Sequential two- and three-photon ionization of noble gas atoms by intense XUV pulses A.N. Grum-Grzhimailo

E.V. Gryzlova, N.M. Kabachnik S. Fritzsche Collaborators in theory E.V. Gryzlova, N.M. Kabachnik Institute of Nuclear Physics, Moscow State University, Russia S. Fritzsche Department of Physical Sciences, University of Oulu, Finland GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany Collaborating experimental groups K. Ueda et al IMRAM, Tohoku University; RIKEN, XFEL Project Head Office, Japan M.J.J. Vrakking et al FOM Institute AMOLF, Amsterdam, Netherlands J. Ullrich, R. Moshammer et al MPI für Kernphysik, Heidelberg, Germany and other institutions

S. Fritzsche, A.N. Grum-Grzhimailo, E.V. Gryzlova, N.M. Kabachnik Angular distributions and angular correlations in sequential two-photon double ionization of atoms J. Phys. B: At. Mol. Opt. Phys., v.41, 165601 (12pp) (2008) Sequential two-photon double ionization of Kr atoms J. Phys. B: At. Mol. Opt. Phys., v. 42, 145602 (6pp) (2009) M. Kurka et al Two-photon double ionization of Ne by free-electron laser radiation: a kinematically complete experiment. J. Phys. B: At. Mol. Opt. Phys., v. 42, 141002 (5pp) (2009) A.N. Grum-Grzhimailo, E.V. Gryzlova, S.I. Strakhova, N.M. Kabachnik, S. Fritzsche Angular distributions and correlations in sequential two-photon atomic double ionization J. Phys. Conf. Ser., v.194, 012004 (10pp) (2009) H. Fukuzawa, et al Photoelectron spectroscopy of sequential three-photon double ionization of Ar irradiated by EUV free-electron laser pulses. J. Phys. B: At. Mol. Opt. Phys., v. 43, 111011 (4pp) (2010) E.V.Gryzlova, A.N.Grum-Grzhimailo, S.Fritzsche, N.M.Kabachnik. Angular correlations between two e lectrons emitted in the sequential two-photon double ionization of atoms. J. Phys. B: At. Mol. Opt. Phys., v.43 225602 (12pp) (2010) A.Rouzée, et al Angle-resolved photoelectron spectroscopy of sequential three-photon triple Ionization of neon at 90.5 eV photon energy. Phys. Rev. A, v.83, 031401(R) (4pp) (2011) Sequential two-photon double ionization of the 4d shell in xenon J. Phys. B: At. Mol. Opt. Phys., v.44 175602 (10pp) (2011) E.V. Gryzlova, et al Double-resonant three-photon double ionization of Ar atoms induced by an EUV free electron laser. Phys. Rev. A (accepted) E.V. Gryzlova, A.N. Grum-Grzhimailo, N.M. Kabachnik,S. Fritzsche Angular distributions and correlations in sequential three-photon triple atomic ionization. J. Phys.: Conf.Ser. (accepted)

Contents Introductory remarks Types of sequential ionization with examples from valence np6-shell ionization of noble gases: - Sequential 2-photon double ionization; selected topics: -angular correlation of photoelectrons and coherence -angular distribution of photoelectrons and entanglement Sequential 3-photon double ionization a) 3-photon resonant double ionization b) 3-photon double resonant double ionization Sequential 3-photon triple ionization Concluding remarks

γ γ γ γ Two-photon double ionization in noble gases: Two mechanisms direct sequential e1+e2 e2 γ 1S0 1S0 1D2 1D2 γ 3P0,1,2 3P0,1,2 np4 np4 e1 2P 2P 1/2 1/2 γ 3/2 3/2 np5 γ np5 1S0 1S0 np6 np6 A A+ A++ A A+ A++

γFEL γFEL γ γ + Ne(2p6) Ne+(2p5) + e1 + Ne+(2p5) Ne2+(2p4) + e2 Photoelectron spectrum of Ne denerated by FEL M. Braune et al, 2007, FLASH 1S0 e2 1D2 γ 3P0,1,2 2p4 e1 2P1/2,3/2 γ 2p5 1S0 2p6 Ne Ne+ Ne++ Photoelectron kinetic energy, eV γFEL + Ne(2p6) Ne+(2p5) + e1 γFEL + Ne+(2p5) Ne2+(2p4) + e2

