Transcript スライド 1 - Center for Nuclear Study, University of TOKYO

Spin-polarization using ns~fs laser pulses
Takashi Nakajima
Institute of Advanced Energy
Kyoto University
[email protected]
Introduction – why spin polarization?
Aim： Develop new (and hopefully simple) method(s) to control
spin-degree of freedom
by purely optical method (but without optical pumping)
our work
Three kinds of spin:
spin of electron
→ spin-polarized electron
electron-spin of ion → electron spin-polarized ions
（nuclear spin
→
polarized ion）
Spin-polarized source
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)
(under progress)
Applications of spin-polarized species
Spin-dependence of various quantities, f, provides more information
on the dynamics
If averaged over spin,
1
f (....)   ms  1/ 2 f (..., ms ,...)
2
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
Nuclear-spin-polarized (doped) atom
★ nuclear physics
Outline
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. 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
Polarized electrons via 2-photon ionization of alkali-metal atom (Rb)
★ far off-resonance (it is as if there were no fine structure)
★ resonance on 5p1/2
P = - 60%
★ resonance on 5p3/2
P = + 70%
→ P = 0%
★ between 5p1/2 and 5p1/2, P~100% due to two-path interference
2-photon ionization of Rb
p3/2
circular light
ω
5p3/2
5p1/2
circular light
ω
Rb
237cm-1
p1/2
5s1/2
Lambropoulos,
Phys.Rev.Lett. 30, 413 (1973)
Polarized electrons via 2-photon ionization of rare-gas atom (Xe)
★Technically, rare gas atoms are much more convenient than alkalis
★ 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
2-photon ionization of Xe
Xe+ 5p5 [2P1/2]
circular light
ω
Xe+ 5p5 [2P3/2]
5p5 [2P1/2] 6s (J=1)
5p5 [2P3/2] 6s (J=1)
circular light
ω
5p6 (J=0)
Xe
9000cm-1
40 times larger splitting
than Rb 5p state
2-photon ionization of Xe
Xe+
Xe
Nakajima and Lambropoulos,
Europhys.Lett. 57, 25 (2002)
9.2 eV photon (134 nm or THG of SHG of 800nm)
σ(2) ~10-49 cm4.s
3-photon ionization of Xe
Xe+
Xe
Nakajima and Lambropoulos,
Europhys.Lett. 57, 25 (2002)
4.8 eV photon (THG of 775nm)
σ(3) ~10-81 cm6.s2
~100% spin-polarization
1.5x1012 electrons/pulse
500 fs, 1mJ pulse
focus to d=150μm , L=1cm
1 Torr Xe gas
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
Production of spin-polarized electrons/ions – Dual spin-polarized source
example) Sr (5s5p 3P1) +  → Sr+ (5s ) + eeelectron
e-
photoelectron
spin angular momentum
orbital angular momentum
electron
ejection
electron
e-
e-
Sr2+
(3) spin of electron
spin-orbit interaction
ns pulse
for ionization
(2) orbital momentum of electron
ion
spin angular momentum
orbital angular momentum
dipole interaction
(1) angular momentum of photon
No guarantee that both electrons and ions are spin-polarized
Careful choice of the scheme is necessary
requirements
nearly pure single LS coupling description
ion core to be Sr+ (5s)
Nakajima and Yonekura, J. Chem. Phys. 117, 2112 (2002)
Level scheme
∴
Triplet state must be used!
 
