Spin-polarization using ns~fs laser pulses

Takashi Nakajima

Institute of Advanced EnergyKyoto University

nakajima@iae.kyoto-u.ac.jp

Introduction – why spin polarization?

Spin-polarized sourceSpin-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

Spin-dependence of various quantities, f, provides more informationon the dynamics

　

If averaged over spin,

subtle spin-dependent effects are easily smeared out

,...)(...,2

1(....) 2/1 sm mff

s

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

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

1.1. Electron spin-polarization upon photoionization of rare gas atoms Electron spin-polarization upon photoionization of rare gas atoms by UV~VUV pulseby UV~VUV pulse

2. Simultaneous production of spin-polarized electrons/ions with ns pulses

3. Ultrafast spin polarization

4. Summary

Outline

5p1/2

5p3/2

Rb5s1/2

ω

ω

2-photon ionization of Rb

circular light

circular light

p1/2

p3/2

★ resonance on 5p3/2 P = + 70%

Polarized electrons via 2-photon ionization of alkali-metal atom (Rb)

237cm-1

Lambropoulos,Phys.Rev.Lett. 30, 413 (1973)

★ resonance on 5p1/2 　 　 P = - 60%

★ between 5p1/2 and 5p1/2, P~100%P~100% due to two-path interferencetwo-path interference

★ far off-resonance (it is as if there were no fine structure) → P = 0%

★ Hopefully, similar behavior to that of the Rb atom, but we must solve a multichannel problem for Xe:

p5 [2P1/2] 6s(J=1) = Σp5[2P1/2]ns1/2 + p5[2P3/2]ns1/2

+ p5[2P1/2]nd3/2 + p5[2P3/2]nd3/2 + p5[2P3/2]nd5/2

5p5 [2P3/2] 6s (J=1)5p5

[2P1/2] 6s (J=1)

Xe5p6 (J=0)

ω

ω

2-photon ionization of Xe

Xe+ 5p5 [2P1/2]

Xe+ 5p5 [2P3/2]

9000cm-1

circular light

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 splittingthan Rb 5p state

2-photon ionization of Xe

Xe+

Xe

9.2 eV photon (134 nm or THG of SHG of 800nm)σ(2) ~10-49 cm4.s

Nakajima and Lambropoulos,Europhys.Lett. 57, 25 (2002)

3-photon ionization of Xe

Xe+

Xe

4.8 eV photon (THG of 775nm)σ(3) ~10-81 cm6.s2

500 fs, 1mJ pulsefocus to d=150μm , L=1cm1 Torr Xe gas

Nakajima and Lambropoulos,Europhys.Lett. 57, 25 (2002)

~100% spin-polarization1.5x1012 electrons/pulse

1. Electron spin-polarization upon photoionization of rare gas atoms by UV~VUV pulse

2. Simultaneous productionSimultaneous production of spin-polarized electrons/ions with ns pulses

3. Ultrafast spin polarization

4. Summary

Production of spin-polarized electrons/ions – Dual Dual spin-polarized sourcespin-polarized source

ns pulsefor ionization

example) Sr (5s5p 3P1) + → Sr+ (5s ) + e-

Nakajima and Yonekura, J. Chem. Phys. 117, 2112 (2002)

Sr2+

e-

e-

electron

electron

No guarantee that both electrons and ions are spin-polarizedCareful 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 momentumorbital angular momentum

photoelectron

spin angular momentumorbital angular momentum

ion

e-

e-

electronejection

nearly pure single LS coupling descriptionion core to be Sr+ (5s)

requirements

Level scheme

Triplet state must be used! 0SL∴

for a singlet statesinglet state

delay

Probe laser

Ionizationlaser

Pump laser

trigger

triggerBox-car

integratorComputer

Vacuumchamber

Srdisk

Ablationlaser

1064nm

(1x10-5Pa)

Monochro-mator

PMT

689nm

308nm

421nm

∥ ⊥

Experimental setup

YAG laser

Pump laser

LIF signal

boxcar gate

ablation

50s

Ionization laser

Probe laser

pulse timing

5ns

15ns

15ns

ns pulsesns pulses are used for ablation, excitation, ionization, and probe (detection)

Optical detection for spin-polarization of Sr+ (52S1/2) ion

Use of laser-Induced fluorescence (LIF)

probe laserleft-circular

example ）　 if Sr+ (52S1/2) is 100% spin-polarized,

No LIF signal

probe laserright-circular

m = -1/2 m = +1/2Sr+ 2S1/2

Sr+ 2P1/2

m = -1/2 m = +1/2Sr+ 2S1/2

Sr+ 2P1/2

LIF

LIF signal detected !

