31 st International Free Electron Laser Conference

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Evidence for Position Based Entanglement in Auger Electron Emission from N and

1 FHI-BERLIN ASG at CFEL MAX-PLANCK-GESELLSCHAFT 3 st International Free Electron Laser Conference 3 rd - 8 th August, 009 BT Convention Centre Liverpool, UK Evidence for Position Based Entanglement in Auger Electron Emission from N and Dissociating O Molecules Uwe Becker Fritz-Haber-Institut der Max-Planck-Gesellschaft Berlin-Dahlem

2 Outline Basic behavior of molecular double-slit experiments in momentum space: Constant versus oscillatory behaviour Dichotomic variables in ordinary space: g/u coherent symmetry states versus f/b emission direction intensities Intramolecular scattering causing electron emission line asymmetries in ordinary space Molecular fragment velocity causing electron emission line splitting in kinetic energy Electron-ion coincidence based quantum eraser

3 Single double slit experiment with single electrons Physics World made a poll on the question what was the most beautiful experiment mankind has ever been done. The result: The single electron double-slit experiment R. P. Crease, Physics World, p5 (September 00) slits detector screen source of electrons aperture No well defined momentum, but localized position C. Jönsson, Zeitschrift für Physik, 6, 454 (96)

4 Single double slit experiment with single electrons Physics World made a poll on the question what was the most beautiful experiment mankind has ever been done. The result: The single electron double-slit experiment R. P. Crease, Physics World, p5 (September 00) slits detector screen source of P =! electrons aperture No well defined momentum, but localized position C. Jönsson, Zeitschrift für Physik, 6, 454 (96)

5 Single double slit experiment with single electrons Physics World made a poll on the question what was the most beautiful experiment mankind has ever been done. The result: The single electron double-slit experiment R. P. Crease, Physics World, p5 (September 00) detector screen source of P =! electrons aperture No well defined momentum, but localized position C. Jönsson, Zeitschrift für Physik, 6, 454 (96)

6 Single double slit experiment with single electrons Physics World made a poll on the question what was the most beautiful experiment mankind has ever been done. The result: The single electron double-slit experiment R. P. Crease, Physics World, p5 (September 00) detector screen source of P =! electrons P =! aperture No well defined momentum, but localized position C. Jönsson, Zeitschrift für Physik, 6, 454 (96)

7 Single double slit experiment with single electrons Physics World made a poll on the question what was the most beautiful experiment mankind has ever been done. The result: The single electron double-slit experiment R. P. Crease, Physics World, p5 (September 00) detector screen source of electrons + P =! P =! aperture C. Jönsson, Zeitschrift für Physik, 6, 454 (96)

8 Single double slit experiment with single electrons Physics World made a poll on the question what was the most beautiful experiment mankind has ever been done. The result: The single electron double-slit experiment R. P. Crease, Physics World, p5 (September 00) detector screen P =! source of + electrons P =! aperture Now momentum well-defined, but position delocalized C. Jönsson, Zeitschrift für Physik, 6, 454 (96)

9 Single double slit experiment with single electrons Physics World made a poll on the question what was the most beautiful experiment mankind has ever been done. The result: The single electron double-slit experiment R. P. Crease, Physics World, p5 (September 00) detector screen P =! source of + electrons P =! P =!+! aperture Now momentum well-defined, but position delocalized C. Jönsson, Zeitschrift für Physik, 6, 454 (96)

10 Wheeler s Delayed-Choice Gedanken Experiment Which way information versus interference pattern B 00 splitter out mirror Single-photon pulse Path BS output D detectors D Counts Phase shift (rad) splitter in BS input Path mirror Mach-Zehnder Interferometer Jaques et al. Science 35, 966 (007) A Counts Phase shift (rad) quantum eraser

= Ν {ψ s (a) + ψ s (b) + ψ s (a)ψ s (b)} b)sign change ungerade u ψ

11 Inversion behavior of homonuclear molecules gerade and ungerade combination a)sign conservation gerade g ψ = Ν {ψ s (a) + ψ s (b)} = Ν {ψ s (a) + ψ s (b) + ψ s (a)ψ s (b)} b)sign change ungerade u ψ = Ν {ψ s (a) - ψ s (b)} = Ν {ψ s (a) + ψ s (b) - ψ s (a)ψ s (b)} Ψ Ψ Ψ Ψ