γFEL γFEL γ γ + Ne(2p6) Ne+(2p5) + e1 + Ne+(2p5) Ne2+(2p4) + e2 Photoelectron spectrum of Ne denerated by FEL M. Braune et al, 2007, FLASH 1S0 e2 1D2 γ 3P0,1,2 2p4 e1 2P1/2,3/2 γ 2p5 1S0 2p6 Ne Ne+ Ne++ Photoelectron kinetic energy, eV γFEL + Ne(2p6) Ne+(2p5) + e1 γFEL + Ne+(2p5) Ne2+(2p4) + e2

Angular distribution of the 2nd step electrons (1st electrons not observed) M. Braune et al, 2007, FLASH

γ γ Two- and three-photon sequential processes: A A+ A++ Two-photon double ionization e2 1S0 1D2 3P0,1,2 np4 γ e1 1/2 γ 2P 3/2 np5 1S0 np6 A A+ A++

γ γ γ γ γ Two- and three-photon sequential processes: A A+ A++ A A+ Two-photon double ionization Three-photon double ionization e2 e2 γ 1S0 1S0 1D2 1D2 3P0,1,2 3P0,1,2 np4 np4 γ γ e1 e1 1/2 1/2 γ np5 2P 3/2 np5 2P 3/2 γ 1S0 1S0 np6 np6 A A+ A++ A A+ A++

γ γ γ γ γ Two- and three-photon sequential processes: A A+ A++ A A+ Two-photon double ionization Three-photon double ionization Braune et al, 2007; FLASH e2 e2 γ 1S0 1S0 1D2 1D2 3P0,1,2 3P0,1,2 np4 np4 γ γ e1 e1 1/2 1/2 γ np5 2P 3/2 np5 2P 3/2 γ 1S0 1S0 Kinetic electron energy, eV np6 np6 A A+ A++ A A+ A++

γ γ γ γ γ Two- and three-photon sequential processes: A A+ A++ A A+ Two-photon double ionization Three-photon double resonant ionization Braune et al, 2007; FLASH e2 e2 γ 1S0 1S0 1D2 1D2 1D2 3P0,1,2 3P0,1,2 3P0,1,2 np4 np4 γ γ e1 e1 1/2 1/2 γ np5 2P 3/2 np5 2P 3/2 γ 1S0 1S0 Kinetic electron energy, eV np6 np6 A A+ A++ A A+ A++

γ γ γ γ γ Two- and three-photon sequential processes: A A+ A++ A A+ Two-photon double ionization Three-photon double-resonant double ionization Braune et al, 2007; FLASH e2 e2 γ 1S0 1S0 1D2 1D2 3P0,1,2 3P0,1,2 np4 np4 γ γ e1 e1 1/2 1/2 γ np5 2P 3/2 np5 2P 3/2 γ 1S0 1S0 Kinetic electron energy, eV np6 np6 A A+ A++ A A+ A++

γ γ γ γ γ γ γ γ Two- and three-photon sequential processes: A A+ A++ A Two-photon double ionization Three-photon double-resonant double ionization Three-photon triple ionization 2P e3 2D 4S np3 γ e2 e2 γ 1S0 1S0 1S0 e2 1D2 1D2 1D2 3P0,1,2 3P0,1,2 3P0,1,2 np4 np4 np4 γ γ γ e1 e1 e1 1/2 1/2 1/2 γ 2P 3/2 np5 np5 2P 3/2 γ np5 2P 3/2 γ 1S0 1S0 1S0 np6 np6 np6 A A+ A++ A A+ A++ A A+ A++ A+++

Double charged ion yield for different mechanisms Makris and Lambropoulos, Phys. Rev. A 77, 023401 (2008) 38,4 eV 42,8 eV direct sequential 2g direct sequential 3g sequential 3g

Selected topics on sequential two-photon double ionization np4 γ e1 1. Angular correlation between e1 and e2 and coherence. 2. Angular distribution of electrons e1 and e2 and entanglement. 1/2 γ np5 2P 3/2 1S0 np6 A A+ A++

FEL Angular distribution of electrons in single photon ionization E θ1 Linearly polarized XUV radiation, Z ║ E Angular distribution of photoelectron FEL E θ1 Z asymmetry parameter e1

1st step: polarization of the ion Polarized ion (Ji=1/2, 3/2) observed Polarization depends on the e1 emission angle Polarization of ion: 1st step photoionization dynamics photon polarization (kγ=0,2) 1st electron angle part Linearly polarized photons Z ║ E

Angular correlations between two photoelectrons Photoionization from polarized ion: 2nd step photoionization dynamics 2nd electron angle part depolarization factor generally: the coherent summation over intermediate ionic levels photon polarization (kγ=0,2) memory of the photoion after the first step Notes: - the angular correlation function actually depends on the difference φ2 – φ1 - the angle θ1 can be chosen θ1 = 0.

