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Attosecond Optical Science
5
V
10
4
Pulse duration (fs)
10
R
3
10
2
10
1
10
0
10
-1
10
1970
1980
1990
Year
2000
2010
The key idea; F=ma
Mapped by
classical physics
to here
Attoseconds
arise first here
Classically an atom’s own electron,
driven by a strong electric field can
interact with its parent within a cycle.
The key idea
c=a(k)eikx-it
1.0
0.8
1.0
0.5
0.0
-0.5
-1.0
0
100
200
300
400
500
0.6
0.4
g
0.2
1.0
0.5
0.0
0.0
-0.5
-1.0
0
0
0
20
20
40
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60
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30 Å
100
200
300
400
500
F=ma
Last or next 1/2
optical cycle
3.17Uosc~200 eV
0~ 31 Å
1015 W/cm2, 800 nm
Collision Perspective
-- 1011 amp/cm2
-- Attosecond precision
-- ~ 1 Å wavelength
-- Time dependent field is present
Coherent
Collision physics and optics
converge
Nature, 417, 917, (2002)
Attosecond and High Harmonic Generation;
an Interferometer
1.0
0.8
1.0
0.5
0.0
-0.5
-1.0
0
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500
0.6
0.4
0.2
1.0
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0.0
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-0.5
-1.0
0
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20
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40
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80
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100
Molecular
interferometer
80
100
Optical
interferometer
Interferometers measure everything
about the waves involved
bound electron
re-collision electron
High Harmonics/Attoseconds pulses
Amplitude, energy
and phase of the
re-collision
electron are
transferred to light
d(t) is essentially
the Fourier
transform of the
wave function
d(t)={ra(k)eikx d3r}ei{(IP+KE)t +}

A second interferometer
If more than one:
If one:
Train of
attosecond pulse
Single
attosecond pulse
Optical interference --- but it is as if it were an
electron interference!
Producing High Harmonics
Jet, cell or fibre
Not single atom -Conversion
efficiency ~10-5
Up to 1,200 eV photons, ~ 1000th
harmonics
Fundamental
and XUV
emission
Ways to manipulate the interferometer
c=a(k)eikx-it
1.0
0.8
1.0
0.5
0.0
-0.5
-1.0
0
100
200
300
400
500
0.6
0.4
g
0.2
1.0
0.5
0.0
0.0
-0.5
-1.0
0
0
20
Move the
wave function
--- Rotate the
molecule
0
20
40
40
60
80
100
100
200
Move the tunnel
80
400
30 Å
Give the
electron a push
60
300
100
Move the arm
500
Time dependence of the oscillating
dipole
Making single
attosecond pulses
---
controlling the
laser field
High Harmonics
Making single attosecond
optical pulses
electric field
1.0
0.5
0.0
-0.5
-1.0
0
20
40
60
80
100
phase
control the laser field
120
140
Producing Attosecond Pulses
Jet, cell or fibre
XUV emission
Filter
250 attoseconds
Nature 427 817 (2004)
Attosecond Pulse Generation with
no Filter
electric field
1.0
0.5
0.0
-0.5
-1.0
0
20
40
60
80
100
120
140
phase
State-of-the-art 130 attoseconds
Attosecond generation and
measurement system
Constructed under contract to ALLS
Measuring attosecond
photon pulses
(MAKE A PHOTOELECTRON
REPLICA AND MEASURE IT)
Streak Camera:
PRL 74, 2933 (1995); Science 291, 1923 (2001);
PRL 88, 173903 (2002)
SPIDER:
PRL 90, 073902 (2003)
Atomic ionization produces a replica
