Looking inside the tunneling process
Nirit Dudovich
Physics of Complex Systems, Weizmann Institute of Science
Dror Shafir
Oren Raz
Hadas Soifer
Oren Pedazur
Michal Dagan
Barry Bruner
Collaborations:
Olga Smirnova
Misha Ivanov
Yann Mairesse
Serguei
Patchkovskii
Caterina Vozzi
Salvatore Stagira2
Co- authors
Time resolved measurements in the
attosecond regime
The optical pulse pump/probe the process
IR pulse
Attosecond pulse
Production
Measurement
The free electron probes the process
The recollision process
Attosecond Science
E>100eV
Re-collision
Tunnel
ionization
Acceleration by the electric field
  I p  Ek
High harmonics generation
Re-collision as a pump – probe scheme
Re-collision
H. Niikura, et al., Nature 421, (2003).
X. M. Tong et al., Phys. Rev. Lett. 91 (2003).
M. Lein, Phys. Rev. Lett. 94, (2005).
M. Lein, J. Phys. B, 40 (2007).
S. Baker et al., Science 312, (2006).
O. Smirnova, et al. Nature 460 (2009).
O. Smirnova et al., PNAS 106, (2009).
B. K. McFarland et al., Science 322, (2008).
Tunnel ionization
Optical
cycle
pump
probe
Field induced tunnel ionization
•Tunneling
Whenthrough
does an
electron
a static
barrier leave the tunneling barrier?
• What is the instantaneous probability?
• Does the process evolve in an adiabatic manner?
• Can we resolve multi-channels ionization?
Field induced tunneling
L. V. Keldysh Sov. Phys. JETP 20 1307 (1965)
Re-collision as a pump – probe scheme
Electric field
How does the time of ionization map into our experiment?
Time [cycle]
P. B. Corkum,, Phys. Rev. Lett. 71, 1994 (1993).
Re-collision as a pump – probe scheme
Re(t0)
induced
dipole
moment
described
by:
•The
When
does an
electron
leave theistunneling
barrier?
• Whatt is the instantaneous probability?
xt    dt0  d pC  p, t , t0  exp iS  p, t , t0 
3
S  p, t , t 0  
• Does0 the process evolve in an adiabatic manner?
• Can we resolve multi-channels ionization?
t
Im(t0)
1
d  p  A 

2 t0
The semi-classical action
The main contribution to the integral comes from
the stationary points:
S  p, t , t0 
0
p
2

p  At0 
S
 Ip 
 Ip  0
t0
2
2
The solution is found in the complex
plane of t0
Recollision as a measurement
• X(t
The0)=0
output is the high harmonic spectrum
- We need additional information
V(t0)=0
• Can we keep it simple?
X(t)=0
• The recollision process provides an Angstrom-attosecond resolution
c
• Any deviations are mapped to the properties of the recolliding electron
“kicking” the recollision process
We add a weak second harmonic field
If the field is much weaker than the fundamental field it acts as an amplitude gate
“kicking” the recollision process
Gating the recollision process - Helium
Energy (harmonic number)
70
60
Gate
50
40
30
20
-0.1
0
0.1
 [cycle]
0.2
max
(t )
0.3 0 -0.4
Harmonic order
Reconstructing the ionization times
D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, Serguei Patchkovskii, M. Yu. Ivanov, O. Smirnova
and N. Dudovich, Nature 485, 343 (2012).
Re-collision as a pump – probe scheme
Re(t0)
induced
dipole
moment
is described
by:
•The
When
does an
electron
leaves the
tunneling barrier?
• Whatt is the instantaneous probability?
xt    dt0  d pC  p, t , t0  exp iS  p, t , t0 
3
S  p, t , t 0  
• Does0 the process evolve in an adiabatic manner?
• Can we resolve multi-channels ionization?
t
Im(t0)
1
d  p  A 

