.0

1.0

0.5

0.0

-0.5

-1.0

• Gauss-quadratures are used to calculate the matrixelements of H (large but sparse).

•Overview

Introduction

Motivation



H2

(Algorithms and





Double Ionization




2






fi(ξ) = Πn6=i


and gk(η) = Πn6=k


ξ

fi(ξ)

139531

1.2

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

η

gk(η)

1.00.50.0-0.5-1.0

1.0

0.5

0.0

-0.5

-1.0


• Diagonal representation of all potentials with respect toDVR bases.

•Overview

Introduction

Motivation



H2

(Algorithms and





Double Ionization




2






fi(ξ) = Πn6=i


and gk(η) = Πn6=k


ξ

fi(ξ)

139531

1.2

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

η

gk(η)

1.00.50.0-0.5-1.0

1.0

0.5

0.0

-0.5

-1.0


• Diagonal representation of all potentials with respect toDVR bases.

• Block structure – vital for massively parallel machines.

•Overview

Introduction

Motivation


Double Ionization

•Double Ionization (DI) in

Laboratory Frame•Time Scaling of the Code




2




Double Ionization (DI) in Laboratory Frame

• H2 + ~ω0 → p+ p+ e−(k1) + e−(k2) (One-photon DI).

•Overview

Introduction

Motivation


Double Ionization






2





• H2 + ~ω0 → p+ p+ e−(k1) + e−(k2) (One-photon DI).• H2 + 2~ω0 → p+ p+ e−(k1) + e−(k2) (Two-photon DI).

•Overview

Introduction

Motivation


Double Ionization






2





• H2 + ~ω0 → p+ p+ e−(k1) + e−(k2) (One-photon DI).• H2 + 2~ω0 → p+ p+ e−(k1) + e−(k2) (Two-photon DI).• Coplanar geometry: molecular axis (ζ), linearly polarized

laser (ǫ), and ejection directions of photoelectrons (k1, k2).

ζ

θN

k1

θ2

k2

ǫ

ζ

θNθ1

k1

θ2

k2

ǫ

•Overview

Introduction

Motivation


Double Ionization






2





• H2 + ~ω0 → p+ p+ e−(k1) + e−(k2) (One-photon DI).• H2 + 2~ω0 → p+ p+ e−(k1) + e−(k2) (Two-photon DI).• Coplanar geometry: molecular axis (ζ), linearly polarized

laser (ǫ), and ejection directions of photoelectrons (k1, k2).

ζ

θN

k1

θ2

k2

ǫ

ζ

θNθ1

k1

θ2

k2

ǫ

• All angles are measured with respect to the direction oflaser polarization vector (ǫ).

•Overview

Introduction

Motivation


Double Ionization






2




Time Scaling of the Code

• The order of the Hamiltonian matrix is ∼ 108 − 109.

▲�✁✂✄☎✆✝ ✭✞❆❈❈✟

❑✝✆✠✂✁ ✭✡☛❈☞✟

✡◆✌❜✂✝ �♦ ❝�✝✂✄ ✭✍✁ ◆✁✍☎✄ �♦ ✶✎✎✎✟

❲❛✏

✏✑✒✓

✔✕

♥✖✗

✖✘✙✖

✚✔✛

✜✢✖✣

✚✤

✹✸✷✶✎

✷✎✎✶✥✎

✶✎✎✥✎

✎

•Overview

Introduction

Motivation


Double Ionization






2





• The order of the Hamiltonian matrix is ∼ 108 − 109.• 2D decomposition on (ξ1, ξ2) plane.

▲�✁✂✄☎✆✝ ✭✞❆❈❈✟

❑✝✆✠✂✁ ✭✡☛❈☞✟

✡◆✌❜✂✝ �♦ ❝�✝✂✄ ✭✍✁ ◆✁✍☎✄ �♦ ✶✎✎✎✟

❲❛✏

✏✑✒✓

✔✕

♥✖✗

✖✘✙✖

✚✔✛

✜✢✖✣

✚✤

✹✸✷✶✎

✷✎✎✶✥✎

✶✎✎✥✎

✎

•Overview

Introduction

Motivation


Double Ionization






2





• The order of the Hamiltonian matrix is ∼ 108 − 109.• 2D decomposition on (ξ1, ξ2) plane.• Time scaling of the code H2MOL: Kraken (NICS) and

Lonestar (TACC).