Angular correlation pattern FLASH 44 eV, ~25 fs, ~5·1013 W/cm2 Ne Ne+ Ne++ 2p6 2P1/2,3/2 1S0 1D2 3P0,1,2 2p5 2p4 γ e2 e1 E FEL Z θ1 θ2 e1 e2 Two-electron angular correlation function perpendicular to the photon beam summed over the Ne++ 2p4 3P0,1,2 final fine-structure levels and over the Ne+ 2p5 2P1/2,3/2 fine-structure intermediate ion levels W(θ1, ϕ1=0; θ2, ϕ2=0) From Kurka et al, J. Phys. B 42, 141002 (2009)

Angular correlation pattern J=1/2 0.097 eV ~ 6.8 fs J=3/2 photon pulse in the frequency domain Ne+(2p5) for very short pulses the excitation could be coherent W(θ1, ϕ1=0; θ2, ϕ2=0) From Kurka et al, J. Phys. B 42, 141002 (2009)

axis is strictly forbidden Selection rules of Maulbetsch and Briggs J.Phys.B 28 551 (1995) Transitions to the 3P final state with emission of electrons along the polarization axis is strictly forbidden Fritzsche et al, 2008

Transition from coherent to incoherent excitation of fine structure intermediate ionic levels coherent (“LS-coupling”) incoherent Ne, 50 eV Kr, 34 eV 4p4 3P final Kr++ state

Angular correlation pattern J=1/2 0.097 eV ~ 6.8 fs J=3/2 photon pulse in the frequency domain Ne+(2p5) for very short pulses the excitation should be coherent W(θ1, ϕ1=0; θ2, ϕ2=0) From Kurka et al, J. Phys. B 42, 141002 (2009)

On the angular distributions of the 1st and 2nd step electrons 2nd step electrons (1st electrons not observed): Alignment of the ion after the 1st step Angular distribution of photoelectrons in single ionization: 1st step electrons (2nd step electrons not observed): a new term due to occurrence of the 2nd step !

On the angular distributions of the 1st step electrons θ1 E If nothing else is further happening with the system and only e1 is observed then W1~ 1 + β2P2(cos θ1) L=0 L=1 γ1 A A+

On the angular distributions of the 1st step electrons θ1 E If nothing else is further happening with the system and only e1 is observed then W1~ 1 + β2P2(cos θ1) L=0 L=1 γ1 A A+ Step 2 e1 θ1 The total yield of A++ depends on polarization of A+, which in turn depends on θ1 E A++ L=1 L' γ2 A+ e2 Therefore if one selects events with production of A++, the e1 angular distribution gets additional θ1 dependence. Unobserved W1~ 1 + β2P2(cos θ1) + β4P4(cos θ1)

On the angular distributions of the 1st step electrons θ1 E If nothing else is further happening with the system and only e1 is observed then W1~ 1 + β2P2(cos θ1) L=0 L=1 γ1 A A+ Step 2 e1 θ1 The total yield of A++ depends on polarization of A+, which in turn depends on θ1 E A++ L=1 L' γ2 A+ e2 Therefore if one selects events with production of A++, the e1 angular distribution gets additional θ1 dependence. Unobserved W1~ 1 + β2P2(cos θ1) + β4P4(cos θ1) Angular distribution of e1 depends on further scenario: either single ionization (one photon absorbed), or double ionization (two photons absorbed), etc.

On the angular distributions of the 1st step electrons SR FEL A+ A++ A+ A++ W1~ 1 + β2P2(cos θ1) W1~ 1 + β2P2(cos θ1) + β4P4(cos θ1)

On the angular distributions of the 1st step electrons SR FEL A+ A++ A+ A++ W1~ 1 + β2P2(cos θ1) W1~ 1 + β2P2(cos θ1) + β4P4(cos θ1) Quantification in terms of entanglement (concurrency) of e1 and A+, e1 and A++, etc. EPR-like paradox Angular distribution of e1 depends on further scenario: either single ionization (one photon absorbed), or double ionization (two photons absorbed), etc.