RCLC

RCLC

II

IIP

PolarizationwhereILC: LIF by RC probe laserIRC: LIF by LC probe laser

Spin-polarization of Sr+ ions determined from the LIF signal

% 964 PPolarization

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-Circular Left-Circular

Probe laser polarization

LIF

inte

nsity

(ar

b.un

its)

0.2

0.4

0.6

0.8

1.0

0

Spin-polarization by the tunable ionization laser

For better efficiency and spin-polarization,

tune the laser to an autoionization resonance

640 nm

Sr 4d5d 3S 1

probe laser421 nm

autoionizationresonance

Matsuo et al., (under preparation for submission)

spin

-po

larization

(%)

spin-polarization ： 78%1-order of magnitude improvementof ionization efficiency

LIF

inten

sity (arb. u

nit

s)

Detuning of the ionization laser (cm-1)

Sr 5s6p 3P1

Sr 5s2 1S 0295 nm

pump laser

tunableIonization laser

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 polarizationUltrafast spin polarization 4. Summary

Depicting the above scheme with magnetic sublevels explicitly,

4s 2S1/2

Mj=+1/2Mj= -1/2

4p 2P1/2

4p 2P3/2

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 structureby ultrafast (broadband) lasers

4s 2S1/2

4p 2P1/2

4p 2P3/2

pump

probe

ΔΔt

Two paths are independent

LS-coupled basis

|D-> = | 1 , 0 , 1/2 , +1/2 >|B-> = | 1 , 1 , 1/2 , -1/2 >

| L=0 , ML=0 , S=1/2 , MS= -1/2 >

MJ= -1/2 　→ MJ= +1/2 　transition

spin-orbitinteraction

S

P P

pump

LS-coupled basis vs. LS-uncoupled basis for a one-electron system

|B+> = | 1 , 1 , 1/2 , +1/2 >

| L=0 , ML=0 , S=1/2 , MS= +1/2 >

MJ= +1/2 　→ MJ= +3/2 　transition

P

S

pump

4s 2S1/2

Mj=+1/2Mj= -1/2

4p 2P1/2

4p 2P3/2

LS-coupled basis

LS-uncoupled basis

Δ-1

Representative result for a one-electron system

Bouchene et al, J.Phys. B 34, 1497 (2001)

For K 4p1/2 and 4p3/2, Δ=57.7 cm-1 ( = 7.15 meV)

Δ-1=580 fs

Advantages of Advantages of twotwo-electron system over a -electron system over a oneone-electron system-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 3D1,2 τ= 1.2 ns

Ca 4s4d 3D1,2 τ= 9.0 ps

Sr 5s5d 3D1,2 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

ultrafast pulse

Nakajima, Appl. Phys. Lett. 84, 3786 (2004)

ns pulse

(a) coherent excitation by pump laser (in LS-coupled basis)

Physical mechanism of polarizing a two-electron system

(b) LS-coupled basis 　 3s3d 3D1 & 3s3d 3D2

state-flipping (state-flipping (LS-coupled basis)LS-coupled basis) ⇔ spin-flipping ( ⇔ spin-flipping (LS-uncouplede basisLS-uncouplede basis))

ultrafast spin polarization !ultrafast spin polarization !

(c) probe laser after some delay to pick up particular spin state

state-flipping after the pump pulse

ΔE

Physical mechanismPhysical mechanism

change basis LS-uncoupled basis (↑,↑), (↑,↓), etc.

Photoelectron yield with↑ or ↓ spin

dipole moment

Photoelectron yield with ↑or↓ spin

As we expect, photoelectron yield into different spin statesAs we expect, photoelectron yield into different spin stateshas different dependence on time delayhas different dependence on time delay

Consider two extreme cases ：

　 |<3sεp |D| 3s3d>| >> |<3sεf |D| 3s3d> |

　 |<3sεp |D| 3s3d>| << |<3sεf |D| 3s3d> |

Photoelectron / photoion yield

Degree of spin-polarization

ΔE

Time delay .vs. photoelectron yield and spin-polarization

Ionization cross section from Mg 3s3d 3D

probe photon energy (eV)