▲�✁✂✄☎✆✝ ✭✞❆❈❈✟

❑✝✆✠✂✁ ✭✡☛❈☞✟

✡◆✌❜✂✝ �♦ ❝�✝✂✄ ✭✍✁ ◆✁✍☎✄ �♦ ✶✎✎✎✟

❲❛✏

✏✑✒✓

✔✕

♥✖✗

✖✘✙✖

✚✔✛

✜✢✖✣

✚✤

✹✸✷✶✎

✷✎✎✶✥✎

✶✎✎✥✎

✎

•Overview

Introduction

Motivation


Double Ionization


•One-photon DI at 75 eV





2




One-photon DI at 75 eV• H2 + ~ω0 → p+ p+ e−(k1) + e−(k2)

• Expt.: PRL 96, 153002 (2006).• Theory: PRA 82, 023423 (2010) [prolate ECS] and PRA

74, 052702 (2006) [spherical ECS].

(d)

θN

= 0oθN

=30o

(c)

θN

= 60o

θ1

= 0o

(b)

θN

= 90o

(a)

ε 0 60 120 180 240 300 3600

2

4

TD

CS

(b

/sr2

eV)

present

ref. 9

(present) X 1.34

0 60 120 180 240 300 360θ

2 (deg)

0

0.5

1

1.5

2

2.5

TD

CS

(b

/sr2

eV)

present

ref. 9

(present) X 1.34

θN

=90o

θN

=30o

•Overview

Introduction

Motivation


Double Ionization







2




One-photon DI at 75 eV• Equal energy sharing (E1 = E2 = 11.8 eV) for θ1 = 0◦.

•Overview

Introduction

Motivation


Double Ionization







2




One-photon DI at 75 eV• Equal energy sharing (E1 = E2 = 11.8 eV) for θ1 = 0◦.• PRA 82, 023423 (2010) [prolate ECS], PRA 74, 052702

(2006) [spherical ECS], PRL 98, 153001 (2007) [revisedTDCC].

spherical TDCCspherical ECS

prolate ECSpresent work

(a)θ1 = 0◦

θN = 90◦

θ2 (deg)

TD

CS

(b/s

r2eV

)

360300240180120600

4

3

2

1

0

(b)θ1 = 0◦

θN = 60◦

θ2 (deg)

TD

CS

(b/s

r2eV

)

360300240180120600

6

5

4

3

2

1

0

(c)θ1 = 0◦

θN = 30◦

θ2 (deg)

TD

CS

(b/s

r2eV

)

360300240180120600

2.5

2.0

1.5

1.0

0.5

0.0

(d)θ1 = 0◦

θN = 0◦

θ2 (deg)

TD

CS

(b/s

r2eV

)

360300240180120600

0.2

0.1

0.0

ζ

θN

k1

θ2

k2

ε

•Overview

Introduction

Motivation


Double Ionization







2








(a)θ1 = 0◦

θN = 90◦

θ2 (deg)

TD

CS

(b/s

r2eV

)

360300240180120600

4

3

2

1

0

(b)θ1 = 0◦

θN = 60◦

θ2 (deg)

TD

CS

(b/s

r2eV

)

360300240180120600

6

5

4

3

2

1

0

(c)θ1 = 0◦

θN = 30◦

θ2 (deg)

TD

CS

(b/s

r2eV

)

360300240180120600

2.5

2.0

1.5

1.0

0.5

0.0

(d)θ1 = 0◦

θN = 0◦

θ2 (deg)

TD

CS

(b/s

r2eV

)

360300240180120600

0.2

0.1

0.0

ζ

θN

k1

θ2

k2

ε

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Prolate ECS results are about 25% lower than ours !!!

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??

•Overview

Introduction

Motivation


Double Ionization







2








(a)θ1 = 0◦

θN = 90◦

θ2 (deg)

TD

CS

(b/s

r2eV

)

360300240180120600

4

3

2

1

0

(b)θ1 = 0◦

θN = 60◦

θ2 (deg)

TD

CS

(b/s

r2eV

)

360300240180120600

6

5

4

3

2

1

0

(c)θ1 = 0◦

θN = 30◦

θ2 (deg)

TD

CS

(b/s

r2eV

)

360300240180120600

2.5

2.0

1.5

1.0

0.5

0.0

(d)θ1 = 0◦

θN = 0◦

θ2 (deg)

TD

CS

(b/s

r2eV

)

360300240180120600

0.2

0.1

0.0

ζ

θN

k1

θ2

k2

ε

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Prolate ECS results are about 25% lower than ours !!!

