1. Spin-polarization using ns~fs laser pulses Takashi Nakajima Institute of Advanced Energy Kyoto University nakajima@iae.kyoto-u.ac.jp

2. Introduction – why spin polarization? Spin-polarized source Aim ： Develop new (and hopefully simple) method(s) to control spin-degree of freedom by purely optical method by purely optical method (but without optical pumping) Three kinds of spin: spin of electron → spin-polarized electron electron-spin of ion → electron spin-polarized ions （ nuclear spin → polarized ion ） (under progress) Europhys.Lett. 57, 25 (2002) Phys.Rev.A 68, 013413 (2003) Appl.Phys. Lett. 84, 3786 (2004) J.Chem.Phys. 117, 2112 (2002) Appl.Phys.Lett. 83, 2103 (2003) J.Chem.Phys. 120, 1806 (2004) our work

3. Spin-dependence of various quantities, f, provides more information on the dynamics If averaged over spin, subtle spin-dependent effects are easily smeared out Spin-polarized electrons ★ high energy physics ★ atomic and molecular processes ★ surface physics, semiconductor physics Electron spin-polarized ions ★ surface physics ★ atomic and molecular processes Applications of spin-polarized species Nuclear-spin-polarized (doped) atom ★ nuclear physics

4. 1.Electron spin-polarization upon photoionization of rare gas atoms by UV~VUV pulse 2. Simultaneous production of spin-polarized electrons/ions with ns pulses 3. Ultrafast spin polarization 4. Summary Outline

5. 1.Electron spin-polarization upon photoionization of rare gas atoms by UV~VUV pulse by UV~VUV pulse 2. Simultaneous production of spin-polarized electrons/ions with ns pulses 3. Ultrafast spin polarization 4. Summary Outline

6. 5p 1/2 5p 3/2 Rb 5s 1/2 ω ω 2-photon ionization of Rb circular light p 1/2 p 3/2 ★ resonance on 5p 3/2 P = + 70% Polarized electrons via 2-photon ionization of alkali-metal atom (Rb) 237cm -1 Lambropoulos, Phys.Rev.Lett. 30, 413 (1973) ★ resonance on 5p 1/2 P = - 60% P~100%two-path interference ★ between 5p 1/2 and 5p 1/2, P~100% due to two-path interference ★ far off-resonance (it is as if there were no fine structure) → P = 0%

7. ★ Hopefully, similar behavior to that of the Rb atom, but we must solve a multichannel problem for Xe: p 5 [ 2 P 1/2 ] 6s(J=1) = Σp 5 [ 2 P 1/2 ]ns 1/2 + p 5 [ 2 P 3/2 ]ns 1/2 + p 5 [ 2 P 1/2 ]nd 3/2 + p 5 [ 2 P 3/2 ]nd 3/2 + p 5 [ 2 P 3/2 ]nd 5/2 5p 5 [ 2 P 3/2 ] 6s (J=1) 5p 5 [ 2 P 1/2 ] 6s (J=1) Xe 5p 6 (J=0) ω ω 2-photon ionization of Xe Xe + 5p 5 [ 2 P 1/2 ] Xe + 5p 5 [ 2 P 3/2 ] 9000cm -1 circular light Polarized electrons via 2-photon ionization of rare-gas atom (Xe) ★ Technically, rare gas atoms are much more convenient than alkalis 40 times larger splitting than Rb 5p state

8. 2-photon ionization of Xe Xe + Xe 9.2 eV photon (134 nm or THG of SHG of 800nm) σ (2) ~10 -49 cm 4.s Nakajima and Lambropoulos, Europhys.Lett. 57, 25 (2002)

9. 3-photon ionization of Xe Xe + Xe 4.8 eV photon (THG of 775nm) σ (3) ~10 -81 cm 6.s 2 500 fs, 1mJ pulse focus to d=150μm, L=1cm 1 Torr Xe gas Nakajima and Lambropoulos, Europhys.Lett. 57, 25 (2002) ~100% spin-polarization 1.5x10 12 electrons/pulse

10. 1.Electron spin-polarization upon photoionization of rare gas atoms by UV~VUV pulse Simultaneous production 2. Simultaneous production of spin-polarized electrons/ions with ns pulses 3. Ultrafast spin polarization 4. Summary

11. Dual spin-polarized source Production of spin-polarized electrons/ions – Dual spin-polarized source ns pulse for ionization example) Sr (5s5p 3 P 1 ) +  → Sr + (5s ) + e - Nakajima and Yonekura, J. Chem. Phys. 117, 2112 (2002) Sr 2+ e-e- e-e- electron No guarantee that both electrons and ions are spin-polarized Careful choice of the scheme is necessary (3) spin of electron dipole interaction (1) angular momentum of photon spin-orbit interaction (2) orbital momentum of electron spin angular momentum orbital angular momentum photoelectron spin angular momentum orbital angular momentum ion e-e- e-e- electron ejection nearly pure single LS coupling description ion core to be Sr + (5s) requirements

