高強度場現象・アト秒科学（2）

石川顕一
東京大学 大学院工学系研究科 光量子科学研究センター
[email protected] http://ishiken.free.fr/
高強度場現象・アト秒科学（２）
高次高調波発生とアト秒
パルス
1
24 | OPN October 2008
www.osa-opn.org
高次高調波発生とアト秒パルス
2
Optics and Photonics News, Vol. 19, Issue 10, pp. 24-29 (2008) トンネル電離後の電子はどうなる？
非逐次2重電離
再結合→高次高調波
3
石川顕一
PHYSICAL REVIEW LETTERS
Measurement
29 AUcUsT 1994
of Strong Field Double Ionization of Helium
. Sheehy, ' L. F. DiMauro, ' P. Agostini, K. J. Schafer,
"
K. C. Kulander
非逐次２重電離
and
try Department, Brookhaven National Laboratory, Upton, New York 11973
Surfaces et l'Irradiation de la Matiere, Centre d'Etudes de Saclay, 91191 Gif Sur Yvette, France
Molecular Physics, Lawrence Livermore National Laboratory, Livermore, California 94551
for Laboratory Astrophysics, University of Colorado, Boulder, Colorado 80309
(Received 27 April 1994)
Non-sequential double ionization (NSDI)
and He + by a 160 fs, 780 nm laser has been measured over an unprecedented
nitude in counting range. Enhanced double electron emission, called nonsequential
was observed over an intensity range where the single ionization dynamics is evolving
to pure tunneling. The NS yield is found to scale with the ac-tunneling rate for the
A rescattering mechanism fails
n tunneling is not the dominant ionization pathway.
erved NS threshold or magnitude.
of He+
.80.Rm, 31.90.+s, 32.80.Fb
on (MPI) of noble gases
be well described by timecal calculations within the
approximation [1,2]. The aps from the fact that for long
ion dynamics are dominated
s, leading to the sequential
ates. In recent experiments,
on of doubly charged ions
as been observed with yields
ion based upon sequential
he high intensities and small
t has been argued [3,6] that
from a direct, nonsequential
her than a resonant process
nt quantitative knowledge of
ization is so limited that even
double ejection has not been
a high precision measurement
He is reported which extends
s experiments by a factor of
the NS production of He
range to directly test current
ls.
onization is clearly linked to
of the first electron. Within
which the NS process has
n of He evolves from being
in character to being purely
in the ionization dynamics
in the photoelectron energy
tly, analysis of the intensity
ndicates that the two-electron
neling component of neutral
on ionization dominates.
which invoke features of a
of strong field ionization have
ionization [3,6]. In the first
'
•
イオン収量
He
1E4
Ne
100 fs
780 nm
1E2
'I
~
1EO
PI
lE-2
He→He+ (トンネル電離)
He+→He2+ (トンネル電離)
1ER
Ne→Ne+ (トンネル電離)
Ne+→Ne2+ (トンネル電離)
lEW
1E14
1E15
intensity (W/cm 2
1E16
)
FIG. 1. Measured He ion yields for linear polarized,
100 fsec, 780 nm light. Calculations are shown as solid (SAE)
Dörner et al., Physik. Blätter, 57, 49 (2001)
Walker et al., PRL 73, 1227 (1994)
and dashed (ac-tunneling) lines. The measured intensities are
multiplied by 1.15. The solid curve on right is the calculated
sequential He + yield.
