Upload
hailee-bull
View
216
Download
0
Tags:
Embed Size (px)
Citation preview
Attosecond Flashes of Light
– Illuminating electronic quantum dynamics –
XXIIIrd Heidelberg Graduate DaysLecture Series
Thomas PfeiferInterAtto Research GroupMPI – Kernphysik, Heidelberg
Contents
Basics of short pulses and general concepts
Attosecond pulse generationMechanics of Electrons
single electronsin strong laser fields
Attosecond Experiments with isolated Atoms
Multi-Particle SystemsMoleculesmulti-electron dynamics (correlation)
Attosecond experiments with molecules / multiple electrons
Ultrafast Quantum Controlof electrons, atoms, molecules
Novel Directions/ApplicationsTechnology
Contents
Basics of short pulses and general concepts
Attosecond pulse generationMechanics of Electrons
single electronsin strong laser fields
Attosecond Experiments with isolated Atoms
Multi-Particle SystemsMoleculesmulti-electron dynamics (correlation)
Attosecond experiments with molecules / multiple electrons
Ultrafast Quantum Controlof electrons, atoms, molecules
Novel Directions/ApplicationsTechnology
Ultrashort Pulses
1000000000000000
power = work
time
Observation of fast processes concentration of energy in time and space
1 fs = 10-15
s
Ref: Ulrich Weichmann, Department of Physics, Wuerzburg University
Short Pulses Intense Laser Fields
femtosecondlaser pulse
Plasma
e-
e- e-e-
X+
e-
X+
X+ X+X+
Power = EnergyTime
100 J5 fs
= = 20 GW
20 GW(100 m)2
= 2 1016 Wcm2
relativistic effects above 1018W/cm2
Attosecond pulse generation
detector/experiment
atomic medium
femtosecondlaser pulse
also known as: High-Order Harmonic Generation
laser intensity:>1014 W/cm2
attosecondx-ray pulse
mechanism based on:sub-optical-cycle electron acceleration
(laboratory-scale table-top)
High-(order) harmonic generationfirst signs
McPherson et al. J. Opt. Soc. Am. B 21, 595 (1987)intensity: 1015-1016 W/cm2
wavelength: 248 nmpulse duration: 1 ps
High-(order) harmonic generationfirst signsM. Ferray, A. L’Huillier et al. J. Phys. B 21, L31 (1988)
intensity: ~1013 W/cm2
wavelength: 1064 nmpulse duration: 1 ps
in Xenon (Xe)H3
H5H7H9H11
H15
H13
80 fs800 nm5·1014 W/cm2
1 kHz
Zr + Parylene-N filter
in Neon (Ne)
80 fs800 nm3·1014 W/cm2
1 kHz
High-harmonic generation (HHG)
Contents TodayAttosecond Pulses
Classical and quantum mechanics of electronsand experiments with isolated atoms
- Classical Motion of Electronsdefinition of important quantities
- Quantum Mechanics· Electron dynamics in (intense) laser fields· Ionization
- High-harmonic generation: quantum mechanical view
- Experiments with attosecond Pulses
- Quantum state interferometry
Forces on Electrons in Atoms
e-F
E(t)Intensity I ~ 1015 W/cm2
Force F = 14 nNMass me= 9.1∙10-31 kgacc. a = 1.5∙1022 m/s2
velocity v = 3 ∙106 m/s = 1% c (speed of light)
“assumed constant acceleration from restfor 200 attoseconds”
2000 as
optical light wave
E(t)
1 attosecond (1 as = 10-18 s) compares to 1 secondas 1 second compares to more than the age of the universe (~15 Billion years)
Electron in Laser Field
E(t)=E0cos(t)
a(t)= -eE0cos(t)
v(t)= - sin(t)eE0
x(t)= cos(t)eE0
linearly polarized along x axis
acceleration
velocity (dt a)
position (dt v)
ponderomotive potential
ponderomotive radius
Up=Ekin,av= e2E0
2
4m
ap= x0 = eE0
= I29.33 eVm1014 W/cm2
High-(order) harmonic generationfirst signsM. Ferray, A. L’Huillier et al. J. Phys. B 21, L31 (1988)
intensity: ~1013 W/cm2
wavelength: 1064 nmpulse duration: 1 ps
High-(order) harmonic generationfirst signsM. Ferray, A. L’Huillier et al. J. Phys. B 21, L31 (1988)
intensity: ~1013 W/cm2
wavelength: 1064 nmpulse duration: 1 ps
H3
H5H7H9H11
H15
H13
High-harmonic generation
P. Corkum, Phys. Rev. Lett. 71, 1994 (1993)
Hentschel et al. (Krausz group) Nature 414, 509 (2001)
Isolated Attosecond-pulse production
high-passfilter
(the conventional method)
Hentschel et al. (Krausz group) Nature 414, 509 (2001)
“cos pulse”
“sin pulse”
Absolute Phase (CEP) effects
5 10 15 20 25 30 35 400.0
0.1
0.2
0.3
0.4
0.5
0.6
Tra
nsm
issi
on
wavelength [nm]
400 nm Al 400 nm Zr
CEP CEP
~ 6 femtosecond CEP (Absolute phase) stabilized laser pulse
Baltuška et al. Nature 421, 611 (2003)
10 11 12 13 14 150
200
400
600
800120 110 100 90
photon energy [eV]
HH77spe
ctra
l in
ten
sity
[a
rb.u
.]