2 t0
The semi-classical action
S  p, t , t0 
0
p
2

p  At0 
S
 Ip 
 Ip  0
t0
2
2
“kicking” the recollision process –
parallel perturbation
Can we measure the imaginary time?
• We can add a parallel perturbation
• This perturbation adds a small phase shift and perturbs the ionization step.
• In the limit of a small Keldysh parameter we are left with a phase shift
• How do we perform the measurement? How can we separate the two
mechanisms?
J M Dahlstr¨om, A L’Huillier and J Mauritsson, J. Phys. B: At. Mol. Opt. Phys. 44 (2011) 095602x
Interferometry in High Harmonic
Generation
17
19
21
23
25
27
29
A(N) exp(-i )
A(N) exp(-i )
A(N) exp(i )
A(N) exp(i) exp(i )
Odd harmonics
Even harmonics
Interferometry in High Harmonic
Generation
Even harmonics
π
Odd harmonics
Two color delay
N. Dudovich, O. Smirnova, J. Levesque, M. Yu. Ivanov, D. M. Villeneuve and P. B. Corkum, Nature Physics 2, 781 (2006).
A(N) exp(-i )
A(N) exp(i )
Odd harmonics
A(N) exp(-i )
A(N) exp(i) exp(i )
Even harmonics
Interferometry in High Harmonic
Generation
Even harmonics
π+
Odd harmonics
Two color delay
)
A(N) exp(-i -)
A(N) exp(i )+)
Odd harmonics
)
A(N) exp(-i -)
A(N) exp(i) exp(i )+)
Even harmonics
Interferometry in High Harmonic
Generation
odd- even
Harmonic Order
Reconstruction of the imaginary times
70
Harmonic order
60
50
40
30
0.05
0.1
0.15
Time [rad]
0.2
Mapping the tunneling process
Moment of Ionization
Probability
Harmonic order
70
60
50
40
30
0.05
0.1
0.15
Time [rad]
0.2
The link between ionization and recollision
Ionization time:
Multiple channel ionization
Destructive interference
O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum and M. Y. Ivanov, Nature 460, 972 (2009)
D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, Serguei Patchkovskii, M. Yu. Ivanov, O. Smirnova and N. Dudovich,
Nature 485, 343 (2012).
Gating multi channels ionization
Ionization gate
HHG
number)
Energy (harmonic
HOMO-2
HOMO

Ionization times
[attosecond]
Phase jump
 [cycle]
Gating multi channels ionization
Single channel - 90 degrees
Two channels - 0 degrees
0 deg, low I
90 deg, low I
1
1
10
10
0.9
0.9
15
0.8
20
0.7
25
0.6
30
0.5
35
40
0.5
1
1.5
2
2.5
red-blue delay (radians)
 [cycle]
3
0.4
HHG
number)
Energy (harmonic
harmonic order
HHGorder
number)
Energy (harmonic
harmonic
15
0.8
20
0.7
25
0.6
30
0.5
35
40
0.5
1
1.5
2
red-blue delay (radians)
2.5
3
0.4
 [cycle]
We observe a clear signature to two channels ionization ,
probing a delay of 50 attoseconds in the ionization times.
D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, Serguei Patchkovskii,
M. Yu. Ivanov, O. Smirnova and N. Dudovich, Nature 485, 343 (2012).
Re-collision as a pump – probe scheme
• Recollision processes provide temporal information with attosecond
resolution.
• We have measured the tunneling ionization time in simple systems,
directly confirming the analysis based on the path integral formalism.
• We can measure a delay related to multiple orbitals tunneling
• In more complex molecular systems the tunneling process involves
attosecond core rearrangements leading to a real time-delay associated
with different tunneling channels.
Gating multi channels ionization
The link between ionization and recollision
Classical
solution
Stationary
solution
M. Lewenstein et al., Phys Rev A 49, 2117 1994.
Reconstructing the ionization times
Tunneling - stationary solution
80
• We have linked the real part to the time at which
the electron leaves the Coulomb barrier
60
Harmonic Order
• The imaginary part is linked to the
instantaneous tunneling probability
70
50
40
30
• Can we measure it?
20
10
0

p  At0 
S
 Ip 
 Ip  0
t0
2
2
200
The stationary solution
is complex
400
600
Gating the recollision process
80
70
Ionization
Return
Harmonic Order
60
50
40
30
20
10
0
200
400
600
800
1000
1200
Time [asec]
Classical
Experiment
Path integral
1400 n 1600
1800
D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, Serguei Patchkovskii, M. Yu. Ivanov, O. Smirnova
and N. Dudovich, Nature 485, 343 (2012).
2000
Gating the recollision process
2D Gate
Displacement Gate: GLmax(N)
12
14
Angular Gate: Gmax(N)
16
18
12
65
65
60
60
55
50
45
GLmax(t0,t)
Gmax(t0,t)
14
16
55
50
45
40
40
35
35
30
30
25
25
20
20
Heperp6s displacement gate
t0
20
t
Heperp6s polarization gate
18
20
Gating the recollision process
Displacement gate
70
60
HHG
50
40
30
20
-0.1
0
-0.2
 [cycle]
How do we reconstruct the dynamics?
There are two unknown parameters – t0 and t
-0.3
-0.4
Recollision as a measurement
• The output is the high harmonic spectrum
- We need additional information
• Can we keep it simple?
The optimal gate
1. Perturbative manipulation
2. A window in the ionization time
3. Can be shifted
Interferometry in High Harmonic
Generation
16
17
18
19
20
21
22
23
24
25
26
27
Delay [fs]
N. Dudovich, O. Smirnova, J. Levesque, M. Yu. Ivanov, D. M. Villeneuve and P. B. Corkum, Nature Physics 2, 781 (2006).
Reconstructing the ionization times
Short trajectories
Long trajectories
Reconstructing the ionization times
Field induced tunnel ionization
Pioneering experiments
M. Uiberacker et al., Nature (2007).
P. Eckle et al., Science (2008)
A. N. Pfeiffer et al., Nature Physics (2012).
Gating the recollision process
Angular gate
14
12
20
16
18
20
65
x̂
60
60
55
50
50
HHG
HHG
45