photoelectron pulse
1/2 mV2 =x - IP
V
Measurement of the photo-electron replica is a
measurement of the pulse
Attosecond Streak Camera
1
Electric Field (10
11
V/cm )
2
0
-1
-2
-1
0
1
2
3
4
5
6
tim e (fs)
7
8
9
10 11
F=ma once again
•linear polarization
•initial velocity (V0x, V0y, V0Z)
Vdrift, x = V0x- {Vd= qE0(t)/m Sin ( tI + )}
Vdrift, y = V0y
vd , y
v0
Vdrift, z = V0z
vd (t )
vd , x
Polarization
Drift velocity distribution
A single sub-cycle X-ray pulse
Vy
1
Electric Field (10
11
V/cm )
2
0
-1
-2
-1
0
1
2
3
4
5
6
7
8
9
10 11
tim e (fs)
Vx
--- photoelectron
replica is streaked
(attosecond streak camera)
Photoelectron spectra (arb. units)
Streaked photoelectron of 100 eV
pulse -- parallel observation
1.0
0.8
(a)
70 attosecond
0.6
I = 6x1014 W/cm2
0.4
0.2
0.0
1.0
0.8
(b)
0.6
0.4
0.2
0.0
20
40
60
80
100
Electron energy (eV)
120
Ways to manipulate the interferometer
c=a(k)eikx-it
1.0
0.8
1.0
0.5
0.0
-0.5
-1.0
0
100
200
300
400
500
0.6
0.4
g
0.2
1.0
0.5
0.0
0.0
-0.5
-1.0
0
0
0
20
20
40
40
60
60
80
100
80
100
30 Å
100
200
300
400
500
Moving the arms --- a phase gate
A (weak)2 2 field breaks symmetry, generating even
harmonics
Each moment of birth (re-collision) has an optimum
phase difference () between  and 2
Experimental Set-Up
calcite
60 BBO
glass
Ti:sapphire amplifier
1mJ , 27 fs @ 50 Hz
/2 Wave plate
grating
Supersonic gas jet
MCP
What Phase difference moves the
interferometer arms optimally?
16
Harmonic order
18
20
22
24
26
Delay [fs]
Attosecond Temporal Phase Gate
d,2(t) ~ d(t) e
(t)
i(t)
SFA
(N)
Re-collision time [rad]
Harmonic number
: two color delay which maximizes the even
harmonic signal
Electron Wave-Packet Reconstruction
Short trajectories
Harmonic order
Long trajectories
SFA
Re-collision time [rad]
Electron wave packet measurement is equivalent to a
xuv pulse measurement up to the transition dipole.
Interferometers
also allow
control
Larger phases
or
Using Interferometry for
everything:
Tomographic Imaging of
electronic orbitals
Nature 432, 867 (2004)
High Harmonics/Attoseconds pulses
d(t) is essentially
the Fourier
transform of the
wave function
d(t)={ra(k)eikx d3r}ei{(IP+KE)t +}

Transient alignment of molecules
time
The Experiment
“Pump”
Alignment pulse
(60fs, 5x1013 W/cm2)
“Probe”
HHG pulse
(30fs, 1.5x1014 W/cm2)
Ti:sapphire CPA
1 TW, 27 fs @ 50 Hz
Space
H15
23.3eV
H21
32.6eV
H27
41.9eV
H33
51.2eV
H39
60.5eV
Angle Dependent High Harmonic Spectrum
Harmonics from N2 and Ar
Note the
relation to
Photoelectron
spectroscopy
2 d()= 2 a(k) greikxdx
Normalized Harmonic Intensities
Harmonic
intensities from N2
at different
molecular angles
EL
Reconstructed N2 g Orbital
• Reconstructed
from 19 angular
projections
• wave function,
not its square
We see electrons!
Amplitude and Phase!
Review:
• Measure orbitals
• Measure attosecond pulses
• Control high harmonics
• Probe atomic or molecular
dynamics
The Attogroup (2007)
Scientists: Paul Corkum, David Villeneuve, Eli
Simova, Andrei Naumov and David Rayner
Technologists: Bert Avery, John Parsons
Postdoctoral Fellows: Nirit Dudovitch, Rajeev
Pattathil, Domagoj Pavicic and Yann Mairesse.
Visitors: Hiromichi Niikura, Gennady Yudin and
Andre Staudte
Ph. D. Students: Kevin Lee (McMaster), Julien
Bertrand and Marina Gertsvolf (Ottawa).