Atomic double slit: Coherence transfer through excitation and (Auger) decay processes. S. Fritzsche, Kassel University Göteborg, 3rd June 2006

Transcription

1 Atomic double slit: Coherence transfer through excitation and (Auger) decay processes S. Fritzsche, Kassel University Göteborg, 3rd June 2006

2 Experiments with double slits (Feynman-Lectures 1962) Interference experiments with balls P I 1 1 P12 = P1 + P2 P1 Double slit Interference experiments with water waves I12 = A1 + A2 2 wall Intensity momentum p λ wave length energy ν frequency E ~ square of amplitudes

3 Quantum particles behave differently (Feynman-Lectures 1962) Interference electrons with experiments P1 ~ φ 2 P12 = φ1 + φ2 2 Doppelschlitz Wand de'broglie Relationen momentum p = h λ wave length energy = h ν frequency E Particle-wave dualism: Quantum particles are neither particles nor waves.

4 Doppelspaltexperiment mit Elektronen A. Tanamura et al., Am. J. Phys. 57 (1989) 117

5 Atomic double slit: Coherence transfer through excitation and (Auger) decay processes S. Fritzsche, Kassel University Göteborg, 3rd June 2006 Evidence of particle-wave dualism even for much larger particles: (single) photons, electrons, neutrons, helium,..., buckyballs Ion-atom collisions, multi-photon processes, atoms in laser fields How becomes the quantum world a classical and macroscopic one? What about the double slit for single atoms and molecules? i) Multipole mixing of the radiation field: Decay of high-z ions ii) Coherence transfer through Auger cascades iii) Spin-state interferences in the photoemission from magnetized materials What can we learn from such coincidence experiments and the observed interferences? Correlation problem --- Electron-electron interactions in many-particle systems Support for other fields: Creation of entanglement in atomic systems

6 Multipole mixing of the radiation field -- in the capture and decay of highly-charged ions

7 Electron capture at storage rings into high-z ions ~ d M 2 So far... polarization total cross sections d ~ M 2 d polarization New directions... angular distributions polarization ~ M 2 Alignment studies No summation over polarization states!

8 So far... total cross sections d ~ M 2 d polarization New directions... angular distributions ESR Alignment studies Collaboration with Andrey Surzhykov and Thomas Stöhlker and coworkers

9 Capture into the 2p3/2 excited states of initially bare ions Magnetic sublevel population of the residual ion can not be measured directly Lyman α 1 But: knowledge on population of excited ion state may be derived from the properties of subsequent decay 1s1/2 U91+ Tp = 310 MeV/u fitting W 1 P 2 cos Theory: 1 =±3 /2 =±1/2 = 2 =±3 /2 =±1/2 b b anisotropy parameter angular distribution (arb. units) 2p3/2 b b alignment of the 2p3/2 state: relative sublevel jb mb> population observation angle (deg) Th. Stöhlker et al. PRL 79 (1997) 3270 beam energy (MeV/u) J. Eichler et al. PRA 58 (1998) 2128

10 Density matrix theory: Time-independent description Initial state Final state t i t f S f = S i S Measurement of physical properties: 'detector operator' describes the experimental setup: P= probability to get a 'click' at the detectors: W =Tr P f = 1... m P f 1... m 1... m - scattering operator

11 Density matrix theory: Radiative Recombination of high-z ions bare ion + free electron H-like ion + emitted photon nb j b b, k RR b n b j b 'b, k RR ' = S fi p m s e p ms S fi ms! e ag t n a v d a t a e Gr Using the density matrix, the system can be accompanied through several steps of the interaction which may lead to the emission of photons, electrons,...