40
40
35

30
30
25
20
20
-0.1
0
polarization gate
Heperp6s
-0.2
-0.3
 [cycle]
-0.4
ŷ
Interferometry in High Harmonic
Generation
odd- even
Harmonic Order
Interferometry in High Harmonic
Generation
The link between ionization and recollision
The link between ionization and recollision
Energy (harmonic number)
Ionization
M. Lewenstein et al., Phys Rev A 49, 2117 1994.
recollision
Short trajectories
Long trajectories
Reconstructing the ionization times
Reconstructing the ionization times
Scaling the gating mechanism –
1.4
Kr - short_area - 110613\scan7
photon energy (eV)
30
35
40
45
0
0.5
1
1.5
2
red-blue delay (radians)
2.5
3
“kicking” the recollision process –
parallel perturbation
• The interference between two adjacent half cycle leads to the
generation of odd harmonics.
• The second harmonic field breaks the symmetry and leads to
the generation of even harmonics.
Re-collision as a pump – probe scheme
Re-collision as a pump – probe scheme
We have an extremely accurate measurement – the electron is born at the origin, propagate
on an attosecond time scale and returns to the origion
• Can we study the internal dynamics? Can we link each trajectory to its ionization time?
• Such a measurement will provide a direct insight into one of the most fundamental strong
field phenomena – field induced tunnel ionization
Attosecond pulse generation process
Re-collision
E>100eV
Acceleration by the electric field
Tunnel ionization
  I p  Ek
Ionization
potential
Kinetic
energy
Optical radiation with attoseconds duration
Attosecond pulse train
The multi-cycle
regime
High harmonics generation
H15
23.3eV
H21
32.6eV
H27
41.9eV
H39
60.5eV
Kicking the recollision process - Helium
13
He - normalized
14
15
16
17
18
19
0.7
65
70
60
Energy (harmonic number)
0.8
55
60
50
0.8
50
45
40
40
0.9
35
30
30
0.9
25
20
-0.1
20
0
0.1
 [cycle]
0.2
max
(t )
0.3 0 -0.4
1
-0.1
0
0.1
 [cycle]
0.2
0.3
-0.4
Kicking the recollision process - Helium
He - normalized
Energy (harmonic number)
70
∆Y()=0
60
50
Gate (“kick”)
40
30
20
-0.1
∆Y(t0)=0
0
0.1
 [cycle]
0.2
max
(t )
0.3 0 -0.4
order
Harmonic
number)
(harmonic
Energy
Reconstructing the ionization times
Why do we observe a significant deviation from the classical model?
order
Harmonic
number)
(harmonic
Energy
Reconstructing the ionization times
Stationary Phase approximation
Weight
M. Lewenstein et al., Phys Rev A 49, 2117 1994.
Catastrophe Theory
• Mapping objects from one dimension to another dimensions
can lead to singularities:
Think of how the density of
the folded “ideal” paper is
mapped to the plane!
• Singularities are classified according to Catastrophe theory
• This classification tells us about the shape, intensity, width
and diffraction pattern of the caustic.
The link between ionization and recollision
The classical description links:
t0
t
E
The quantum description:
E t  
tr
 dt At , t exp iS t , t 
0
0
0

The quantum picture approaches the classical at
the stationary points
M. Lewenstein et al., Phys Rev A 49, 2117 1994.
  p  At '2


S   dt ' 
 I p 
2
t0


t
S
0
t 0
Field induced tunnel ionization
Pioneering experiments
P. Eckle et al., “Attosecond Ionization and Tunneling Delay Time Measurements in Helium”, Science (2008)
A. N. Pfeiffer et al., “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms”, Nature Physics (2012).
Return times
70
Harmonic order
60
Classical
Experimental
50
40
30
20
10
800
M. Hentschel et al., Nature 414, (2001)
Y. Mairesse, et al., Science 302, (2003).
N. Dudovich et al., Nature Physics 2, (2006).
1000
1200 1400 1600
Return time [asec]
1800
2000
Ionization times
70
Classical
Experimental
Harmonic order
60
50
40
30
?
20
10
100
200
300
400
500
Ionization time [asec]
600
700
Interferometry in High Harmonic
Generation
odd- even
Harmonic Order
Multiple channel ionization
-13.8 eV
-17.3 eV
-18.1 eV
O. Smirnova, et al., Nature 460, 972 (2009).
B. K. McFarland et al., Science 322, (2008).
The link between ionization and recollision
Ionization
Energy
(harmonic number)
Real times
c
70
c
Classical solution
50
30
recollision
Stationary solution
0.2
0.6
Time [rad]
1
3
Imaginary times
c
70
1.4
4
5
Time [rad]
6
c
50
30
0
0.4
Time [rad]
M. Lewenstein et al., Phys Rev A 49, 2117 1994.
0.8
1.2
0
0.4
0.8
Time [rad]
1.2