Quantum Dynamics in Few-Body System
K. Hino and X. M. Tong
Division of Materials and Life Sciences

Oct. 31, 2007

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Outlines¾ Introduction
What we are working onz Why we belong to the Centerz¾ What we have done
Wannier Stark Ladderz Intense Laser-Material Interactionsz¾ What we plan to do
Develop new numerical toolsz Investigate dynamics in few-body system
zOct. 31, 2007

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What we are working on
Study the dynamical processes in few-body system by solving
non-perturbative
perturbative

numerically.
Particles:

nuclei, electrons, photons etc.

Processes:

electrons, atoms, molecules in the external fields
collisions between electrons, ions, atoms, molecules
ionic, atomic, molecular structures (excited states)

Objects:

Understand the processes;
Provide the data;
Control the quantum dynamical processes.

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Why we belong to the Center
Characteristics of the Study:
The number of particles involved is accountable with the finger
z Interactions between the particles are well known
z Most of the dynamical processes cannot be solved analyticallyz

Example: Helium atoms (® + 2 e),e

The transition from quantum to classic physics (~ → 0).
e

To do the simulation, we need a big computer.
To learn things, we have to discuss with our colleagues
Common interests (computation) and common tools (computer)put us together.
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Example I: Wannier-Stark Ladder
WSL energy structure

WSL space structure:Fdc of WSL
Schematic Diagram

n=2

n =1
n=0

n=2Conduction
Static E-Field FBand

Valence Bandn = −1ValenceBandcontinuum

Conduction Bandn = −n2: WSL Index

n=1n=0n=-1n=-23s2s1s

WSL index: ndiscrete
n=-2Quantum Dynamics & Quantum Control

n=-1n=0n=1

WSL index (Channel)

Fano ResonanceOct. 31, 2007

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Linear Optical Response

Absorption Spectra

67Å-GaAs / 17Å-Ga0.7Al0.3As (F=13.3kV/cm)(c) Experimental

Photon Energy (eV)Theory:Experiment:

Oct. 31, 2007

K. Hino and N. Toshima, PRB 71, 205326 (2005).
C. P. Holfeld et al., PRL 81, 874 (1998).

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Quantum Control: DWSL
Schematic Diagram of the DWSL

x10

Fdc + F(t)PATΩIntersite Transition(dc-&ac-ZTs)

Ωl=-2
l=-1

Intrasite Transition(dc-&ac-ZTs)
PAT

Ω
l=0

Ω
Ω

l=1

Quasienergy (Ry)

10

b=2
b=1-3

98
7
6
0

l=2

The energy structure can be controlled by Fac
and measured by a weak probe field.

300

200100Fac (kV/cm)

E: quasienergy calculatedby Floquet theory

K. Hino, X. M. Tong and N. Toshima, PRB, accepted (2007).

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Example II: Laser Material Interactions
V

1. Tunneling Ionization

2. Rescattering

RescatteringzF(t)e’)t(zFeｚ3. Electron-Core Collision

IpStrong, coherent electron beameeeee

Direct ionization

Electron beame

Oct. 31, 2007

conventional
non-coherent• Radiative Rec.
• Ion. or Dis.
• Scatteringrescatteringcoherent(HHG)(Mol. Clock)(Imaging )External Review on Center for Computational Sciences,

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Computational SchemewithVinH0,H(t),τTime

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TD-momentum distribution
Io = 2x1014 W/cm2TD- Space Distribution

λ = 800 nm

TD- Momentum Distribution

X. M. Tong, S. Watahiki, K. Hino and N. Toshima, PRL 99, 093001 (2007).

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Future Plan
Develop a time-dependent Floquet method:
to study atoms, molecules, clusters or semiconductors ina periodic time-dependent external field.

withTime-independent method:a coupled channel eigen-value problem;/ n3Time-dependent method:
propagate the w.f. for one period and dig out the dynamic
information based on the Floquet theory.
/nOct. 31, 2007

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Future Plan
Develop a time-dependent method: to study the photoionizationof many-electron system [DFT + Configuration Interaction (CI)]Interference

Difficulties: too many ionization channels and continuum w.f.
Suggested: Structures calculated by DFT and CI (well developed);
Dynamics investigated by time-dependent method.

Key step:
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the continuum w.f. in the outer region will be absorbed.
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Future Plan
Study capture processes by our newly developed TD-method [1].

Basic research:
Application:formation and properties of anti-material
charge capture processes in astrophysics [2][1] “State-specified protonium formation in low-energy antiproton-hydrogen-atom collisions”,
X. M. Tong, K. Hino, and N. Toshima, PRL 97, 243202 (2006).
[2] “X-ray emission from comets”, T. E. Cravens, Science 296, 1042 (2002)

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Future Plan
Study intense laser material interactions by our TD-method [3].

LaserMaterials

Steer the rescattering wavepacket by tuning laser parameters;
Study the dynamics in the femto-second (10-15s) time scale [4];Study the tomographic imaging of molecular orbitals [5].
[3] “Numerical Observation of the Rescattering Wavepacket in Laser-Atom Interactions”,
X. M. Tong, S. Watahiki, K. Hino and N. Toshima, PRL 99, 093001 (2007).
[4] “X-ray driven femtosecond molecular dynamics”,
E. Gagnon, P. Ranitovic, X. M. Tong, C. L. Cocke et al., Science 317, 1374 (2007).
[5] “Tomographic imaging of molecular orbitals”,
J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin et al., Nature, 432, 867 (2004).

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