Spin-polarization using ns~fs laser pulses Takashi Nakajima Institute of Advanced Energy Kyoto University [email protected]
Dec 30, 2015
Spin-polarization using ns~fs laser pulses
Takashi Nakajima
Institute of Advanced EnergyKyoto University
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
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 )()(
)()(
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
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)