トンネル電離が順次起こるのでは説明できないkneeあるいはshoulderがある。
step an electron is released near the peak of the oscillating
field amplitude. The electron either passes over or tunnels
through the effective barrier created by the Coulombic
attraction of the ion core and the laser's instantaneous
electric field. At that point (second step), the electron's
evolution is dominated by its interaction with the laser
field since its motion is essentially removed from the
4
石川顕一
PHYSICAL REVIEW LETTERS
Measurement
29 AUcUsT 1994
of Strong Field Double Ionization of Helium
. Sheehy, ' L. F. DiMauro, ' P. Agostini, K. J. Schafer,
"
K. C. Kulander
非逐次２重電離
and
try Department, Brookhaven National Laboratory, Upton, New York 11973
Surfaces et l'Irradiation de la Matiere, Centre d'Etudes de Saclay, 91191 Gif Sur Yvette, France
Molecular Physics, Lawrence Livermore National Laboratory, Livermore, California 94551
for Laboratory Astrophysics, University of Colorado, Boulder, Colorado 80309
(Received 27 April 1994)
Non-sequential double ionization (NSDI)
and He + by a 160 fs, 780 nm laser has been measured over an unprecedented
nitude in counting range. Enhanced double electron emission, called nonsequential
was observed over an intensity range where the single ionization dynamics is evolving
to pure tunneling. The NS yield is found to scale with the ac-tunneling rate for the
A rescattering mechanism fails
n tunneling is not the dominant ionization pathway.
erved NS threshold or magnitude.
of He+
.80.Rm, 31.90.+s, 32.80.Fb
on (MPI) of noble gases
be well described by timecal calculations within the
approximation [1,2]. The aps from the fact that for long
ion dynamics are dominated
s, leading to the sequential
ates. In recent experiments,
on of doubly charged ions
as been observed with yields
ion based upon sequential
he high intensities and small
t has been argued [3,6] that
from a direct, nonsequential
her than a resonant process
nt quantitative knowledge of
ization is so limited that even
double ejection has not been
a high precision measurement
He is reported which extends
s experiments by a factor of
the NS production of He
range to directly test current
ls.
onization is clearly linked to
of the first electron. Within
which the NS process has
n of He evolves from being
in character to being purely
in the ionization dynamics
in the photoelectron energy
tly, analysis of the intensity
ndicates that the two-electron
neling component of neutral
on ionization dominates.
which invoke features of a
of strong field ionization have
ionization [3,6]. In the first
'
•
イオン収量
He
1E4
トンネル電子が再衝突する際に、親イオンをさらにイオン化
100 fs
780 nm
1E2
'I
~
1EO
PI
lE-2
He→He+ (トンネル電離)
He+→He2+ (トンネル電離)
1ER
lEW
1E14
1E15
intensity (W/cm 2
電子相関の顕著な例
1E16
)
FIG. 1. Measured He ion yields for linear polarized,
100 fsec, 780 nm light. Calculations are shown as solid (SAE)
Walker et al., PRL 73, 1227 (1994)
and dashed (ac-tunneling) lines. The measured intensities are
multiplied by 1.15. The solid curve on right is the calculated
sequential He + yield.
トンネル電離が順次起こるのでは説明できないkneeあるいはshoulderがある。
step an electron is released near the peak of the oscillating
field amplitude. The electron either passes over or tunnels
through the effective barrier created by the Coulombic
attraction of the ion core and the laser's instantaneous
electric field. At that point (second step), the electron's
evolution is dominated by its interaction with the laser
