1. Strong field atomic ionization
Momentum Imaging of
Strong field atomic ionization
Spectra
Cusps
Time Delay
Good morning everyone and thank you to the organizers who invited to me to participate in this exciting program and offered me a chance to give a talk. After some negotiation with the organizers, I chose this subject of my talk which is very recent and hot to the point that it burns our finger. We really do not know what we have stumbled upon, either a numerical artifact or a new and interesting physical effect. That’s why I wanted to discuss it with such a distinguished audience. I will try to wrap it up rather quickly. And, hopefully, there will be some time left to discuss another subject of my recent work which is the atto-second time delay. So you will receive the two talks at a price of one.
I will be talking about strong field ionization with the XUV pulses which impose a non-zero displacement on a free electron. This is calculated as a time integral of the vector potential of the pulse duration. In the meantime, the same time integral of the electric field should be zero because it is proportional to the momentum transferred by the photon to a free electron and it is zero in a non-relativistic approximation. Of course, in non-relativistic theory, it can be finite.
A plane-wave laser cannot accelerate an electron in free space, according to the Lawson–Woodward theorem, posited in 1979.
Anatoli Kheifets and Igor Ivanov

2. Motivation Interrogation of the target electronic structure
Experimental technique
Experimental Observable
Pump / Probe pulses
Laser pulse polarization
References
Tunneling and Diffraction
3D Momentum
Diffraction pattern IR
Linear
Science 320, 1478 (2008)
High Harmonics Generation
HHG Spectrogram
IR / IR
Nature Physics 5, 412 (2009)
Tunneling and Momentum Imaging
Transverse momentum p⊥
Circular
Phys. Rev. Lett. 105, (2010)
Sequential pump-probe double ionization
Spin-orbit wave packets
Phys. Rev. Lett. 112, (2014).

3. Motivation Timing of ionization processes Experimental technique
Experimental Observable
Pump / Probe pulses
Laser pulse polarization
References
Attosecond Streaking Camera
p|| momentum
Kinetic Energy Spectrogram
XUV / IR
Linear
Science 328, 1658 (2010).
RABBITT
Sideband oscillation
Phys. Rev. Lett. 106, (2011).
Angular Streaking
Attoclock
2D Momentum Rotation angle IR
Circular
Science 322, 1525 (2008).
OTC sub-cycle control
2D Momentum
IR / IR
Phys. Rev. Lett. 95, (2005)
RABBITT: Reconstruction of Attosecond Beating By Interference of Two-photon Transitions OTC: Orthogonally polarized Two-Color

4. Outline 2D momentum spectra P⊥ momentum imaging Time Delay
OTC momentum mapping in Ne
P⊥ momentum imaging
From Cusp to Gaussian
Hydrogen with linear and circular pulses
Ar and Ne* in tunneling and OBI regimes
Pump-probe sequential double ionization of Ar
Time Delay
Circular pulses
Attoclock: He
Finite tunneling time?
Retro-Action: How the small affects the LARGE
Here is the outline of my presentation on this subject.
I will start with purely numerical results on resonant ionization of atomic hydrogen in the region of the Autler-Townes doublet.
I will show an extreme sensitivity of the calculated spectra with the details of the ramping on and off of a fairly long flat-top pulse. It appears that the sin2 and trapezoidal ramp on/off produce profoundly different photoelectron spectra. On top of this line distortion, it appears that the angular momentum composition and the photoelectron angular distribution vary significantly depending on the ramp on/off.
Then I will give you theoretical interpretation to this sensitivity using the concept of the Kramers-Henneberger atom. In this concept, the receding photoelectron, in its rest frame feels a combined potential of the strong EM field and the parent ion. The static component of this potential can support a large number of bound states which can be visualized experimentally and can be made responsible for stabilization effect of the strong field atomic ionization.
Finally, I will discuss implications of the finite displacement effect for theory and experiment.
Friday October 14, 2016