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??

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now resolved in favor of our results

•Overview

Introduction

Motivation


Double Ionization



•Two-photon DI at 30 eV


•Two-photon DI at 26 - 33

eV•Two-photon DI at 30 eV







2





• H2 + 2~ω0 → p+ p+ e−(k1) + e−(k2)

•Overview

Introduction

Motivation


Double Ionization













2





• H2 + 2~ω0 → p+ p+ e−(k1) + e−(k2)

• Non-sequential (direct) double ionization

•Overview

Introduction

Motivation


Double Ionization













2





• H2 + 2~ω0 → p+ p+ e−(k1) + e−(k2)

• Non-sequential (direct) double ionization• How do the two photoelectrons share the excess energy?

(a) parallel geometry (b) perpendicular geometry

E1 (eV)

E2

(eV

)

15

15

10

10

5

50

00.0

0.5

1.0

1.5

2.0

2.5

(a)

E1 (eV)

E2

(eV

)

25

20

15

15

1510

10

105

5

5

00

0

(b)

◦ Sine-squared laser pulse of I0 = 1014 W/cm2 and 10optical cycles.

◦ The color bars are in units of 10−7 eV−2.

•Overview

Introduction

Motivation


Double Ionization













2





• Total integral cross section (σtot):

σtot =(ω0

I0

)2( 1

Teff

)xdE1dE2

( d2P

dE1dE2

)

◦ Time-independent ECS:σ‖tot = 6.68× 10−53 cm4s; σ⊥

tot = 5.76× 10−52 cm4sTime-dependent TDCC:

σ‖tot = 1.7× 10−53 cm4s; σ⊥

tot = 4.7× 10−52 cm4sTime-dependent FE-DVR:

σ‖tot = 2.25× 10−53 cm4s; σ⊥

tot = 2.63× 10−52 cm4s

•Overview

Introduction

Motivation


Double Ionization













2






σtot =(ω0

I0

)2( 1

Teff

)xdE1dE2

( d2P

dE1dE2

)



σ‖tot = 1.7× 10−53 cm4s; σ⊥


σ‖tot = 2.25× 10−53 cm4s; σ⊥

tot = 2.63× 10−52 cm4s• Time-dependent and time-independent results may not be

directly comparable with each other due to autoionizingstates and finite energy resolution!

•Overview

Introduction

Motivation


Double Ionization













2






σtot =(ω0

I0

)2( 1

Teff

)xdE1dE2

( d2P

dE1dE2

)



σ‖tot = 1.7× 10−53 cm4s; σ⊥


σ‖tot = 2.25× 10−53 cm4s; σ⊥



• If we use the same (or at least similar) laser parameters,what happens when we compare our time-dependentFE-DVR and time-dependent results?

•Overview

Introduction

Motivation


Double Ionization













2






σtot =(ω0

I0

)2( 1

Teff

)xdE1dE2

( d2P

dE1dE2

)



σ‖tot = 1.7× 10−53 cm4s; σ⊥


σ‖tot = 2.25× 10−53 cm4s; σ⊥



• If we use the same (or at least similar) laser parameters,what happens when we compare our time-dependentFE-DVR and time-dependent results?

• Other independent calculations are needed!

•Overview

Introduction

Motivation


Double Ionization













2




Two-photon DI at 26 - 33 eV

• Total integral cross section (σtot).

•Overview

Introduction

Motivation


Double Ionization













2





• Total integral cross section (σtot).• Simonsen et al. PRA 85, 063404 (2012).

� Ref.[51]: Guan et al., Phys. Rev. A 84, 033403 (2011).H Ref.[34]: Colgan et al., J. Phys. B 41, 0121002 (2008). Ref.[50]: Morales et al., J. Phys. B 42, 0134013 (2009).

•Overview

Introduction

Motivation


Double Ionization













2





• Total integral cross section (σtot).• Simonsen et al. PRA 85, 063404 (2012).

� Ref.[51]: Guan et al., Phys. Rev. A 84, 033403 (2011).H Ref.[34]: Colgan et al., J. Phys. B 41, 0121002 (2008). Ref.[50]: Morales et al., J. Phys. B 42, 0134013 (2009).