field since its motion is essentially removed from the
5
石川顕一
トンネル電離後の電子はどうなる？
非逐次2重電離
再結合→高次高調波
6
石川顕一
高次高調波発生
HIGH-HARMONIC GENERATION (HHG)
discovered in 1987
再結合の際に
運動エネルギー + イオン化ポテンシャル
のエネルギーの光子を放出
高次高調波
XUV = extreme ultraviolet (極端紫外)
7
石川顕一
高調波発生
結晶等
ω
非線形光学効果
€
ω,3ω,5ω,
物質の応答が、入射光強度に非線形に依存
€
3ω：３次高調波 (3rd harmonic)
D = ε0 E + P
P = ε0 [ χ (1) E + χ (2) E 2 + χ (3) E 3 +]
€
非線形分極 (nonlinear)
€
€
波長変換
5ω：５次高調波 (5th harmonic)
線形分極 linear polarization€
反転対称な媒質では、
χ (2) = 0
∂ 2D
∇ × ∇ × E = −µ 0 2
∂t
€
€
8
石川顕一
摂動論的高調波発生
３次高調波発生の概念図
Ionization
電離
遷移行列要素
MTHG =
� � �3 · D1h �1 · Dhi �1 · Dij �1 · Dj1
h,i,f
Virtual level
仮想準位
ω
ω
€
€
€
ω
+
�1 · D1h �3 · Dhi �1 · Dij �1 · Dj1
(−ω1 − ωh )(2ω1 − ωi )(ω1 − ωj )
+
�1 · D1h �1 · Dhi �3 · Dij �1 · Dj1
(−ω1 − ωh )(−2ω1 − ωi )(−ω1 − ωj )
+
�1 · D1h �1 · Dhi �1 · Dij �3 · Dj1
(−ω1 − ωh )(−2ω1 − ωi )(−3ω1 − ωj )
3ω
Ground state
基底状態
(3ω1 − ωh )(2ω1 − ωi )(ω1 − ωj )
€
次数が高くなるほど、発生効率は減少。
9
石川顕一
プラトーとカットオフ
Wahlström et al., Phys. Rev. A 48, 4709 (1993)
Harmonic intensity (arb. unit)
plateau
cutoff
1015 W/cm2
10
2
10
1
10
0
10
-1
10
-2
10
-3
10
-4
10
-5
10
-6
10
-7
10
-8
800 nm, 1.6×1014 W/cm2
plateau
cutoff
TDSE Simulation
0
10
20
30
Harmonic order
40
50
プラトー(plateau)：Efficiency does NOT decrease with
increasing harmonic order. 次数が上がっても強度が落ちない。
カットオフ(cutoff)：Maximum energy of harmonic photons
e2 E02
2 2
−14
Up (eV) =
=
9.3
×
10
I(W/cm
)λ (µm)
Ec ≈ Ip + 3.17Up
2
4mω
ポンデロモーティブエネルギー
• 摂動論的には解釈できない
10
石川顕一
高次高調波発生のメカニズム
３ステップモデル
③再結合→発光（高次高調波）
②電場中の古典
的運動（加速）
①トンネル電離
Paul B. Corkum, Phys. Rev. Lett. 71, 1994 (1993)
K. C. Kulander et al., in Super-Intense Laser-Atom Physics, NATO ASI Ser. B, Vol. 316, p. 95 (1993)
Paul B. Corkum
11
石川顕一
高次高調波発生の３ステップモデル
時刻 t0 でイオン化。原点に初速ゼロで出現
mz̈ = −eE0 cos ωt
規格化
ż(t0 ) = 0
z(t0 ) = 0
φ = ωt φ0 = ωt0
E0
z = 2 [(cos φ − cos φ0 ) + (φ − φ0 ) sin φ0 ]
ω
再衝突
Ekin = 2Up (sin φ − sin φ0 )2
z = 0 となる φ = φret (φ0 )
レーザー電場 E(t) = E0 cos ωt
③再結合→発光
①トンネル
電離
12
②電場中の古典
的運動（加速）
石川顕一
再衝突時刻
(cos φret − cos φ0 ) + (φret − φ0 ) sin φ0 = 0
z=0
(cos φ) |φ0
�
cos φret − cos φ0
=
φret − φ0
イオン化時刻と再衝突時刻の関係
1.0
Phase of recombination (phi_r)
350
0.5
0.0
-0.5
-1.0
0
40
φ0
80
120
160
200
phi (degree)
240
φret
280
320
300
200
の場合再結合できない
150
100
50
0
0
360
π
< φ0 < π
2
250
50
100
150
Phase of electron release (phi0)
13
石川顕一
Field (in E0)
1
field
0
-1
recombination
ionization
3
再結合時の運動エネルギーの最大値
3.17Up
1
0
0
long
short
short
2
long
Electron kinetic energy (in Up)
カットオフ則のシンプルな説明
カットオフ
Ec = Ip + 3.17Up
90
180
270
360
Phase (degrees)
同じ高調波次数（光子エネルギー）に
short trajectory
long trajectory
対応するイオン化時刻と再結合時刻の
ペアは２つある。
14
石川顕一
なぜ、高次高調波スペクトルは離散的なのか？
Takahashi et al., Appl. Phys. Lett. 93, 041111 (2008)
レーザー電場 E(t) = E0 cos ωt
③再結合→発光
①トンネル
電離
Harmonic intensity (arb. unit)
2
FIG. 4. !Color
10 online" Experimentally obtained harmonic spectra in Ar. Red
10
1
10
0
10
-1
10
-2
10
-3
10
-4
10
-5
10
-6
10
-7
10
-8
②電場中の古典
的運動（加速）
トンネル電離と高調波の発生は、レー
ザーの半周期ごとに起こる。
0
10
20
30
Harmonic order
40
50
15
石川顕一
高調波の電場波形の概念図
harmonic field
harmonic intensity
実験的にも観測されている
fundamental field
PHYSICAL REVIEW
PRL Nabekawa
97, 153904et(2006)
al., Phys. Rev. Lett. 97, 153904 (2006)
-3
-2
0
-1
1
2
3
time [fs]
-2
-1
0
1
Fundamental optical cycle
f (t) = −f (t − π/ω0 )
FIG. 3 (colorレーザーの１周期(2.7
online). Estimated intensity profile
fs) of the atto-
2 second pulse train (dark-green curve with hatched area) and the
optical field (dark-blue curve).