12 Phototelectron spectroscopy and electron configuration N p s s initial state atomic levels

13 Phototelectron spectroscopy and electron configuration N N N 3σ u p π g p 3σ g π u s σ u s σ g s σ u s σ g initial state atomic levels molecular levels atomic levels

14 Phototelectron spectroscopy and electron configuration N N N N + 3σ u p π g p 3σ g π u s σ u s 00 mev σ g hν photoelectron s σ u s σ g initial state atomic levels molecular levels atomic levels final ionic state

15 Molecule frame angular distributions of the energy resolved g/u symmetry photoline components: Proof of delocalized electron emission in inversion symmetric systems 4x0 3 N : N(s) hν = 49 ev (shape resonance) 0. ev Intensity [counts] ev v=3 0. ev v= v= g u N N N N Kinetic energy [ev] 9.5 Rolles et al., Nature 437, 7 (005)

16 Proof of molecular double slit s in nature Subtracting the various scattering processes reveals the basic behavior of molecular Which way information versus interference pattern Kinetic energy (ev) photoemission in momentum space. Non-oscillating flat behavior for heteronuclear molecules Intensity (arb. units) f b π.0 π.5 π.0 π.5 π 3.0 π - k (R eff ). Oscillating behavior for homonuclear molecules. The oscillation period is proportional to R - Intensity (arb. units) g u Zimmermann et al. Nature Physics 4, 649 (008)

17 The two-fold double slit experiment: EPR s proposal to prove the completeness of QM in ordinary space screen detector detector screen source of spatially entangled electrons Entanglement of position and momentum Einstein, Podolski and Rosen, Phys. Rev. 47, 777 (935)

18 The two-fold double slit experiment: EPR s proposal to prove the completeness of QM in ordinary space screen detector detector screen P =! source of spatially entangled electrons P =! Entanglement of position and momentum Einstein, Podolski and Rosen, Phys. Rev. 47, 777 (935)

19 The two-fold double slit experiment: EPR s proposal to prove the completeness of QM in ordinary space screen detector detector screen P =! source of spatially entangled electrons P =! Entanglement of position and momentum Einstein, Podolski and Rosen, Phys. Rev. 47, 777 (935)

20 The two-fold double slit experiment: EPR s proposal to prove the completeness of QM in ordinary space screen detector detector screen P =! source of spatially P =! P =! entangled electrons P =! Entanglement of position and momentum Einstein, Podolski and Rosen, Phys. Rev. 47, 777 (935)

21 The two-fold double slit experiment: EPR s proposal to prove the completeness of QM in ordinary space screen detector detector screen P =! source of spatially P =! P =! entangled electrons P =! Entanglement of position and momentum Einstein, Podolski and Rosen, Phys. Rev. 47, 777 (935)

22 The two-fold double slit experiment: EPR s proposal to prove the completeness of QM in ordinary space screen detector detector screen P =! source of spatially P =! P =! entangled electrons P =! Entanglement of position and momentum Einstein, Podolski and Rosen, Phys. Rev. 47, 777 (935)

23 The two-fold double slit experiment: EPR s proposal to prove the completeness of QM in ordinary space screen P =! detector detector screen P =! source of spatially? P =! entangled electrons P =! Entanglement of position and momentum Einstein, Podolski and Rosen, Phys. Rev. 47, 777 (935)

24 The two-fold double slit experiment: EPR s proposal to prove the completeness of QM in ordinary space screen P =! detector detector? + P =! P =!+! P =! source of spatially + screen entangled electrons P =! Entanglement of position and momentum Einstein, Podolski and Rosen, Phys. Rev. 47, 777 (935) P =!+!

25 Bell s analytic realization of ERP s original proposal to prove the completeness of quantum mechanics variably selected phase variably selected phase screen P =! detector detector + Δϕ P =! Δϕ + P =! source of spatially P =!+! screen entangled electrons P =! Entanglement of position and momentum Einstein, Podolski and Rosen, Phys. Rev. 47, 777 (935) P =!+!

26 Bell s analytic realization of ERP s original proposal to prove the completeness of quantum mechanics variably selected phase fixed selected phase screen P =! detector detector + Δϕ P =! Δϕ + P =! source of spatially P =!+! screen entangled electrons P =! Entanglement of position and momentum Einstein, Podolski and Rosen, Phys. Rev. 47, 777 (935) P =!+!