L  S  0 for a singlet state
Experimental setup
ns pulses are used for ablation, excitation, ionization, and probe (detection)
Vacuum
chamber
(1x10-5Pa)
Probe laser
421nm
pulse timing
YAG laser
5ns
308nm
Ionization
laser
trigger
∥
⊥
Sr
disk
15ns
ablation
Pump laser
Ionization laser
Ablation
laser
1064nm
15ns
Probe laser
LIF signal
50ms
delay
Pump laser
689nm
trigger
Box-car
Computer
integrator
Monochromator
PMT
boxcar gate
Optical detection for spin-polarization of Sr+ (52S1/2) ion
Use of laser-Induced fluorescence (LIF)
example） if Sr+ (52S1/2) is 100% spin-polarized,
Sr+ 2P1/2
Sr+ 2P1/2
probe laser
right-circular
Sr+ 2S1/2
m = -1/2
probe laser
left-circular
LIF
m = +1/2
Sr+ 2S1/2
m = +1/2
LIF signal detected !
No LIF signal
Polarization
m = -1/2
I  I RC
P  LC
I LC  I RC
where
ILC: LIF by RC probe laser
IRC: LIF by LC probe laser
LIF intensity (arb.units)
Spin-polarization of Sr+ ions determined from the LIF signal
1.0
0.8
0.6
0.4
0.2
0
Right-Circular Left-Circular
Probe laser polarization
Polarization
P  64  9 %
Agree well with our theoretical prediction (60%)
Nakajima et al., Appl. Phys. Lett. 83, 2103 (2003)
Yonekura et al., J. Chem. Phys. 120, 1806 (2004)
(Nakajima and Yonekura, J. Chem. Phys. 117, 2112 (2002))
Spin-polarization by the tunable ionization laser
For better efficiency and spin-polarization,
tune the laser to an autoionization resonance
autoionization
resonance
640 nm
pump laser
295 nm
tunable
Ionization laser
1
LIF intensity (arb. units)
Sr 4d5d 3S
spin-polarization (%)
probe laser
421 nm
Sr 5s6p 3P1
Sr 5s2 1S
0
Matsuo et al., (under preparation for submission)
Detuning of the ionization laser (cm-1)
spin-polarization：78%
1-order of magnitude improvement
of ionization efficiency
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
Spin-polarization using short laser pulses ― one-electron system
example）
K atom
LS-coupled basis
Coherent excitation of fine structure
by ultrafast (broadband) lasers
probe
Δt
Δ
4p 2P3/2
4p 2P1/2
pump
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
4s 2S1/2
Depicting the above scheme with magnetic sublevels explicitly,
Two paths are independent
4p 2P3/2
4p 2P1/2
Mj= -1/2
4s 2S1/2
Mj=+1/2
Bouchene et al, J.Phys. B 34, 1497 (2001)
LS-coupled basis vs. LS-uncoupled basis for a one-electron system
LS-coupled basis
4p 2P3/2
4p 2P1/2
Mj= -1/2
4s 2S1/2
Mj=+1/2
LS-uncoupled basis
MJ= -1/2 → MJ= +1/2 transition
|B-> = | 1 , 1 , 1/2 , -1/2 >
P
|D-> = | 1 , 0 , 1/2 , +1/2 >
P
pump
spin-orbit
interaction
S
| L=0 , ML=0 , S=1/2 , MS= -1/2 >
MJ= +1/2 → MJ= +3/2 transition
|B+> = | 1 , 1 , 1/2 , +1/2 >
P
pump
S
| L=0 , ML=0 , S=1/2 , MS= +1/2 >
Representative result for a one-electron system
For K 4p1/2 and 4p3/2, Δ=57.7 cm-1 ( = 7.15 meV)
Δ-1=580 fs
Δ-1
Bouchene et al, J.Phys. B 34, 1497 (2001)
Spin-polarization using short laser pulses ― two-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
example) Mg atom
Coherent excitation of
fine structure manifolds
ultrafast pulse
Δ
spin-orbit coupling time τ=Δ-1
ultrafast pulse
Mg 3s3d 3D1,2 τ= 1.2 ns
Ca 4s4d 3D1,2 τ= 9.0 ps
ns pulse
Sr 5s5d 3D1,2 τ= 2.2 ps
Nakajima, Appl. Phys. Lett. 84, 3786 (2004)
Physical mechanism of polarizing a two-electron system
Physical mechanism
(a) coherent excitation by pump laser (in LS-coupled basis)
ΔE
state-flipping after the pump pulse
(b) LS-coupled basis 3s3d 3D1 & 3s3d 3D2
change basis
LS-uncoupled basis (↑,↑), (↑,↓), etc.
(c) probe laser after some delay to pick up particular spin state
state-flipping (LS-coupled basis) ⇔ spin-flipping (LS-uncouplede basis)
ultrafast spin polarization !
Photoelectron yield with ↑or↓ spin
Photoelectron yield with↑ or ↓ spin
dipole moment
As we expect, photoelectron yield into different spin states
has different dependence on time delay
Time delay .vs. photoelectron yield and spin-polarization
Photoelectron / photoion yield
ΔE
Degree of spin-polarization
Consider two extreme cases：
Ionization cross section from Mg 3s3d 3D
|<3sεp |D| 3s3d>| >> |<3sεf |D| 3s3d> |
|<3sεp |D| 3s3d>| << |<3sεf |D| 3s3d> |
Either case can be realized by the proper
choice of the probe photon energy
probe photon energy (eV)
Representative results for a two-electron system
Mg atom
probe laser photon energy = 4.47 eV
|<3sεp |D| 3s3d>| >> |<3sεf |D| 3s3d> |
probe laser photon energy = 4.03 eV
|<3sεf |D| 3s3d>| >> |<3sεp |D| 3s3d> |
spin↑
spin↓
Nakajima, Appl. Phys. Lett. 84, 3786 (2004)
change of delay leads to the
change of spin-polarity !
Dependence of spin-polarization on laser polarization
Since spin-polarization is based on the momentum transfer from photons to electrons,
the dynamics of spin-polarization depends on the laser polarization
pump: linear
probe: linear
probe
pump
excitation
At ωprobe= 4.47 eV
At ωprobe= 4.03 eV
pump: linear
probe: r-circular
probe
pump
pump: linear
probe: l-circular
probe
pump
Summary
○ Discussed three different schemes to polarize
spin of photoelectron
upon photoionization
spin of valence electron
○ Alkaline-earth atoms are conveniently used for the
proof-of-principle experiment
easy to optically analyze spin of the valence electron of photoions
○ Our methods are purely optical by pulsed (ns~fs) lasers
no optical pumping
no spin-exchange collision
Collaborators
Yukari Matsuo (RIKEN)
Tohru Kobayashi (RIKEN)
Proof-of-principle experiment
Financial support
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
Comparison with experimental data
（for 1-photon ionization of Xe)
Phys. Rev. A 58, 1589 (1998)
(Heinzmann’s group)
Xe 7d’
experiment
our
theory
Xe 9s’
experiment
our
theory
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 polarization within transition rate approximation
beyond transition rate approximation
4. Summary
Ultrafast spin polarization beyond transition rate approximation (1)
Time-dependent Schrödinger equation
u0  i1u1  i 2u 2
 