基本波の奇数倍の周波数
the emission of a pulse of a high-order harmonic field every
half-cycle
period. In this model, the trajectory of the
成分のみを含む。
In
lock
ric a
from
enab
puls
of th
ing t
mea
field
optic
reali
W
gene
ciall
Scie
Scie
electron, moving along the direction of the electric field
of the fundamental laser, determines the phase of the
emitted harmonic field. Therefore, our finding of the
!-flipped phase in the attosecond pulse train verifies that
[1]
16 harmonic pulses are certainly from electrons detached
石川顕一[2]
from opposite sides at every half-cycle period of the fun-
１つの次数のみが存在するときの光電界
1.0
1.0
0.5
0.5
電場
電場
Electric field
Eh (t) = Eq cos(qω + φq ) = E2n+1 cos[(2n + 1)ω + φ2n+1 ]
0.0
0.0
-0.5
-0.5
-1.0
-1.0
-2
-1
0
1
時間（フェムト秒）
2
-0.40
-0.30
-0.20
時間（フェムト秒）
Time (fs)
Time (fs)
連続波（パルスではない）
Continuous wave (no pulse)
17
石川顕一
複数の次数（奇数次）が混在するときの光電界
Eh (t) =
!
Eq cos(qω + φq ) =
q
!
E2n+1 cos[(2n + 1)ω + φ2n+1 ]
q
1.0
電場
0.5
0.0
•
アト秒パルス列になっている。
•
パルスの間隔は、基本波の半周期
•
隣り合うパルスは位相が反転
-0.5
-1.0
-2
-1
0
1
時間（フェムト秒）
2
等間隔の周波数成分
等間隔のパルス列
18
石川顕一
高次高調波の奇数次のみを含む離散的
なピークは、二通りに解釈できる。
• 光子エネルギーの整数倍＋反転対称性
• 基本波の半サイクルごとの光放出
19
石川顕一
一定の時間間隔で放出される電子波束のエネ
ルギースペクトルは離散的になる
トンネル電離
• アト秒パルス列に（１光子）イオン化された電子
•
Photoelectron probability density (a.u.)
Soft X-ray electric field (a.u.)
1.5
1.0x10-6
h̄ω = 1.55 eV (λ = 800 nm)
τ = π/ω
1.0
0.5
0.0
-0.5
-1.0
-2
-1.5x10
-3
-2
-1
0
Time (fs)
1
2
3
1.0x104
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
10
0.0
0
100
Single pulse
Double pulse
Spectrum (arb. unit)
H23, H25, H27, H29, H31 of
∆E · τ = h
20
30
40
Photoelectron energy (eV)
200
300
400
50
500
Distance from the nucleus (a.u.)