5. OTC sub-cycle time-to-momentum mapping
800 nm
400 nm
This project started with a purely numerical investigation of the strong field ionization of atomic hydrogen. This is an ATI spectrum driven by a very long, 40-cycle pulse with the central energy tuned to the energy of the Autler-Townes doublet This doublet originates from the 2p state resonantly coupled to the 1s ground state. The first two peaks in the photoelectron spectrum correspond to one-photon absorption and then follow their multi-photon replicas. The problem in this spectrum was flattening of the spectrum in the previous calculation by some other authors and was not confirmed in the previous work. It is a rather numerical issue given the drop in intensity by 10 orders of magnitude

6. OTC sub-cycle time-to-momentum mapping
800 nm
400 nm

7. Transverse Electron Momentum Distribution
Any component of a wave function where p II E is wasted.
An electron with p⊥≠ 0 experiences a larger effective barrier
Paul Corkum, JASL
ADK formula
Momentum space wave function
Just a few words about the Autler–Townes effect, also known as a dynamical or AC Stark effect corresponding to the case when an oscillating electric field is tuned in resonance (or close) to the transition frequency of a given spectral line, and resulting in a change of the shape of the absorption/emission spectra of that spectral line.
Originally, the Autler-Townes effect was discovered in the microwave frequency and explained in classical terms. This was very common for Charles Townes who got his Nobel prize for masers, not lasers. But later the Autler-Townes effect was rediscovered in laser physics and there is a very nice chapter in a book dedicated to Townes by Claude Cohen-Tannoudji which gives a simple introduction of this effect in terms of quantum physics. The two atomic levels coupled by the laser frequency form a pair of dressed state which avoid crossing and thus determine the energy of the Autler-Townes doublet depending on the laser frequency.
Arbitrary ellipticity e:

8. Transverse Electron Momentum Distribution
Circular polarization

9. Transverse Electron Momentum Distribution
No Coulomb potential
With Coulomb potential

10. Transverse Electron Momentum Distribution
Cross-over: From Linear to Circular polarization: 1014 W/cm2
e=0
e=0.6
e=0.2
e=0.7
e=0.4
e=0.8
e=0.5
e=1

11. Transverse Electron Momentum Distribution
Cross-over: From Linear to Circular polarization: 1014 W/cm2
mp=0: l→ l+1 → l …
mp=1: l→ l+1 → l+2 …
Centrifugal barrier: l ~ ka l↑→ a↑

12. Transverse Electron Momentum Distribution
Classically forbidden trajectory
Classically allowed trajectory
a x>a
x>0

13. Transverse Electron Momentum Distribution
Ground state 4.8x1014 W/cm2
Metastable 2x1014 W/cm2

14. Transverse Electron Momentum Distribution
Ground state 4.8x1014 W/cm2
From Cusp
to Gaussian

15. Transverse Electron Momentum Distribution
Metastable 2x1014 W/cm2
always Cusp

16. Transverse Electron Momentum Distribution
Ground state 4.8x1014 W/cm2
Metastable 2x1014 W/cm2
Gaussian a=2
Cusp 1<a<2
s= x1014 W/cm2
s=0.25 5x1014 W/cm2 Arissian et al PRL 105, (2010).

17. Pump-probe sequential double ionization

18. Pump-probe sequential double ionization

19. Pump-probe sequential double ionization

20. Pump-probe sequential double ionization

21. Pump-probe sequential double ionization
Linear polarization

22. Pump-probe sequential double ionization
Circular polarization

23. Summary Strong field ionization for
momentum imaging of the target orbitals
OTC momentum mapping in Ne
Sub-cycle sensitivity
Strong Coulomb field effect
Transverse electron momentum distribution in H, Ne*, Ar
Imprint of the target orbital in momentum space
Strong Coulomb distortion: from Gaussian to Cusp
Intricate effect of ellipticity
Different in tunneling and OBE regimes
Pump-probe sequnetial double ionization of Ar
Angular precession of spin-orbit wave packets
Simple tunneling formula: from Gaussian to Cusp
Simple tunneling formula vs. TDSE
Conclulsion:
Useful tool but should be taken with a grain of salt