12. Level scheme Triplet state must be used! ∴ singlet state for a singlet state

13. delay Probe laser Ionization laser Pump laser trigger Box-car integrator Computer Vacuum chamber Sr disk Ablation laser 1064nm (1x10 -5 Pa) Monochro- mator PMT 689nm 308nm 421nm ∥ ⊥ Experimental setup YAG laser Pump laser LIF signal boxcar gate ablation 50  s Ionization laser Probe laser pulse timing 5ns 15ns ns pulses ns pulses are used for ablation, excitation, ionization, and probe (detection)

14. Optical detection for spin-polarization of Sr + (5 2 S 1/2 ) ion Use of laser-Induced fluorescence (LIF) probe laser left-circular example ） if Sr + (5 2 S 1/2 ) is 100% spin-polarized, No LIF signal probe laser right-circular m = -1/2 m = +1/2 Sr + 2 S 1/2 Sr + 2 P 1/2 m = -1/2 m = +1/2 Sr + 2 S 1/2 Sr + 2 P 1/2 LIF LIF signal detected ! Polarization where I LC : LIF by RC probe laser I RC : LIF by LC probe laser

15. Spin-polarization of Sr + ions determined from the LIF signal Polarization Nakajima et al., Appl. Phys. Lett. 83, 2103 (2003) Yonekura et al., J. Chem. Phys. 120, 1806 (2004) Agree well with our theoretical prediction (60%) (Nakajima and Yonekura, J. Chem. Phys. 117, 2112 (2002)) Right-CircularLeft-Circular Probe laser polarization LIF intensity (arb.units) 0.2 0.4 0.6 0.8 1.0 0

16. Spin-polarization by the tunable ionization laser For better efficiency and spin-polarization, tune the laser to an autoionization resonance 640 nm Sr 4d5d 3 S 1 probe laser 421 nm autoionization resonance Matsuo et al., (under preparation for submission) spin-polarization (%) spin-polarization ： 78% 1-order of magnitude improvement of ionization efficiency LIF intensity (arb. units) Detuning of the ionization laser (cm -1 ) Sr 5s6p 3 P 1 Sr 5s 2 1 S 0 295 nm pump laser tunable Ionization laser

17. 1.Electron spin-polarization upon photoionization of rare gas atoms by UV~VUV pulse 2. Simultaneous production of spin-polarized electrons/ions with ns pulses Ultrafast spin polarization 3. Ultrafast spin polarization 4. Summary

18. Depicting the above scheme with magnetic sublevels explicitly, 4s 2 S 1/2 M j =+1/2 M j = -1/2 4p 2 P 1/2 4p 2 P 3/2 Spin-polarization using short laser pulses ― one-electron system example ） K atom Bouchene et al, J.Phys. B 34, 1497 (2001) spin-orbit coupling time ~ Δ -1 ∴ If pulse duration τ<< Δ -1, the system does not see spin-orbit interaction during the pump pulse→ LS-uncoupled basis Coherent excitation of fine structure by ultrafast (broadband) lasers 4s 2 S 1/2 4p 2 P 1/2 4p 2 P 3/2 pump probe Δ Δt Two paths are independent LS-coupled basis

19. |D - > = | 1, 0, 1/2, +1/2 >|B - > = | 1, 1, 1/2, -1/2 > | L=0, M L =0, S=1/2, M S = -1/2 > M J = -1/2 → M J = +1/2 transition spin-orbit interaction S PP pump LS-coupled basis vs. LS-uncoupled basis for a one-electron system |B + > = | 1, 1, 1/2, +1/2 > | L=0, M L =0, S=1/2, M S = +1/2 > M J = +1/2 → M J = +3/2 transition P S pump 4s 2 S 1/2 M j =+1/2 M j = -1/2 4p 2 P 1/2 4p 2 P 3/2 LS-coupled basis LS-uncoupled basis

20. Δ -1 Representative result for a one-electron system Bouchene et al, J.Phys. B 34, 1497 (2001) For K 4p 1/2 and 4p 3/2, Δ=57.7 cm -1 ( = 7.15 meV) Δ -1 =580 fs