光パルス（アト秒ダブルパルス）のスペクトルが離散的
２つの電子波束が空間的に重なることによる干渉
どちらのパルスにイオン化されたか分からないこと
による干渉縞（ヤングのダブルスリットの時間版）
20
K.L. Ishikawa, Phys. Rev. A 74, 023806 (2006) 石川顕一
次数によって高調波の発生時刻が異なる
Long
300
250
200
Figure 4. XFROG measurements [20]. The images on the right and left sides of
represent the photoelectron signal as a function of the delay between pump a
trajectory
and energy of the photoelectron (vertical). On the left, several sidebands w
22, 20, 18, 16, 14 from the測定
top to the bottom obtained for a Fourier-transform
laser pulse are shown. On the right, the sideband 18 is shown for three fun
chirps: bfund ¼ 1:2, 0, "0:8 # 1027 s"2. The graph in the middle shows the m
(filled symbols) and simulated (open symbols) chirp rates as a function of
理論
the three different fundamental
chirp cases (see text). The black straight line
the simulated points; the blue and red lines are obtained from the latter
equation (7).
short trajectory
150
100
0.0
Ne
高調波放出時刻
350
40
0.5
1.0
1.5
2.0
2.5
3.0
Electron energy (in Up)
ショートトラジェクトリーの場合
低次が先に高次が後で発生する。
ポジティブチャープ
Intensity (arb.units)
Phase of recombination (phi_r)
3.8×1014 W/cm2
30
20
10
0
0
500
1000
1500
Time (as)
2000
Mairesse et al., Science 302, 1540 (2003)
Figure 5. Attosecond pulse train corresponding to the superposition of gro
21
Varju et
al., J. Mod.
Opt.
379
14
consecutive harmonics
generated
in neon
at 52,
3:8 #
10(2005)
W cm"2: 石川顕一
harmonics
次数によって高調波の発生時刻が異なる
Phase of recombination (phi_r)
TDSEシミュレーション
350
Long trajectory
300
250
200
short trajectory
150
100
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Electron energy (in Up)
ショートトラジェクトリーの場合
ポジティブチャープ
ロングトラジェクトリーの場合
ネガティブチャープ
K. L. Ishikawa, “High-harmonic generation” in Advances in SolidState Lasers, ed. by M. Grishin (INTECH, 2010) 439-464
22
石川顕一
Time of recombination (as)
強度によって高調波の発生時刻が異なる
Long trajectory
2500
14
2
3.8 x 10 W/cm
2000
14
Xe
2
1.2 x 10 W/cm
1500
Ne
short trajectory
1000
20
30
40
50
Ar
60
70
Harmonic order
ショートトラジェクトリーの場合
次数が同じなら、高強度の時
の方が、早く発生する
Mairesse et al., Science 302, 1540 (2003)
同じ次数でも、強度によって発生時刻が異なる。
23
石川顕一
次数が同じなら、高強度の時の方が、早く発生する
強度上昇時は発生間隔が短い（ブルーシフト）
強度下降時は発生間隔が長い（レッドシフト）
ネガティブチャープ
Varju et al., J. Mod. Opt. 52, 379 (2005)
24
石川顕一
高調波のチャープのまとめ
•
異なる次数間 → ポジティブチャープ
•
１つの次数の中 → ネガティブチャープ
本来量子力学的なこれらの現象（実験的
にも観測されている）が、シンプルな３
ステップモデルで説明できる。
25
石川顕一
高次高調波発生の量子論
Lewensteinモデル
Lewenstein et al., Phys. Rev. A 49, 2117 (1994)
26
高強度場近似
Strong-field approximation (SFA)
• 励起状態の寄与を無視 The contribution of all the excited bound
states can be neglected.
• 連続状態に対する原子のポテンシャルの効果を無視
（連続状態を平面波で近似）The effect of the atomic potential on
the motion of the continuum electron can be neglected.
• 基底状態の減少を無視 The depletion of the ground state can be
neglected.
27
石川顕一
�
�
∂ψ(r, t)
1 2
i
= − ∇ + V (r) + zE(t) ψ(r, t)
∂t
2
双極子モーメント
x(t) ≡ �ψ(r, t) | z | ψ(r, t)�
Time-dependent dipole moment
=i
�
t
dt�
−∞
�
３ステップ
モデル
=i
�
t
−∞
dt�
� � t
�
��
�� 2
[p + A(t )]
3
iIp t
��
�
�
iIp t�
d p �ϕ(r)e |z|p + A(t)� exp −i
dt
�p + A(t )|zE(t )|ϕ(r)e
� + c.c.