wavelength [nm]
HH51
6-fs IR pulseCEP stabilized
Iris
Splitmirror
Filter onpellicle
CCD
Metalfilter
XUV grating
X-rayCCD
High-harmonicgeneration
Velocity-Map imagingof electrons or ions
piezoMCP
Piezo-controlledsplit mirror
Time-of-Flight Detectionof electrons
Attosecond Beamline at Berkeley
Mo/Si multilayer mirror
86 88 90 92 94 96 98 1000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.855 57 59 61 63
Harmonic order (800 nm fundamental)
p-polarized
s-polarized
Ref
lect
ivity
photon energy (eV)
86 88 90 92 94 96 98 1000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.855 57 59 61 63
Harmonic order (800 nm fundamental)
Ref
lect
ivity
photon energy (eV)86 88 90 92 94 96 98 100
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.855 57 59 61 63
Harmonic order (800 nm fundamental)
10 Layers
20 Layers
40 Layers
Ref
lect
ivity
photon energy (eV)
6-fs IR pulseCEP stabilized
Iris
Splitmirror
Filter onpellicle
CCD
Metalfilter
XUV grating
X-rayCCD
High-harmonicgeneration
Velocity-Map imagingof electrons or ions
piezoMCP
Piezo-controlledsplit mirror
Time-of-Flight Detectionof electrons
Attosecond Beamline at Berkeley
Short pulse measurement“to measure a fast event, you need an at least equally fast probe”
- Autocorrelation‘Auto...’ -> self...
- Frequency-Resolved Optical GatingFROG, building upon Autocorrelation
- Temporal Analysis by Dispersing a Pair Of Light Electric FieldsTADPOLE
- Spectral Interferometry for Direct Electric Field ReconstructionSPIDER, building upon TADPOLE
Attosecond autocorrelation measurementsisolated pulses
Sekikawa et al.(Watanabe)Nature 432, 605 (2004)
Attosecond autocorrelation measurementspulse trains
Tzallas et al.(Witte, Tsakiris)Nature 426, 267 (2003)
FROG idea
Ref: http://www.physics.gatech.edu/frog/
measure spectrum asa function of time delay
2-dim. data sets: ‘FROG-trace’
analysis by iterative algorithm
D. J. Kane and R. Trebino, Opt. Lett. 18, 823 (1993)
high-harmonic generationintense laser field acting on single atom
probability distribution p(x,y)=|(x,y)|2 for the electronic wavefunction
laser polarization
Time-dependent quantum mechanicsposition and momentum space representation
),(exp),(),( ttitat rkrrr
),(~exp),(~),(
~tititat pr
ppp
~~ ~
Ionization
Strong electric field(Tunneling)
Photoelectric effect(direct transition)
1st order perturbation theory
t
tietEtdta )(1
10)(~)(
|1>
|0>
tunneling rate
ttEmU
tEw
c etda))((2
))((
~
w: barrier width
U: barrier height
Electron in Laser Field
E(t)=E0cos(t)
a(t)= -eE0cos(t)
v(t)= - sin(t)eE0
x(t)= cos(t)eE0
linearly polarized along x axis
acceleration
velocity (dt a)
position (dt v)
ponderomotive potential
ponderomotive radius
Up=Ekin,av= e2E0
2
4m
ap= x0 = eE0
= I29.33 eVm1014 W/cm2
Electron in Laser Field
E(t)=E0cos(t)
a(t)= -eE0cos(t)
v(t)= - sin(t)eE0
linearly polarized along x axis
acceleration
velocity (dt a)
Vector potential (Coulomb gauge) A(t)= -e dt’ E(t’) = v(t)
-
t
Schrödinger equation: (dipole approximation)
m
teApΗ
ti
2
))((ˆ2
)(2
ˆ2
terEm
pΗ
ti length gauge
momentum/velocitygauge
Electron in Laser Field
E(t)=E0cos(t)
a(t)= -eE0cos(t)
v(t)= - sin(t)eE0
linearly polarized along x axis
acceleration
velocity (dt a)
Vector potential (Coulomb gauge,
A=0)
A(t)= -e dt’ E(t’) = v(t)-
t
Schrödinger equation: (dipole approximation)
m
teApΗ
ti
2
))((ˆ2
momentum/velocitygauge
[H,p]=0 p conserved, solution: )(~)(exp)(~),(~
ppp ttiat
t
tdm
tett
2
)(1)(
2Ap
Keldysh formalism
Photoelectric effect(direct transition)
1st order perturbation theory
t
tietEtdta )(1
10)(~)(
|1>
|0>
Strong electric field(Tunneling)
tunneling rate
ttEmU
tEw
c etda))((2
))((
~
w: barrier width
U: barrier height
p
p
U
I
2 11
t
tin etEtdta )(1
10)(~)(
ADK formulaAmmosov, Delone, and Krainov, Sov. Phys. JETP 64, 1191 (1986)
Experimental checks: Augst et al., J. Opt. Soc. Am. B 8, 858 (1991)
Ionization rate (in a.u.):
Strong electric field(Tunneling)
tunneling rate
ttEmU
tEw
c etda))((2
))((
~
w: barrier width
U: barrier height
1
Keldysh formalism
tunneling rate
Strong electric field(Tunneling)
ttEmU
tEw
c etda))((2
))((
~
w: barrier width
U: barrier height
Strong-Field Approximation
Strong electric field
e-
V(t)=rE(t)
V
r
)()(2
1ˆ 2 trErVpm
Ηt
i
m
teApΗ
ti
2
))((ˆ2
)(~)(exp)(~),(~
ppp ttiat
t
tdm
tetSt
2
)(1)()(
2Ap
high-harmonic generationintense laser field acting on single atom
probability distribution p(x,y)=|(x,y)|2 for the electronic wavefunction
laser polarization