27 A coherence time based experiment of ERP s proposal to prove the completeness of quantum mechanics 3/.. splitter out (Δϕ = 90º) 4567)$ / 0 3.!"#$%&$"'()& *+#,-!".*&&%&!"#"$#%&' Δϕ!# () %-#,-# 45#37 45#36 () *+,-#.*&&%& entangled double-photon pair )*+/0",%#% ,-0'" Mach-Zehnder Interferometer 45)6$+#+ %%%35-) 70,,+,./ 03# '()*+,!"#$%'!"#$%&!"##!$## %## &##!# Δϕ!"./ +3#3# ()#)*#+,- 70,,+, # # $ & " %!# -./,0,.3+ 45/67 Entanglement of position and momentum splitter in (Δϕ = 0º) Jacques et al., Science 35, 966 (007) & Einstein, Podolski, Rosen, Phys. Rev. 47, 777 (935)

28 Einstein, Podolski and Rosen s key argument against the completeness of quantum mechanics This makes the reality of P and Q depend upong the process of measurement carried out on the first system, which does not disturb the second system in any way. No reasonable definition of reality could be expected to permit this. Einstein, Podolski and Rosen, Phys. Rev. 47, 777 (935)

29 The two-fold polarizer experiment: Bohm s adaption to prove the completeness of QM in spin space (+45º) + polarizer source of spin polarizer + (+45º) (-45º) - a direction entangled photons b direction - (-45º) Entanglement of spin orientations being either up or down (σz) or left or right (σx) A. Aspect, Nature, 446, 866 (007)

direction entangled photons b direction - (-45º) Entanglement of spin orientations

30 The two-fold polarizer experiment: Bohm s adaption to prove the completeness of QM in spin space (+45º) + polarizer source of spin polarizer + (+45º) Δϕ Δϕ (-45º) - a direction entangled photons b direction - (-45º) Entanglement of spin orientations being either up or down (σz) or left or right (σx) A. Aspect, Nature, 446, 866 (007)

31 Entanglement of spin and polarization eigenstates a) spin eigenstates (z-component) b) Polarization eigenstates state flipper phase flipper state flipper phase flipper

32 Entanglement of parity and momentum eigenstates a) Parity eigenstates b) Momentum eigenstates state flipper phase flipper state flipper phase flipper

33 Continuous variable EPR measurement Representation in momentum space on the f/b-poincaré sphere Position dependent behavior Right detection direction εp,d electron angular distribution of signal detector (signal beam) εp εd εp,d = electron momentum direction of reference detector (idler beam) Left detection direction

34 Phototelectron and Auger electron coincidence N N N 3σ u p π g p 3σ g π u s σ u s σ g s σ u s σ g initial state atomic levels molecular levels atomic levels

35 Phototelectron and Auger electron coincidence N N N N + 3σ u p π g 3σ g π u p s σ u σ g s hν photoelectron s σ u s σ g initial state atomic levels molecular levels atomic levels final ionic state

36 Phototelectron and Auger electron coincidence N N N N + 3σ u p π g 3σ g p Auger electron π u s σ u s σ g hν photoelectron s σ u s σ g initial state atomic levels molecular levels atomic levels final ionic state

s σ u s σ g hν photoelectron σ u s s σ g initial state

37 Phototelectron and Auger electron coincidence N N N N + 3σ u p π g 3σ g p Auger electron coincident detection π u s σ u s σ g hν photoelectron σ u s s σ g initial state atomic levels molecular levels atomic levels final ionic state

38 Auger electron-photoelectron coincidences: Proof of coherent superposition based localization L -90º g 90º u R u g Auger electron total Photoelectron gated (u) Photoelectron gated (g) Electron emission asymmetries in the molecule frame of N fr L R fl Photoelectron gated (L) Photoelectron gated (R) Schöffler et al., Science 30, 90 (008)

39 L Auger electron-photoelectron coincidences: Evidence for a violation of Bell s inequality -45º +45º g u R -45º fr +45º fl Auger electron total L R!!! -90º fr +90º fl momentum π π/ 0 +π/ π Reference detector angle (normalized fringe units) L R

40 L Auger electron-photoelectron coincidences: Evidence for a violation of Bell s inequality -45º +45º g u R -45º fr +45º fl Auger electron total L R!!! -90º fr +90º fl momentum π π/ 0 +π/ π Reference detector angle (normalized fringe units) L R