2
t�
再結合
�
レーザー場中での運動
イオン化
� � t
�
��
�� 2
�
[p + A(t )]
d3 p �ϕ(r)eiIp t |z|p + A(t)� exp −i
dt��
�p + A(t� )|zE(t� )|ϕ(r)eiIp t � + c.c.
2
t�
再衝突電子波束と基底状態と
の間の双極子モーメント
x(t) = i
�
t
−∞
dt�
�
イオン化
再衝突電子波束
d3 p d∗ (p + A(t)) · exp[−iS(p, t, t� )] · E(t� )d(p + A(t� )) + c.c.
遷移双極子行列要素
transition dipole
半古典的作用積分
semiclassical action
S(p, t, t� ) =
�
t
dt��
t�
28
�
[p + A(t )]
+ Ip
2
��
2
�
石川顕一
高調波スペクトル＝双極子モーメントのフーリエ変換
x̂(ωh ) = i
�
∞
−∞
dt
�
t
−∞
dt�
�
d3 p d∗ (p + A(t)) · exp[iωh t − iS(p, t, t� )] · E(t� )d(p + A(t� )) + c.c.
５重積分
five-dimensional integral
鞍点解析
saddle-point analysis
cf. 経路積分
29
石川顕一
鞍点解析
saddle-point analysis (SPA)
Saddle-point equations 解→トラジェクトリー trajectory
2
�
[p + A(t� )]
= −Ip
2
t
[p + A(t�� )]dt�� = 0
トンネル電離
t’ イオン化時刻
t 再結合時刻
イオン化と再結合の位置が同じ
t�
2
[p + A(t)]
+ Ip = ωh
2
x̂(ωh ) =
�
s
�
π
� + 2i (ts − t�s )
高調波の光子エネルギー
＝ 再結合時の運動エネルギー
＋ イオン化ポテンシャル
�3/2
�
i2π
det S �� (t, t� )|s
d∗ (ps + A(ts ))
× exp[iωh ts − iS(ps , ts , t�s )]E(t�s )d(ps + A(t�s )),
• ３ステップモデルに物理的に対応
30
石川顕一
鞍点解の例
E(t) = E0 cos ωt
φ� = ωt�
φ = ωt
Ar (Ip = 15.7596 eV)
1.6 × 1014 W/cm
2
の実部（上）と虚部（下）
破線は３ステッ
プモデルの解
カットオフ
Ec = 3.17Up + gIp
(g ≈ 1.3)
「トンネル時間」
に対応すると解釈
されている
•
３ステップモデルは、量子力学的なLewensteinモデルのよい近似に
なっている。→ ３ステップモデルの成功の理由
31
石川顕一
attosecond pulse train (APT)
アト秒パルス列
と
単独アト秒パルス
isolated attosecond pulse (IAP)
32
高次高調波は、基本波レーザーの半周期ごとにア
ト秒のバーストとして発生する（アト秒パルス列）
Paul et al., Science 292, 1689 (2001)
世界初
PHYSICAL REVIEW
PRL
97,
153904
(2006)
Nabekawa et al., Phys. Rev. Lett. 97, 153904 (2006)
-3
-2
-1
0
1
2
3
time [fs]
FIG. 3 (colorレーザーの１周期(2.7
online). Estimated intensity profile
fs) of the attosecond pulse train (dark-green curve with hatched area) and the
optical field (dark-blue curve).