12 Effective anisotropy parameter -- Contributions from higher multipoles W 1 eff P 2 cos effective anisotropy parameter eff = 1 ±3 / 2 ±1 / 2 f E1, M2 2 ±3 / 2 ±1 / 2 alignment parameter structure function f E1, M M2 E1 P1 ~ φ 2p3/2 2 E1 M2 1s1/2 P12 = φ1 + φ2 2 Double slit screen

13 Effective anisotropy parameter -- Contributions from higher multipoles W 1 eff P 2 cos effective anisotropy parameter eff = 1 ±3 / 2 ±1 / 2 f E1, M2 2 ±3 / 2 ±1 / 2 alignment parameter structure function f E1, M p3/2 E1 1s1/2 M2 M2 E1

14 Effective anisotropy parameter -- Contributions from higher multipoles W 1 eff P 2 cos effective anisotropy parameter eff = 1 ±3 / 2 ±1 / 2 f E1, M2 2 ±3 / 2 ±1 / 2 alignment parameter structure function f E1, M M2 E1 2p3/2 E1 1s1/2 M2 In contrast, contributions to decay rates appear additive: M2 tot 2 M E1 even for U91+

15 A. Surzhykov, S.F. et al. PRL 88 (2002) U91+ Tp = 310 MeV/u W 1 eff P 2 cos fitti ng effective anisotropy parameter angular distribution (arb. units) E1-M2 multipole mixing: Alignment of the 2p3/2 state observation angle (deg) Alignment studies allow us to explore magnetic interactions in the bound-bound transitions in H-like ions! Proposal for measuring M2 contributions: Experiment at GSI: Γ M2 = ± Γ E1 eff beam energy (MeV/u) Theory: A. Muthig, PhD thesis, GSI (2004)

16 A.Surzhykov et al. PRA 71 (2004) Two-photon decay of highly-charged ions 2s1/2 E1E1 + E1M2 + M1M1+E2E2 + E2M1... 1s1/2 Higher multipoles give rise to an asymetrical shift tot E1E1=8.229 Z 6 2 W ~1 cos

17 Lyman-a vs. K-a emission from high-z ions -- Influence of the shell structure (initially) bare ion (initially) H-like ion Ly-a1 is strongly anisotropic X. Ma et al, PRA 68 (2003) U92+ Tp = 309 MeV/u U91+ Tp = 102 MeV/u K-α1 is isotropic

18 Lyman-a vs. K-a emission from high-z ions -- Influence of the shell structure (initially) bare ion (initially) H-like ion Ly-a1 is strongly anisotropic X. Ma et al, PRA 68 (2003) U92+ Tp = 309 MeV/u E1: W E1~1 U91+ Tp = 102 MeV/u 1 A2 J =1 P 2 cos 2 M2: W M2 ~1 5 A2 J =2 P 2 cos 14 K-α1 is isotropic

19 Lyman-a vs. K-a emission from high-z ions -- Influence of the shell structure (initially) bare ion (initially) H-like ion Alignment of the 2p3/2 state U91+ A. Surzhykov et al., PRA (2005) submitted

20 K-α1 decay of highly-charged ions A.Surzhykov et al., PRL (2006) submitted -- angular distribution as observed in experiment W K ~ N J =1 W E1 N J =2 W M2 1 =1 N J =1 N J =1, N J =2 1 5 A 2 J =1 N J =2 A2 J =2 P 2 cos 14 2 relative populations of J=1, 2 states N J =1 =N J =2 = 1 2 N J =1= 3 5 N J =2= 8 8 Calculations have been done for L-REC of U91+ with Tp = 100 MeV/u E1+M2 E1 only

21 Coherence transfer through Auger cascades -- superposition of decay pathes in Hilbert space Electron emission from excited states: A* A+(*) + e-auger A++ + e-auger +... dominant process Auger cascades A++(*) + e-auger,1 + e-auger,2 double Auger decay A++(*) + e-auger + hω radiative Auger decay

22 Auger emission of excited atomic states A+(K-1) energy εauger excitation A++(L-2) L A K H = i decay H = hi u r i hi i i j 1 r ij Wentzel's ansatz: Autoionization is caused by electron-electron interactions which cannot be considered in an one-particle picture. i j 1 r ij i u r i Ideal tool for a better understanding of electronic correlations!