• Excellent agreement between our results and those ofSimonsen et al. in both parallel and perpendiculargeometries.

•Overview

Introduction

Motivation


Double Ionization













2





• Angular distributions in the parallel geometry:

TDCC (×2)ECS (/2)FE-DVR

(a)

θ1 = 0◦

θ2 (deg)

TD

CS

(10−

55cm

4s/

sr2

eV)

360300240180120600

2

1

0

(b)

θ1 = 30◦

θ2 (deg)

TD

CS

(10−

55cm

4s/

sr2

eV)

360300240180120600

2

1

0

(c)

θ1 = 60◦

θ2 (deg)

TD

CS

(10−

55cm

4s/

sr2

eV)

360300240180120600

1.5

1.0

0.5

0.0

(d)

θ1 = 90◦

θ2 (deg)T

DC

S(1

0−55

cm4

s/sr

2eV

)360300240180120600

0.2

0.1

0.0

JPB 41, 121002 (2008) [TDCC], JPB 42, 134013 (2009) [ECS],and PRA 84, 041404(R) (2010) [FE-DVR].

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Note the scale factors! ECS x 0.5; TDCC x 2.0 !!!

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?

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?

•Overview

Introduction

Motivation


Double Ionization













2





• Angular distributions in the perpendicular geometry:

(a)

θ1 = 0◦

θ2 (deg)

TD

CS

(10−

55cm

4s/

sr2

eV)

360300240180120600

60

50

40

30

20

10

0

(b)

θ1 = 30◦

θ2 (deg)

TD

CS

(10−

55cm

4s/

sr2

eV)

360300240180120600

40

30

20

10

0

(c)

θ1 = 60◦

θ2 (deg)

TD

CS

(10−

55cm

4s/

sr2

eV)

360300240180120600

10

8

6

4

2

0

(d)

θ1 = 90◦

θ2 (deg)T

DC

S(1

0−55

cm4

s/sr

2eV

)360300240180120600

1.0

0.8

0.6

0.4

0.2

0.0

JPB 41, 121002 (2008) [TDCC], JPB 42, 134013 (2009) [ECS],and PRA 84, 041404(R) (2010) [FE-DVR].

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No scale factors, but BIG DISCREPANCIES for small TDCS!

•Overview

Introduction

Motivation


Double Ionization













2





• Alignment effect in angular distributions: θ1 = 60◦

k1

θN = 0◦ (×6) θN = 10◦ (×6) θN = 30◦ (×5)

θN = 50◦ (×3) θN = 70◦ (×2) θN = 90◦

X. Guan et al., PRA 84, 033403 (2011)

ζ

θN

θ1

k1

θ2

k2

ε

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Study New Physics with Reliable Code

•Overview

Introduction

Motivation


Double Ionization













2





• Alignment effect in angular distributions: θ1 = 90◦

k1

\ θN = 0◦ (×20) \ θN = 10◦ (×8) \ θN = 30◦ (×2.5)

\ θN = 50◦ \ θN = 70◦ \ θN = 90◦ (×3)

X. Guan et al., PRA 84, 033403 (2011)

ζ

θN

θ1

k1

θ2

k2

ε

•Overview

Introduction

Motivation


Double Ionization













2





• What is the difference between H2 and He?

H2 θN = 90◦H2 θN = 60◦H2 θN = 30◦H2 θN = 0◦

12

He

ǫ

(a) θ1 = 0◦

8

(b) θ1 = 30◦

1.5

(c) θ1 = 60◦

0.3

(d) θ1 = 90◦

X. Guan et al., PRA 84, 033403 (2011)

•Overview

Introduction

Motivation


Double Ionization













2





• What is the difference between H2 and He?

H2 θN = 90◦H2 θN = 60◦H2 θN = 30◦H2 θN = 0◦

12

He

ǫ

(a) θ1 = 0◦

8

(b) θ1 = 30◦

1.5

(c) θ1 = 60◦

0.3

(d) θ1 = 90◦

◦ The H2 molecule:

Σg

‖//

⊥ ❇

❇

❇

❇

❇

❇

❇

❇

Σu

‖//

⊥

!!❈

❈

❈

❈

❈

❈

❈

❈

Σg

Πu

‖//

⊥!!❈

❈

❈

❈

❈

❈

❈

❈

Πg

Σg ,∆g

◦ The He atom:Se

→ P o→ (Se, De)