Either case can be realized by the properchoice of the probe photon energy

change of delay leads to the change of spin-polarity !

probe laser photon energy = 4.03 eV

　 |<3sεf |D| 3s3d>| >> |<3sεp |D| 3s3d> |

spin↑

spin↓

Mg atom

Nakajima, Appl. Phys. Lett. 84, 3786 (2004)

probe laser photon energy = 4.47 eV

　 |<3sεp |D| 3s3d>| >> |<3sεf |D| 3s3d> |

Representative results for a two-electron system

Dependence of spin-polarization on laser polarization

Since spin-polarization is based on the momentum transfer from photons to electrons,the dynamics of spin-polarizationdynamics of spin-polarization depends on the laser polarizationlaser polarization

pump: linearprobe: linear

pump: linearprobe: r-circular

pump: linearprobe: l-circular

pump

probe

excitation

pump pump

probe probe

At ωprobe= 4.47 eV

At ωprobe= 4.03 eV

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

easy to optically analyzeoptically analyze spin of the valence electronspin of the valence electron of photoions

○ Our methods are purely opticalpurely optical by pulsed (ns~fs) lasers

no optical pumping no spin-exchange collision

upon photoionization

CollaboratorsCollaborators

Yukari Matsuo (RIKEN)Tohru Kobayashi (RIKEN)

Proof-of-principle experiment

Ministry of Education and ScienceMinistry 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 FoundationCasio Foundation Sumitomo FoundationSumitomo Foundation

Financial supportFinancial support

Comparison with experimental data（ for 1-photon ionization of Xe)

Phys. Rev. A 58, 1589 (1998)(Heinzmann’s group)

Xe 9s’

Xe 7d’

experiment ourtheory

experimentourtheory

1. Electron spin-polarization of rare gas atoms by UV~VUV pulse

2. Simultaneous production of spin-polarized electrons/ions with ns pulses

3. Ultrafast spin polarizationUltrafast spin polarization within transition rate approximation

4. Summary

beyond transition rate approximation

Ultrafast spin polarization beyond transition rate approximation (1)

Δ

pump

excitation

1

2

0

12

Time-dependent Schrödinger equation

1)2(

12022

222

2)2(

12011

111

22110

2

2

uiuiSiu

uiuiSiu

uiuiu

21,)2(

12 2-photon Rabi frequency (complex ）1-photon Rabi frequency

j laser detuning of state j

j Ionization width for state j

jS Stark shift for state j

probe

Spin-polarized electron yield

probefd

pd

fd

pd

IRuuRuu

RuuRuudtQ

2

3

2

21

2

3

2

21

2

3

2

21

2

3

2

21)(

105

2

75

6

60

1

10

3

70

3

145

3

15

2

35

2 589.0

probefd

fd

pd

IRuu

RuuRuudtQ

2

3

2

21

2

3

2

21

2

3

2

21)(

21

1

35

3

105

2

75

6

60

1

10

3 589.0

spin-polarization )()(

)()(

QQ

QQP

dipole moment

Ultrafast spin polarization beyond transition rate approximation (2)

Intensity-dependent spin-polarization (1)

ωprobe=4.01 eV , Ipump=105 W/cm2

τpump=τprobe=10 ps

quantum beat

saturation

no dependence on Iprobe

Intensity-dependent spin-polarization (2)

ωprobe=4.46 eV , Ipump=105 W/cm2

τpump=τprobe=10 ps

Why this happens?

Origin of intensity dependence

Why spin-polarization exhibits dependence on Iprobe ？

probefd

pd

fd

pd

IRuuRuu

RuuRuudtQ

2

3

2

21

2

3

2

21

2

3

2

21

2

3

2

21)(

105

2

75

6

60

1

10

3

70

3

145

3

15

2

35

2 589.0

probefd

fd

pd

IRuu

RuuRuudtQ

2

3

2

21

2

3

2

21

2

3

2

21)(

21

1

35

3

105

2

75

6

60

1

10

3 589.0

　　　　　　 depend on Iprobe)( , )( 21 tutu

Spin-polarized electron yield

Time evolution of for ωprobe=4.01eV)( , )( 21 tutu

pump pulse at t=0 (ps) probe pulse at t=500 (ps)

rapid decrease of u2 by the probe pulse

Time evolution of for ωprobe=4.46eV)( , )( 21 tutu

pump pulse at t=0 (ps) probe pulse at t=500 (ps)