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

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, 133002 (2010) Sequential pump-probe double ionization Spin-orbit wave packets Phys. Rev. Lett. 112, 213001 (2014).

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, 143002 (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, 253001 (2005) RABBITT: Reconstruction of Attosecond Beating By Interference of Two-photon Transitions OTC: Orthogonally polarized Two-Color

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

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

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

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:

Transverse Electron Momentum Distribution Circular polarization

Transverse Electron Momentum Distribution No Coulomb potential With Coulomb potential

Transverse Electron Momentum Distribution Cross-over: From Linear to Circular polarization: H @ 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

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

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

Transverse Electron Momentum Distribution Ground state Ar @ 4.8x1014 W/cm2 Metastable Ne* @ 2x1014 W/cm2

Transverse Electron Momentum Distribution Ground state Ar @ 4.8x1014 W/cm2 From Cusp to Gaussian

Transverse Electron Momentum Distribution Metastable Ne* @ 2x1014 W/cm2 always Cusp

Transverse Electron Momentum Distribution Ground state Ar @ 4.8x1014 W/cm2 Metastable Ne* @ 2x1014 W/cm2 Gaussian a=2 Cusp 1<a<2 s=0.25 Ar @ 4.8x1014 W/cm2 s=0.25 Ar @ 5x1014 W/cm2 Arissian et al PRL 105, 133002 (2010).

Pump-probe sequential double ionization

Pump-probe sequential double ionization

Pump-probe sequential double ionization

Pump-probe sequential double ionization

Pump-probe sequential double ionization Linear polarization

Pump-probe sequential double ionization Circular polarization

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