41 Time dependency of symmetry superimposed photoelectrons detected non- or coincidently with correspondently superimposed Auger electrons gerade channel ungerade channel forward channel backward channel 5 4 gerade ungerade intensity N 5 4 forward backward intensity N Intensity (arb. units) 3 Intensity (arb. units) O Doppler Time dependence Graph0_8 hidden intensity oscillation g Time (fs) u σg O Doppler Time dependence Graph0_7 σu b Time (fs) f revealed asymmetry oscillation Real time measurement of electron tunneling in momentum space

42 Specific symmetry state excitation & localized electron emission O * (σg) 3σ u π g (O+O*)+(O*+O) (O+O + )+(O + +O) + π u 3σ g σ u σ g hν σ u initial state σ g molecular levels final ionic state resonant Auger electron

43 Specific symmetry state excitation & localized electron emission O * (σg) 3σ u π g (O+O*)+(O*+O) (O+O + )+(O + +O) + π u 3σ g σ u coincident detection σ g hν σ u initial state σ g molecular levels final ionic state resonant Auger electron

44 Symmetry state excitation and localized electron emission "/-0'",+,0##$-0&'0"+#'&'" "!!"#$%&%' ()*"!+,"-&. 45$'$+"/-0'&'0$%!"#$%"&' ()(#*&+,!-54.+%$0(&&(/, 0%&3+0$%0-+#'&'" *!$)%,+#'&'" Björneholm et al., PRL 84, 86 (000)!"#$%&'()*$+%"(,$%!" $"$-*./,%0/$&%"/,3%4(*'%*'$%(/,

45 Symmetry state excitation and localized electron emission "/-0'",+,0##$-0&'0"+#'&'" "!!"#$%&%' ()*"!+,"-&. 45$'$+"/-0'&'0$% (&%)*%+!"!#$%&' (,!-.!#$"/'%%',+ 0%&3+0$%0-+#'&'" *!$)%,+#'&'" Björneholm et al., PRL 84, 86 (000)!"#$%&'()"#$*'+"$!" "*"0)!,+$/,"%$.-.$(!,/$)&"$',+

46 Experimental set-up!! 3/ 0&'(%4,/(." /99 :;<97/999 )'"'*+(')%&'(,-.&/0$.& +!"" # # 3

47 Experimental set-up +!"" # 3 #

48 counts Electron emission in dissociating O Proof of emitter velocity based localization early ions B coincidence results hν = ev Doppler localization A late ion late ions B early ion + 50 counts A O. Kugeler et al., PRL 93, 3300 (004) kinetic energy [ev] O.Kugeler et al., Phys. Rev. Lett. 93, 3300 (004)

Localized electron emission in dissociating O 50 00 early ions coincidence results hν = 539.

49 Localized electron emission in dissociating O early ions coincidence results hν = ev wrongly shifted Doppler components counts B A late ion late ions B early ion + 50 counts A O. Kugeler et al., PRL 93, 3300 (004) kinetic energy [ev] O.Kugeler et al., Phys. Rev. Lett. 93, 3300 (004)

50 Experimental set-up +!"" # 3 #

51 early Intensity (arb. units) molecular b e f e b s f s 0º "#$ 0 "#% Analys_O_V3 Graph_Pruemper Kinetic energy (ev) &'()*+,)-+'. "#"!"#%!"#$ " 6.)(>?@A%@B/ &'()*@C?@6.7(8 $ 5" :! " #$#% " <=:! " #&#% " < / 4" 6.7(89:;< %% %3" / /0"

52 '()*(+,)-./03.4(,)+5!"#!$#!## %# &# "# =>?*:4?0! " # "! $ # $ 90º "#$ $# "#% # C0DE!!AF4*=D*#6# "6$3# "6$38 "673# 9,(*),:.*(*;-./*<5 "6738 "6"3# &'()*+,)-+'. "#"!"#%!"#$ " 6.)(>?@A%@B/ &'()*@C?@6.7(8 $ 5" :! " #$#% " <=:! " #&#% " < / 4" 6.7(89:;< %% %3" / /0"

53 late Intensity (arb. units) molecular b e f e b s f s 80º "#$ 0 "#% Analys_O_V3 Graph_Pruemper Kinetic energy (ev) &'()*+,)-+'. "#"!"#%!"#$ " 6.)(>?@A%@B/ &'()*@C?@6.7(8 $ 5" :! " #$#% " <=:! " #&#% " < / 4" 6.7(89:;< %% %3" / /0"

54 early Intensity (arb. units) molecular b e f e b s f s 360º "#$ 0 "#% Analys_O_V3 Graph_Pruemper Kinetic energy (ev) &'()*+,)-+'. "#"!"#%!"#$ " 6.)(>?@A%@B/ &'()*@C?@6.7(8 $ 5" :! " #$#% " <=:! " #&#% " < / 4" 6.7(89:;< %% %3" / /0"