21. Advantages of two-electron system over a one-electron system Advantages of two-electron system over a one-electron system : （１） spin-polarization of ion is easy to monitor by optical method (LIF) （２） spin-flip (change of polarity) can take place （３） Influence of hyperfine structure is much smaller spin-orbit coupling time τ=Δ -1 Mg 3s3d 3 D 1,2 τ= 1.2 ns Ca 4s4d 3 D 1,2 τ= 9.0 ps Sr 5s5d 3 D 1,2 τ= 2.2 ps Spin-polarization using short laser pulses ― two-electron system Coherent excitation of fine structure manifolds example) Mg atom Δ ultrafast pulse Nakajima, Appl. Phys. Lett. 84, 3786 (2004) ns pulse

22. (a) coherent excitation by pump laser (in LS-coupled basis) Physical mechanism of polarizing a two-electron system (b) LS-coupled basis 3s3d 3 D 1 & 3s3d 3 D 2 state-flipping (LS-coupled basis) ⇔ spin-flipping (LS-uncouplede basis) ultrafast spin polarization ! (c) probe laser after some delay to pick up particular spin state state-flipping after the pump pulse ΔE Physical mechanism change basis LS-uncoupled basis (↑,↑), (↑,↓), etc.

23. Photoelectron yield with↑ or ↓ spin dipole moment Photoelectron yield with ↑or↓ spin As we expect, photoelectron yield into different spin states has different dependence on time delay

24. Consider two extreme cases ： | | >> | | | | | Photoelectron / photoion yield Degree of spin-polarization ΔE Time delay.vs. photoelectron yield and spin-polarization Ionization cross section from Mg 3s3d 3 D probe photon energy (eV) Either case can be realized by the proper choice of the probe photon energy

25. change of delay leads to the change of spin-polarity ! probe laser photon energy = 4.03 eV | | >> | | spin↑ spin↓ Mg atom Nakajima, Appl. Phys. Lett. 84, 3786 (2004) probe laser photon energy = 4.47 eV | | >> | | Representative results for a two-electron system

26. Dependence of spin-polarization on laser polarization Since spin-polarization is based on the momentum transfer from photons to electrons, dynamics of spin-polarizationlaser polarization the dynamics of spin-polarization depends on the laser polarization pump: linear probe: linear pump: linear probe: r-circular pump: linear probe: l-circular pump probe excitation pump probe At ω probe = 4.47 eV At ω probe = 4.03 eV

27. Summary ○ Discussed three different schemes to polarize spin of photoelectron spin of valence electron ○ Alkaline-earth atoms are conveniently used for the proof-of-principle experiment optically analyzespin of the valence electron easy to optically analyze spin of the valence electron of photoions purely optical ○ Our methods are purely optical by pulsed (ns~fs) lasers no optical pumping no spin-exchange collision upon photoionization

28. Collaborators Yukari Matsuo (RIKEN) Tohru Kobayashi (RIKEN) Proof-of-principle experiment Ministry of Education and Science Grant-in-Aid for Basic Research (C) (year 2002-2004) Priority Research Area (year 2002- ) Basic Research (A) (year 2005- ) Casio Foundation Sumitomo Foundation Financial support

29. Comparison with experimental data （ for 1-photon ionization of Xe) Phys. Rev. A 58, 1589 (1998) (Heinzmann’s group) Xe 9s’ Xe 7d’ experimentour theory experiment our theory

30. 1. Electron spin-polarization of rare gas atoms by UV~VUV pulse 2. Simultaneous production of spin-polarized electrons/ions with ns pulses Ultrafast spin polarization 3. Ultrafast spin polarization within transition rate approximation 4. Summary beyond transition rate approximation

31. Ultrafast spin polarization beyond transition rate approximation (1) Δ pump excitation Time-dependent Schrödinger equation 2-photon Rabi frequency (complex ） 1-photon Rabi frequency laser detuning of state Ionization width for state Stark shift for state probe

32. Spin-polarized electron yield spin-polarization dipole moment Ultrafast spin polarization beyond transition rate approximation (2)

33. Intensity-dependent spin-polarization (1) ω probe =4.01 eV, I pump =10 5 W/cm 2 τ pump =τ probe =10 ps quantum beat saturation no dependence on I probe

34. Intensity-dependent spin-polarization (2) ω probe =4.46 eV, I pump =10 5 W/cm 2 τ pump =τ probe =10 ps Why this happens?

35. Origin of intensity dependence Why spin-polarization exhibits dependence on I probe ？ depend on I probe Spin-polarized electron yield

36. Time evolution of for ω probe =4.01eV pump pulse at t=0 (ps)probe pulse at t=500 (ps)

37. rapid decrease of u 2 by the probe pulse Time evolution of for ω probe =4.46eV pump pulse at t=0 (ps)probe pulse at t=500 (ps)