( 2)
u1  i 1  S1   1   i1u0  i12
u2
2


 

( 2)
u 2  i  2  S 2   2   i 2u0  i12
u1
2

2
probe
1
pump
2
1
Δ
0
excitation
1 ,2
( 2)
12
j
j
Sj
1-photon Rabi frequency
2-photon Rabi frequency (complex）
laser detuning of state j
Ionization width for state j
Stark shift for state j
Ultrafast spin polarization beyond transition rate approximation (2)
dipole moment
Spin-polarized electron yield
2
Q
()
2
 2
2
3
3
2
u 2 R3df
u1 
u 2 R3dp 
u1 
 0.589  dt 

15
70
5 14
 5 3


2
6
f 2
u 2 R3d  I probe
u1 

105
5 7


2
2
1
3
u2 R
u1 

10
60
p 2
3d
2
Q ()
2

2
3
1
6
2
 0.589  dt  
u1 
u 2 R3dp  
u1 
u2 R3df

105
60
5 7
 10


3
1
f 2
u1 
u2 R3d  I probe
35
21


2

spin-polarization
Q ()  Q ()
P  ()
Q  Q ()
2
2
Intensity-dependent spin-polarization (1)
ωprobe=4.01 eV , Ipump=105 W/cm2
τpump=τprobe=10 ps
no dependence
on Iprobe
saturation
quantum beat
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？
Spin-polarized electron yield
2
Q ()
2
 2
2
3
3
p 2
 0.589  dt 
u1 
u 2 R3d 
u1 
u 2 R3df

15
5 14
70
 5 3

2
2
2

2
3
1
6
2
p
f 2

u1 
u 2 R3d  
u1 
u 2 R3d  I probe
10
105
60
5 7


2
Q
()

3
1
6
2
p 2
 0.589  dt  
u1 
u 2 R3d  
u1 
u2 R3df

105
60
5 7
 10


2

3
1
f 2
u1 
u2 R3d  I probe
35
21


u1 (t ) , u2 (t ) depend on Iprobe
2
2
Time evolution of u1 (t ) , u2 (t ) for ωprobe=4.01eV
pump pulse at t=0 (ps)
probe pulse at t=500 (ps)
Time evolution of u1 (t ) , u2 (t ) for ωprobe=4.46eV
pump pulse at t=0 (ps)
probe pulse at t=500 (ps)
rapid decrease
of u2 by the
probe pulse