Ne Angular distribution of the 2nd step electrons Final state Ne++ 3P (1st electrons not observed) Ne (unresolved 2p4 3P0,1,2 and 2p5 2P1/2,3/2) Final state Ne++ 3P Braune et al, 2007 Kurka et al, 2009 (Fritzsche et al, 2008; Kurka et al, 2009) MCHF MCDF HF Kheifets, 2007

Ne Angular distribution of the 2nd step electrons Final state Ne++ 3P (1st electrons not observed) Ne (unresolved 2p4 3P0,1,2 and 2p5 2P1/2,3/2) Final state Ne++ 3P Kurka et al, 2009 JPB 42, 141002 (2009) (Fritzsche et al, 2008; Kurka et al, 2009) MCHF MCDF HF Kheifets, 2007

γ γ γ γ γ Two- and three-photon sequential processes A A+ A++ A A+ A++ Two-photon double ionization Three-photon double resonant ionization e2 e2 γ 1S0 1S0 1D2 1D2 3P0,1,2 3P0,1,2 np4 np4 γ γ e1 e1 1/2 1/2 γ np5 2P 3/2 np5 2P 3/2 γ 1S0 1S0 np6 np6 A A+ A++ A A+ A++

γ γ γ Three-photon sequential double resonant ionization of Ar e2 1S H. Fukuzawa et al, J. Phys. B, v.43, 111001 (2010) e2 γ 1S 3rd step 1D 3P Ar++ 3p4 Ar+* 3p4 nl γ 2nd step e1 γ Ar+ 3p5 2P1/2,3/2 1st step 24.47 eV 100 fs 2 ∙1012 W/cm2 Ar 3p6 1S SPring-8 Compact SASE Source (SCSS) , Japan

Three-photon sequential double resonant ionization of Ar 24.47 eV H. Fukuzawa et al, J. Phys. B, v.43, 111001 (2010)

γ γ γ Three-photon sequential double resonant ionization of Ar e2 e1 Y. Hikosaka et al, Phys. Rev. Lett. 105, 133001 (2010) SCSS, Japan 100 fs, 20 Hz, shot-by-shot 21.0, 21.2, 21.4 eV 47.51 γ 1S e2 45.13 1D 43.4 3P2,1,0 +(2P) 3p4 3p4(1D)3d2D 3/2 37.19 5/2 37.13 γ e1 γ 1/2 15.94 3/2 15.76 3p5 2P 3p6 1S Ar Ar+ Ar2+

γ γ γ Three-photon sequential double resonant ionization of Ar e2 e1 N. Miyauchi et al, J. Phys. B 44, 071001 (2011) SCSS, Japan 100 fs, 20-30 Hz 3 ∙1013 W/cm2 21.4 eV (TOF under θ=0) 47.51 γ 1S e2 45.13 1D 21.65 eV 43.4 3P2,1,0 +(2P) 3p4 3p4(1D)3d2D 3/2 37.19 5/2 37.13 γ 23.8 eV e1 γ 1/2 15.94 3/2 15.76 3p5 2P 24.6 eV 3p6 1S Ar Ar+ Ar2+

Three-photon sequential double resonant ionization of Ar N. Miyauchi et al, J. Phys. B 44, 071001 (2011)

Three-photon sequential double resonant ionization of Ar Experiments by groups of M.J.J.Vrakking and K. Ueda (PSD with MPSs) SCSS, Japan 100 fs, 30 Hz 1.5 ∙1013 W/cm2 21.3; 21.45 eV 21.3 eV

γ γ γ Three-photon sequential double resonant double ionization of Ar Experiments by groups of M.J.J.Vrakking and K. Ueda (PSD with MPSs) 3p3n1ℓ1n2ℓ2 58.2-58.7 21.3 eV 47.51 γ 1S e2 45.13 1D 43.4 3P2,1,0 +(2P) 3p4 3p4(1D)3d 2D 3/2 37.19 5/2 37.13 γ e1 γ 1/2 15.94 3/2 15.76 3p5 2P 3p6 1S Ar Ar+ Ar2+