X. Guan et al., PRA 84, 033403 (2011)

•Overview

Introduction

Motivation


Double Ionization




2

• Interference Effect of H+

2in

FELs•Quantum Imaging of H+

2in

FELs




Interference Effect of H+2 in FELs

~ω0 = 500 eV

4.8

4.6

4.4

4.2

4.0

3.8

3.6

3.4

3.2

3.0

2.8

2.6

2.4

2.2

2.0

1.8

1.6

1.4

1.2

1.0

~ω0 = 400 eV

4.8

4.6

4.4

4.2

4.0

3.8

3.6

3.4

3.2

3.0

2.8

2.6

2.4

2.2

2.0

1.8

1.6

1.4

1.2

1.0

Double-slit interferencebehavior of H+

2in the

parallel geometry. Theinternuclear separationdistance R ranges from1.0 to 4.8 bohr. Weobserve the dynamicallyforbidden mode (orconfinement effect)in contrast to beinggeometrically forbiddenby a selection rule. Theangular distributions inthe parallel geometrydo show similarity tothe classical double-slitinterference, but alsonoticeable differences.

X. Guan et al., PRA85, 043419 (2012)

•Overview

Introduction

Motivation


Double Ionization




2

• Interference Effect of H+

2in

FELs•Quantum Imaging of H+

2in

FELs




Quantum Imaging of H+2 in FELs

• Parallel geometry.• ~ω0 = 300 eV, 20 o.c., and I0 = 1016 W/cm2.• dP/dk is in units of 10−6 per momentum in a.u.

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•Overview

Introduction

Motivation


Double Ionization




2


•Progress Toward Moving

Nuclear Effect in H+

2



Progress Toward Moving Nuclear Effect in H+2

• How do the nuclei and photoelectron share the excessenergy?

•Overview

Introduction

Motivation


Double Ionization




2




2





• One-photon (in units of 10−3) Two-photon (in units of 10−5)(1.84 a.u., 1014W/cm2, 6 o.c.) (0.80 a.u., 1013W/cm2, 10 o.c.)

ǫele (a.u.)

Eµ

(a.u

.)

3

2

1

0

0.0 0.5 1.0 1.5

0.0

0.2

0.4

0.6

0.8

1.0

ǫele (a.u.)

Eµ

(a.u

.)

4

3

2

1

00.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

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•Overview

Introduction

Motivation


Double Ionization




2




2





• One-photon (in units of 10−3) Two-photon (in units of 10−5)(1.84 a.u., 1014W/cm2, 6 o.c.) (0.80 a.u., 1013W/cm2, 10 o.c.)

ǫele (a.u.)

Eµ

(a.u

.)

3

2

1

0

0.0 0.5 1.0 1.5

0.0

0.2

0.4

0.6

0.8

1.0

ǫele (a.u.)

Eµ

(a.u

.)

4

3

2

1

00.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

• Single-electron molecule: dissociative ionization →Coulomb explosion.

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•Overview

Introduction

Motivation


Double Ionization




2



•Summary and Future

Plans•



• We use the XSEDE supercomputer facilities to investigatethe double photoionization of laser-driven H2 molecules inultrafast time domain. Example Results for:◦ One-photon DI at 75 eV.◦ Two-photon DI at 30 eV.

•Overview

Introduction

Motivation


Double Ionization




2




Plans•



• We use the XSEDE supercomputer facilities to investigatethe double photoionization of laser-driven H2 molecules inultrafast time domain. Example Results for:◦ One-photon DI at 75 eV.◦ Two-photon DI at 30 eV.

• Future Studies:◦ Effects of doubly excited states in H2 on cross section.◦ Non-sequential double photoionization.◦ Go beyond the fixed-nuclei approximation.◦ Go beyond the Born-Oppenheimer approximation.◦ Effect of moving nuclei on cross sections for multiphoton

ionization (start with H+2 ; then H2).

◦ Further improve the computer codes by using graphicalprocessing units (GPUs) for additional speedup.

•Overview

Introduction

Motivation


Double Ionization




2




Plans•


We gratefullyacknowledge support

from XSEDE!

Thank You for YourAttention!

Benchmark Calculations for Multi-Photon Ionization of the … · 2012. 9. 5. · Theoretical...

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Transcript of Benchmark Calculations for Multi-Photon Ionization of the … · 2012. 9. 5. · Theoretical...