23 Coherence transfer in the Auger cascades of noble gases -- a signature of the atomic double slit resonantly excited noble gas np --> (n+2)s, (n+2)d Well isolated resonances! ω12 >> Γ A2+ Decay branches are independent; path can be determined by measuring the energy spectrum. Collaboration with Nicolai Kabachnik (Bielefeld); experiments by Kyioshi Ueda and coworkers at SPring8, Japan

24 Coherence transfer in the Auger cascades of noble gases -- a signature of the atomic double slit resonantly excited noble gas np --> (n+2)s, (n+2)d Overlapping resonances! ω12 < Γ Young's experiment: (Feynman-Lectures 1962) P1 ~ φ 2 A2+ How depend the Auger electron emission and, in particular, their angular distributions on the splitting of the resonances? Initial state Final state t i P12 = φ1 + φ2 2 double slit wall t f f = S i S

25 Coherence transfer in the Auger cascades of noble gases -- a signature of the double slit Angular distribution of the second-step electron for double-slit decay: J J ' c W = J 1, J 1 ' ; J 2 J 1, J 1 ' k,j J ' J J ' J 1 1, coherent summation 1 dynamics of Auger emission electron-electron correlations 1 1 P k cos 1 1 J1' memory on the creation process geometry of the double slit Many-particle Auger amplitudes <J, lj H-E J'> Accurate evaluation: Multiconfiguration Dirac-Fock wave functions for the inner-shell hole states and use of the RATIP package for calculating atomic amplitudes for different transition and ionization properties and for different computational models.

26 S. Fritzsche, JESRP (2001) 1155; Phys. Scr. T100 (2002) 46 RATIP Relativistic Atomic Transition and Ionization Properties (CPC library) Relativistic CI wave functions including QED estimates and mass polarization RELCI, CPC 148 (2002) 103 LSJ spectroscopic notation from jj-coupled computations LSJ, CPC 157 (2003) 239 nc P J M = cr r P J M r Auger rates, angular distributions and spin polarization; level widths AUGER Many-electron basis (wave function expansions) Construction and classification of N-particle Hilbert spaces Shell model: Systematically enlarged CSF basis Interactions Photoionization cross sections and (non-dipole) angular parameters PHOTO Breit interactions + QED Radiative and dielectronic recombination; angle-angle correlations Electron continuum; scattering phases REC Dirac-Coulomb Hamiltonian Coherence transfer and Rydberg dynamics...

27 Excitation and two-step Auger cascades in noble gases: Argon Photoabsorption: Ar (2p6 3s2 3p6 1S0) + hν Ar*(2p5 3s2 3p6 4s 1P1) First decay: Ar*(1P1) Ar*+(3s 3p5 (1,3P) 4s 2P or 4P) + ea1 Second decay: Ar*+ (3s 3p5 (1P) 4s 2P1/2,3/2) Ar2+ (3p4 3P or 1D) + ea2

28 Angular distribution of the resonant Auger electrons -- recorded in coincidence with the second-step electron Second-step electron perpendicular to the photon polarization θ = 270 Coincidence between the resonance Ar(1P1) - Ar+(3s3p5 (1P)4s 2 P1/2,3/2) and the second-step electron Ar+ (3s 3p5 (1P) 4s 2P1/2,3/2) - Ar2+ (3p4 3P) und - Ar2+ (3p4 1D2) I(θ) = A0 + A2 cos 2θ + A4 cos 4θ Experimental data and compared with calculated parameters A0, A2, and A4. Ueda et al., JPB 34 (2001) 107 Ueda et al., Phys. Rev. Lett. 95 (2003)

29 Excitation and two-step Auger cascades in noble gases Photoabsorption: Ar (2p6 3s2 3p6 1S0) + hν Ar*(2p5 3s2 3p6 4s 1P1) First decay: Ar*(1P1) Ar*+(3s 3p5 (1,3P) 4s 2P or 4P) + ea1 Second decay: Ar*+ (3s 3p5 (1P) 4s 2P1/2,3/2) Ne: 500 : 1 Ar: 80 : 1 Kr: 25 : 1 Xe: 8:1 Ar2+ (3p4 3P or 1D) + ea2 Aresonance Aintercombination excitation hν Xenon: 4d-16p 1,3P 1 5s-26p; 5s5p56p Kitajima et al., JPB 34 (2001) 3829; JPB 35 (2002) ω12 < Γ subsequent decay Radiative and Auger processes are not longer independent!