γ γ γ Three-photon sequential double resonant double ionization of Ar E. Gryzlova et al, PRA, accepted 3p3n1ℓ1n2ℓ2 58.2-58.7 21.3 eV 47.51 γ 1S e2 45.13 1D 43.4 3P2,1,0 +(2P) 3p4 3p4(1D)3d 2D 3/2 37.19 5/2 37.13 γ e1 γ 1/2 15.94 3/2 15.76 3p5 2P 3p6 1S Ar Ar+ Ar2+

γ γ γ Three-photon sequential double resonant double ionization of Ar E. Gryzlova et al, PRL, accepted 3p3n1ℓ1n2ℓ2 58.2-58.7 21.3 eV 47.51 γ 1S e2 45.13 1D 43.4 3P2,1,0 +(2P) 3p4 3p4(1D)3d2D 3/2 37.19 5/2 37.13 γ e1 γ 1/2 15.94 3/2 15.76 3p5 2P 3p6 1S Ar Ar+ Ar2+

Three-photon sequential double resonant double ionization of Ar E. Gryzlova et al, PRA, accepted Angular distribution of photoelectrons Exp (groups of M.J.J.Vrakking and K. Ueda) “single resonant” “double resonant” k = 2,4,6

γ γ γ γ γ γ γ γ Two- and three-photon sequential processes: A A+ A++ A Two-photon double ionization Three-photon double-resonant double ionization Three-photon triple ionization 2P e3 2D 4S np3 γ e2 e2 γ 1S0 1S0 1S0 e2 1D2 1D2 1D2 3P0,1,2 3P0,1,2 3P0,1,2 np4 np4 np4 γ γ γ e1 e1 e1 1/2 1/2 1/2 γ 2P 3/2 np5 np5 2P 3/2 γ np5 2P 3/2 γ 1S0 1S0 1S0 np6 np6 np6 A A+ A++ A A+ A++ A A+ A++ A+++

γ Three-photon sequential triple ionization of Ne NeI NeII NeIII NeIV A. Rouzée et al, Phys. Rev. A 83, 031401(R) (2011) FLASH 5 Hz, ~20 fs 1∙1013 W/cm2 90.5 eV (13.7 nm) e3 2P e3 e2 e1 2D 20 40 60 Electron kinetic energy, eV e2 4S 2p3 γ e1 1S0 1D2 3P0,1,2 2p4 1/2 3/2 2p5 2P 1S0 2p6 NeI NeII NeIII NeIV

Three-photon sequential triple ionization of Ne A. Rouzée et al, Phys. Rev. A 83, 031401(R) (2011) 20 40 60 Electron kinetic energy, eV θ3=mag θ3=0 θ3=90

Concluding remarks Experiments with FELs combined with photoelectron spectroscopy directly confirm sequential mechanism of double and triple ionization from the outer shells of noble gas atoms in the XUV. Studies of sequential ionization give a new tool for probing ionic continua, including autoionizing states of the ions which can crucially influence photoelectron spectra and angular distributions of photoelectrons. Theoretical calculations within the stepwise model are so far in accordance with the observed photoelectron spectra; additional studies, both experimental and theoretical are needed for angular distributions and angular correlations of photoelectrons. Within the stepwise model, dynamic connection between different ionization steps is due to polarization of the intermediate ionic states. This polarization is important in shaping of the angular distributions and angular correlations of photoelectrons.

Some attractive points for further investigation: Ionization from the inner shells: competition between sequential photoionization and Auger decay. More on competition and interference between sequential and direct mechanisms of multiple ionization Sequential photoionization in the region of autoionizing states, both atomic and ionic Entanglement of photoelectrons and photoions from different photoionization steps Nondipole effects in sequential photoionization

Thank you for attention!

Focusing the FEL for electron spectroscopy (from K. Ueda) Top view TOF-B TOF-A hv = 24.47 eV (51 nm) Facility mirrors FEL TOF-C Molecular beam TOF-D TOF length = 256 mm Acceptance = 0.0015 x 4p sr Spring-8 Compact SASE Source test accelerator; details in JPB 43, 111001 (2010) 50

! Kr , hv = 34 eV Some more angular correlation functions Intermediate state: Kr+ 4p5 2P3/2 ! (because of P-state)