Modern Methods Experimental Physics - Lecture 10 - 22 1 2021 Marc Vrakking marc.vrakking@mbi berlin.de

Modern Methods Experimental
 Physics

 Lecture 10 – 22‐1‐2021

 Marc Vrakking
 marc.vrakking@mbi‐berlin.de

Tentative schedule and topics
Lecture
Fr : 10:00 – 11:45
https://fu‐berlin.webex.com/meet/vrakking

Working group
Fr : 8.00 – 9.45 (every other week, first time 20‐11‐2020)
https://fu‐berlin.webex.com/meet/vrakking
• Active participation in the working group requires a laptop
• Slides will be posted following each lecture, incl. suggestions
 for further reading:
 http://staff.mbi‐berlin.de/vrakking/lecture/index.html
• The exam will consist of a 15‐page paper on a selected topic
• Last lecture: 28‐2‐2021; paper due 1‐5‐2021

Schedule of Lecture Wintersemester 2020‐2021 (tentative)
November 6, 2020 Lecture 1 Introduction
November 13, 2020 Lecture 2 Pump‐probe spectroscopy
November 20, 2020 Lecture 3+WG1 Pump‐probe spectroscopy (cont.)
November 27, 2020 Lecture 4 Lasers – I
December 4, 2020 Lecture 5+WG2 Lasers – II
December 11, 2020 Lecture 6 Lasers – III
December 18, 2020 Lecture 7+WG3 Atoms in strong laser fields – I
Januari 8, 2021 Lecture 8 Atoms in strong laser fields – II
Januari 15, 2021 Lecture 9 Molecules in strong laser fields
Januari 22, 2021 Lecture 10+WG4 HHG – I
Januari 29, 2021 Lecture 11 HHG ‐ II
Februari 5, 2021 Lecture 12+WG5 Attosecond pulse generation WG5
Februari 12, 2021 Lecture 13 Attosecond pump‐probe spectroscopy ‐ I
Februari 19, 2021 Lecture 14+WG6 Attosecond pump‐probe spectroscopy ‐ II
Februari 26, 2021 Lecture 15 HHG in solids + Labtour at MBI (if possible)

Working groups (tentative):

WG 1 ‐ vibrational wavepackets WG 4 ‐ dressed states
WG 2 – velocity map imaging WG 5 – SFA
WG 3 ‐ lasers WG 6 – t.b.d.

High Harmonic Generation

 4

Mid‐1980´s: studies of ATI
 6.4x1013 W/cm2

 4.4x1013 W/cm2

 3.4x1013 W/cm2

 2.4x1013 W/cm2 Experimental setup at Saclay to measure the light
 emitted during above‐threshold ionization experiments
 A. L´Huillier et al., in ‘Atoms in Intense Laser Fields ’,
 edited by Gavrila and Muller, (Academic Press, 1992)

P. Kruit et al., Phys. Rev. A 28, 248 (1983)

Discovery of High‐Harmonic
 Generation (HHG)

High‐harmonic generation in Xe using a 30 ps,
1064 nm laser focused to ca. 1013 W/cm2 + similar observations around the
 time in the Rhodes‐group using 248
M. Ferray et al., J. Phys. B 21 L31 (1988) nm driver lasers

Intensity and pressure dependence
 Plateau formation shows non‐
 perturbative nature of HHG

 Coherent addition from
 many emitters revealed
 by quadratic power
 dependence

A. L´Huillier et al., in ‘Atoms in Intense Laser Fields ’, edited by Gavrila and Muller, (Academic
Press, 1992)

Distortion of the Coulomb potential
Over‐the‐barrier 
 ,
ionization: 16 1 a.u. = 3.51x1016 W/cm2

Hydrogen atom (IP=0.5 a.u.) : 0.0039 a.u. = 1.4x1014 W/cm2

Below , the electron can escape the atom by tunneling
through the Coulomb + laser electric field potential, provided that
the potential is sufficiently quasi‐static

This condition is expressed by the
Keldysh parameter 

 ≪1
 2 

Tunneling formulas
Provided suitable approximations are made, the rate of tunnel
ionization can be described by simple formulas

Strong field approximation:
Assume that after the ionization process the interaction of the
electron with the core is negligible, and that the electron only
interacts with the laser electric field

Adiabatic approximation:
Assume that in the presence of the laser field the atom remains in
the lowest available state, and that no population is transferred to
excited states

Single active electron approximation:
Assume only the most weakly bound electron is ionized

After ionization: Propagation assuming
 the strong‐field approximation (SFA)
Assume that the electron does not feel the ion anymore as soon as it
has tunneled out
Assume, moreover, that the Coulomb‐free motion starts with v=0 at
r=0, and that the laser amplitude is constant

 / = (a.u.)
 / / (a.u.)
 / = / (a.u.)

N.B. E / , . . 
P. Corkum. Phys. Rev. Lett. 71, 1994 (1993)

Maximum recollision energy
 3.17 Up

 11

Cut‐off law:

 The main triumph of the three‐step model
P. Corkum. Phys. Rev. Lett. 71, 1994 (1993) was that it explained the cut‐off law

HHG via short and long trajectories

 13
 M. Bellini et al., Phys. Rev. Lett. 81, 297 (1998)

14
M. Bellini et al., Phys. Rev. Lett. 81, 297 (1998)

Phase‐matching
In the HHG medium, the driver laser and the generated harmonics
move with a different phase velocity
   laser frequency
 = = Lecture 1
 2 laser wavevector

  
 = = Phase matching: ∆ 0
 
Coherence length: 
 ∆ 

 Thesis Amy Lytle, JILA 2008

Phase‐matching
 ~pressure
 ∆ ∆ ∆ ∆ ∆ 

 ~intensity
In the HHG medium, phase matching is affected by
 
(i) The density of neutral gas ∆ 
 2 
 
(ii) The density of free electrons ∆ 
 2 
 
(iii) The laser focusing (no waveguiding assumed) ∆ ~
 
(iv) The electron trajectories ∆ 
 

Serendipity in Phase‐matching
 
 ∆ 
 
∆ 
 2 0
 0 long trajectory Varju et al.,
 2 J. Mod. Opt.
L‘Huillier et al., JOSA B 7, 529 (1990) 2, 379 (2004)

Useful materials for further reading (strong field
ionization):
C.J. Joachain, N.J. Kylstra and R.M. Potvliege, Atoms in Intense Laser
Fields, (Cambridge University Press, 2012)

M. Ivanov et al., Anatomy of strong field ionization, J. Mod. Optics
52, 165 (2005)

L. DiMauro and P. Agostini, Adv. At. Mol. And Opt. Physics 35, 79
(1995)

+ several chapters (DiMauro, Ivanov, Smirnova, L´Huillier) in
upcoming book „Attosecond and XUV Physics“ (ed. by M.J.J. Vrakking
and Th. Schultz, Wiley, december 2013)
 18