30 Angular correlations between the subsequently emitted Auger electrons Resonantly excited xenon: a) 4d-1 6p J=1 -- 5s5p5 (1P)6p -- 5s2 5p4 1D2 b) 4d-1 6p J=1 -- 5s5p5 (1P)6p -- 5s2 5p4 3P2 Ueda et al., JPB 36 (2003) 319 Angular dependence of the first-step Auger electron relative to the polarization of the incoming light and measured in coincidence with the second-step Auger electron at a fixed angle of 270.

31 Spin-state interferences -- in the emission of photoelectrons from magnetized Gd

32 4f photoemission of metallic gadolinium -- in the vincinity of the 4d - 4f giant resonance γ + Gd (4d 4f ; S7/2) E = ev Gd (4d10 4f 6; 7FJ) + ε l Experiments at BESSY in Berlin Normal incident and normal electron emission Metallic gadolinium ep ~ ez Collaboration with Nicolai Kabachnik and the group of Ullrich Heinzmann

33 4f photoemission of metallic gadolinium -- in the vincinity of the 4d - 4f giant resonance γ + Gd (4d 4f ; S7/2) E = ev Gd (4d10 4f 6; 7FJ) + ε l Super Coster-Kronig Gd (4d 9 4f 8; 8D9/2) Normal incident and normal electron emission Mechanisms: Metallic gadolinium ep ~ ez Polarization transfer from the circular polarized light to the photo electron due to spin-orbit interaction (~ Pz) Enhanced by the resonant process owing to the intermediate state with well-defined total J

34 4f photoemission of metallic gadolinium -- electron polarization without magnetization Normal incident and normal electron emission Metallic gadolinium ep ~ ez at E = ev Pz = < 0.04 Experiments at BESSY in Berlin off-resonance

35 4f photoemission of metallic gadolinium -- ferromagnetic case due to external field γ + Gd (4d 4f ; S7/2) E = ev Gd (4d10 4f 6; 7FJ) + ε l Super Coster-Kronig Gd (4d 9 4f 8; 8D9/2) Normal incident and normal electron emission Mechanisms: Metallic gadolinium ep ~ ez Polarization transfer from the circular polarized light to the photo electron due to spin-orbit interaction (~ Pz) Polarization due to magnetization of the target (~ Px) M ~ ex Initial orientation of 4f electrons is conserved in direct emission. Coherent superposition results in Py component φ = a φa + b φb Interferences in spin space of the photoelectron!

36 N. Müller et al., PRL (2006) submitted 4f photoemission of metallic gadolinium -- ferromagnetic case due to external field Coherent superposition results in Py component φ = a φa + b φb Calculations for open f-shell elements performed with RATIP in the MCDF model.

37 Summary and outlook Particle-wave dualism has been confirmed in a large number of experiments; many gedanken experiments can be carried out today which - for a long time - have been discussed only theoretically. The comparison of these experiments with our theoretical concepts shows: There is no simple (nor obvious) alternative to quantum mechanics, although the Born interpretation of the amplitudes is usually sufficient to understand most observations. Experimental challenge consists not only in the verification of the wave phenomena for ever larger objects but also in a better understanding of the dynamics of many-particle systems. For example, it appears unlikely that the area of quantum information would be as lively as it is today both theoretically and experimentally if quantum phenomena had not be demonstrated for/with individual particles. Present and future challenges for atomic theory : Improved treatment of open-shell structures and highly excited states, including the coupling of bound states to the continuum (capture and emission of electrons, Fano resonances, complete experiments ).

38 (Chicago University)