55 early Intensity (arb. units) molecular b e f e b s f s 360º "#$ 0 "#% Analys_O_V3 Graph_Pruemper Kinetic energy (ev) &'()*+,)-+'. "#"!"#%!"#$ " 6.)(>?@A%@B/ &'()*@C?@6.7(8 $ 5" :! " #$#% " <=:! " #&#% " < / 4" 6.7(89:;< %% %3" / /0"

56 early Intensity (arb. units) molecular b e f e b s f s 360º "#$ 0 "#% Analys_O_V3 Graph_Pruemper Kinetic energy (ev) &'()*+,)-+'. "#"!"#%!"#$ " 6.)(>?@A%@B/ &'()*@C?@6.7(8 $ 5" :! " #$#% " <=:! " #&#% " < / 4" 6.7(89:;< %% %3" / /0"

57 early Intensity (arb. units) molecular b e f e b s f s 360º "#$ 0 "#% Analys_O_V3 Graph_Pruemper Kinetic energy (ev) &'()*+,)-+'. "#"!"#%!"#$ " 6.)(>?@A%@B/ &'()*@C?@6.7(8 $ 5" :! " #$#% " <=:! " #&#% " < / 4" 6.7(89:;< %% %3" / /0"

58 (b-f)/(b+f) polarization of the Doppler signal in dependence of the fragment-ion beam direction #" )*+!,-.!/-*0 %&' %&( %&% $%&( $%&' % )*+!,-.!/-*0 7+4</:5!+4" 7!,&,' ">7!,-,' " "#&%! "#%! *034/45/-*0!06+47,!3" 8*99+4,:;-</ 7,-6;/:5!+4" 7+!,&,+ ' ">( "#$%!! $%&' $%&( %&% %&( %&' 8*99+4,:;-</3-<<4,4054'+74="

59 Polarization Polarization correlations in momentum space revealed by electron-electron and electron-ion coincidence measurements: Proof of position based entanglement of two massive particles Tunnelling time (fs) Polarization (f - b)/(f + b) g/u symmetry states local realism prediction 0 0.5!!.5!! Interference fringe angle (rad) Polarization PI Tunnelling time (fs) Polarization (left scale) ( f - b )/( f + b ) 0 0.5!!.5!! Analys_O_V33 Graph9_Polar_vs_Angle_fig4_ Ion detection angle (rad) Doppler shift (right scale) ( E f - E b )/ Doppler shift difference!e (ev) Normalized coincidence rate Aspect et al., PRL. 47, 460 (98) 0 0.5! 0.5! 0.75!! Relative angle of polarizers (rad)

60 red channel Intensity (arb. units) BS BS M B 600 A 00 path path 00 Counts O Doppler Time dependence Graph0_ !! Quantum eraser %#&"%&'(")!! *!"!! which way information M Time (fs) 4 D D 6 electron based Doppler localization Intensity (arb. units) photon based Counts O Doppler Time dependence Graph0_ gerade!!! Beam splitter localization!! "!"#"$%#&"%&'(")!! *!"!! " Time (fs) 4 red channel!!! coherent superposition M BSout D M 6 D Phase shift (rad) Phase shift (rad) Jaques et al. Science 35, 966 (007)

61 Berlin Group Frankfurt Group Sendai Group Fritz-Haber-Institut der Max-Planck-Gesellschaft R. Hentges B. Langer O. Kugeler M. Braune S. Korica J. Viefhaus D. Rolles U. Hergenhahn Pasadena Group M. Schöffler J. Titze N Petridis T. Jahnke K. Cole L. Schmidt A. Czasch D. Akoury O. Jagutzki H. Schmidt-Böcking R. Dörner H. Fukuzawa X. Liu Y. Tamenori M. Hoshino H. Tanaka K. Ueda B. Zimmermann V. McKoy

62 Thank you for your attention! I am indebted to the MPG-ASG at CFEL and the BMBF-FSP 30 FLASH for financial support.

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION Realization of quantum Wheeler s delayed-choice experiment Jian-Shun Tang, 1 Yu-Long Li, 1 Xiao-Ye Xu, 1 Guo-Yong Xiang, 1 Chuan-Feng Li, 1 and Guang-Can Guo 1 1 Key Laboratory of Quantum Information,