1. Looking inside the tunneling process
Nirit Dudovich
Physics of Complex Systems, Weizmann Institute of Science

2. Co- authors 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

3. 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
Generating attosecond pulses has required a radically different approach from previous ultrafast optical methods. Attosecond pulses arise from highly nonlinear laser-atom interaction, while femtosecond pulses involve low order processes. The technology of attosecond measurement, however, is built on established methods of characterizing femtosecond pulses: the pulse is measured after it has left the region where it was produced. We offer a completely different approach: in-situ measurement. That is, we integrate attosecond pulse production and measurement in a manner that can be applied to many high-order non-linear interactions.
The recollision process

4. Attosecond Science High harmonics generation E>100eV
Acceleration by the electric field
Re-collision
Tunnel ionization
Generating attosecond pulses has required a radically different approach from previous ultrafast optical methods. Attosecond pulses arise from highly nonlinear laser-atom interaction, while femtosecond pulses involve low order processes. The technology of attosecond measurement, however, is built on established methods of characterizing femtosecond pulses: the pulse is measured after it has left the region where it was produced. We offer a completely different approach: in-situ measurement. That is, we integrate attosecond pulse production and measurement in a manner that can be applied to many high-order non-linear interactions.
High harmonics generation

5. Re-collision as a pump – probe scheme
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).  
Re-collision
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

6. Field induced tunnel ionization
When does an electron leave the tunneling barrier?
What is the instantaneous probability?
Does the process evolve in an adiabatic manner?
Can we resolve multi-channels ionization?
Tunneling through a static barrier
Field induced tunneling
How can we look at this process? All we have is the emitted specrtum
L. V. Keldysh Sov. Phys. JETP (1965) 6

7. Re-collision as a pump – probe scheme
Electric field
How does the time of ionization map into our experiment?
Time [cycle]
Distance
P. B. Corkum,, Phys. Rev. Lett. 71, 1994 (1993).

8. Re-collision as a pump – probe scheme
When does an electron leave the tunneling barrier?
What is the instantaneous probability?
Does the process evolve in an adiabatic manner?
Can we resolve multi-channels ionization?
The induced dipole moment is described by:
Re(t0)
Im(t0)
The semi-classical action
The main contribution to the integral comes from the stationary points:
The solution is found in the complex plane of t0

9. Recollision as a measurement
The output is the high harmonic spectrum - We need additional information
X(t0)=0
V(t0)=0
X(t)=0
Can we keep it simple? c
The recollision process provides an Angstrom-attosecond resolution
Any deviations are mapped to the properties of the recolliding electron

10. “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

11. “kicking” the recollision process

12. Gating the recollision process - Helium70 60
Gate 50
Energy (harmonic number) 40 30 20
max (t0)
-0.1
0.1
0.2
0.3
-0.4
 [cycle]

13. Reconstructing the ionization times
Harmonic order
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).

14. Re-collision as a pump – probe scheme
When does an electron leaves the tunneling barrier?
What is the instantaneous probability?
Does the process evolve in an adiabatic manner?
Can we resolve multi-channels ionization?
The induced dipole moment is described by:
Re(t0)
Im(t0)
The semi-classical action

15. “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) x

16. Interferometry in High Harmonic Generation17 19 21 23 25 27 29
exp(-i )
A(N)
exp(-i )
A(N)
A(N)
exp(i )
A(N)
exp(i)
exp(i )
Odd harmonics
Even harmonics

17. 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 )
A(N)
exp(i )
A(N)
exp(i)
exp(i )
Odd harmonics
Even harmonics

18. Interferometry in High Harmonic Generation
Even harmonics π +
Odd harmonics
Two color delay
A(N)
exp(-i -)
exp(-i )
A(N)
exp(-i -)
exp(-i )
A(N)
exp(i +)
exp(i )
A(N)
exp(i)
exp(i +)
exp(i )
Odd harmonics
Even harmonics

19. Interferometry in High Harmonic Generation
odd- even
Harmonic Order

20. Reconstruction of the imaginary times30 40 50 60 70
0.05
0.1
0.15
0.2
Harmonic order
Time [rad]

21. Mapping the tunneling process
Moment of Ionization
Probability 30 40 50 60 70
0.05
0.1
0.15
0.2
Harmonic order
Time [rad]

22. The link between ionization and recollision
Ionization time:
190 attoseconds
170 attoseconds
210 attoseconds
250 attoseconds
270 attoseconds
230 attoseconds

23. 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).

24. Gating multi channels ionization
Ionization gate
HOMO-2
HHG
Energy (harmonic number)
HOMO 
 [cycle]
Ionization times [attosecond]
Phase jump

25. Gating multi channels ionization
Single channel degrees
Two channels - 0 degrees
Energy (harmonic number)
HHG
Energy (harmonic number)
HHG
 [cycle]
 [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).

26. 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.

27. Gating multi channels ionization

28. The link between ionization and recollision
Classical solution
Stationary solution
M. Lewenstein et al., Phys Rev A 49,

29. Reconstructing the ionization times

30. Tunneling - stationary solution
We have linked the real part to the time at which the electron leaves the Coulomb barrier
The imaginary part is linked to the instantaneous tunneling probability
Can we measure it?
The stationary solution is complex

31. Gating the recollision process
Ionization
Return
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).

32. Gating the recollision process
2D Gate
Displacement Gate: GLmax(N)
Angular Gate: Gmax(N)
GLmax(t0,t)
Gmax(t0,t) t0 t

33. Gating the recollision process
Displacement gate 70 60 50
HHG 40 30 20
-0.1
-0.2
-0.3
-0.4
 [cycle]
How do we reconstruct the dynamics?
There are two unknown parameters – t0 and t

34. Recollision as a measurement
The output is the high harmonic spectrum - We need additional information
Can we keep it simple?
The optimal gate
Perturbative manipulation
A window in the ionization time
Can be shifted

35. Interferometry in High Harmonic Generation
Delay [fs] 16 18 20 22 24 26 17 19 21 23 25 27
N. Dudovich, O. Smirnova, J. Levesque, M. Yu. Ivanov, D. M. Villeneuve and P. B. Corkum, Nature Physics 2, 781 (2006).

36. Reconstructing the ionization times
Short trajectories
Long trajectories

37. Reconstructing the ionization times

38. Field induced tunnel ionization Pioneering experiments
How can we look at this process? All we have is the emitted specrtum
P. Eckle et al., Science (2008)
A. N. Pfeiffer et al., Nature Physics (2012).
M. Uiberacker et al., Nature (2007). 38

39. Gating the recollision process
Angular gate 60  50
HHG 40
HHG  30 20
-0.1
-0.2
-0.3
-0.4
 [cycle]

40. Interferometry in High Harmonic Generation
odd- even
Harmonic Order

41. Interferometry in High Harmonic Generation

42. The link between ionization and recollision

43. The link between ionization and recollision
Short trajectories
Energy (harmonic number)
Long trajectories
M. Lewenstein et al., Phys Rev A 49,

44. Reconstructing the ionization times

45. Reconstructing the ionization times

46. Scaling the gating mechanism – 1.4

47. “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.

48. Re-collision as a pump – probe scheme

49. 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

50. Attosecond pulse generation process
Re-collision
Acceleration by the electric field
E>100eV
Tunnel ionization
Ionization potential
Kinetic energy
Optical radiation with attoseconds duration

51. Attosecond pulse train
The multi-cycle regime
High harmonics generation
H15
23.3eV
H21
32.6eV
H27
41.9eV
H39
60.5eV

52. Kicking the recollision process - Helium
He - normalized 70 60 50
Energy (harmonic number) 40 30 20
max (t0)
-0.1
0.1
0.2
0.3
-0.4
-0.1
0.1
0.2
0.3
-0.4
 [cycle]
 [cycle]

53. Kicking the recollision process - Helium
He - normalized 70
∆Y()=0
∆Y(t0)=0
Gate (“kick”) 60 50
Energy (harmonic number) 40 30 20
max (t0)
-0.1
0.1
0.2
0.3
-0.4
 [cycle]

54. Reconstructing the ionization times
Energy (harmonic number)
Harmonic order
Why do we observe a significant deviation from the classical model?

55. Reconstructing the ionization times
Energy (harmonic number)
Harmonic order

56. Stationary Phase approximation
Weight
M. Lewenstein et al., Phys Rev A 49,

57. Catastrophe Theory
Mapping objects from one dimension to another dimensions can lead to singularities:
Singularities are classified according to Catastrophe theory
This classification tells us about the shape, intensity, width and diffraction pattern of the caustic.
Think of how the density of the folded “ideal” paper is mapped to the plane!

58. The link between ionization and recollision
The classical description links:
t t E
The quantum description:
The quantum picture approaches the classical at the stationary points
M. Lewenstein et al., Phys Rev A 49,

59. Field induced tunnel ionization Pioneering experiments
How can we look at this process? All we have is the emitted specrtum
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). 59

60. Return times M. Hentschel et al., Nature 414, (2001)
Y. Mairesse, et al., Science 302, (2003).
N. Dudovich et al., Nature Physics 2, (2006).

61. Ionization times ?

62. Interferometry in High Harmonic Generation
odd- even
Harmonic Order

63. 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).

64. The link between ionization and recollision
Energy
(harmonic number)
Real times
0.2
0.6 1
1.4 30 50 70 c 3 4 5 6 c
Classical solution
Stationary solution
Time [rad]
Time [rad] c
0.4
0.8
1.2 30 50 70
Imaginary times
Time [rad]
M. Lewenstein et al., Phys Rev A 49,