超短パルスレーザーを用い、１回だけバーストが発
the emission of a pulse of a high-order harmonic field every
half-cycle period. In this model, the trajectory of the
electron, moving along the direction of the electric field
生するようにすれば、単独パルスになる。
of the fundamental laser, determines the phase of the
In
lock
ric a
from
enab
puls
of th
ing t
mea
field
optic
reali
W
gene
ciall
Scie
Scie
emitted harmonic field. Therefore, our finding of the
!-flipped phase in the attosecond pulse train verifies that
[1]
33
石川顕一
harmonic pulses are certainly from electrons detached
[2]
~11° ( / 16 rad). (C to E) Spectra measured at the CE phase setting closest to
*#4 ,$+22 ,+/#223/# 1-2,#,: !"# +11#+%+'(# )* ,+/#223/#, ,#1+%+/#0 .6 ,#()'0 1%#
Fig. 1A. The zero+!!
ofDMNthe
CE phase scale in (A) was set to yield the best agreem
*%)$ /"# (#'/%+2 1-2,# 2#+0, /) + ,1#(/%+2 $)0-2+/3)' 43/" + )* /"# 4+;
spectra in (B). 1#%3)0 )* /43(# /"# 2+,#% 1")/)' #'#%&6L +, %#;#+2#0 .6 /"# (+2(-2+/#0 +$123/-0#
70
60
50
40
30
光の放出は１回だけ
6
86
4
0.8
0.6
94
2
–4
–2
0
Time (fs)
60
τx = 530 as
50
40
30
4
6
2
0.4
1
0.2
-200
-100
0
100
Time (as)
200
300
3'& /"# #;
+//),#()'0
*#45(6(2#
"3&"5"+%$
H$)%# 23T#
)/"#% /"+'
*%+(/3)' )
/3)' /) /"
0%3;#% 13$1%);# /"
$#'/,:
!"#$%&' (%
V3/" 3/, 0
%+6 1-2,#
#;)2-/3)'
3',/+'/+'#
;3,3.2# 23&
,3'-,)30+2
!"# 0)/, 3'
0 %#
$+''#%L
Delay
(fs
!9BD '$
"+;# /) %#$
)'# &#'#%+
(+2(-2+/#0
75%+6 ,)-%
!"# $#+
2+%&#% /"+'
/3;#26 /"#
/"+/ /"# ).
−2 5 P'($3('%#+
0 .'&<E#(+8
2 1#'&<'Q*2 4%#7"-&'( *1%#12*%; "&-E(# -. ' 2-.%<@<&';
−4
−2
2%'3""3(2#4
Delay
(fs)
5,# @<&'; "3(2# *2 "&-+3$#+ *1 ' G<77<(-16 IDD<7>'& 1#-1 6'2 =-(37# >; ' B<.28 BCD<
17 6'322*'1 ('2#& "3(2# )*%, '1 -1<'Q*2 "#'J *1%#12*%; -. L " FDF0 H $7!I4 R-& %,#
#(#$%&*$ E#(+ -. %,# ('2#& "3(2#8 %9# : ! #Q"9!# IS%IT :$-29&D# U !: )*%, ! O D 9$-2*1# "3(2#:8
1.0
),#&# %T *2 %,# "3(2# +3&'%*-18 &D *2 %,# '163('& $'&&*#& .&#?3#1$; '1+ ! *2 %,# V'>2-(3%#W
",'2#4 5,# +'2,#+ (*1# 2,-)2 %,# -1<'Q*2 #(#$%&*$
4 E#(+ -. %,# ('2#& "3(2# (#'=*16 %,#
*1%#&'$%*-1 &#6*-14 5,# $'($3('%#+ @<&'; &'+*'%*-1 *2 2#(#$%#+ )*%,*1 0.8
' C<#M 2"#$%&'( &'16#
1#'& LD #M4 N12#%8 $'($3('%#+ 9.3(( (*1#: '1+ 7#'23&#+ 9+-%%#+ (*1#: @<&'; "3(2# 2"#$%&37
τx2#(#$%#+
= 80 ±>;
5 as
%,# X-S!* &#Y#$%-&8 2,-)*16 %,'% '>-3% LDZ -. %,# %-%'( Y3#1$# *2 )*%,*1 '
3
C<#M &'16# '&-31+ LD #M4
0.6
)*+
-300
2
70
XUV spectral intensity (arb.u.)
C
90
Energy (eV)
phase (rad)
XUV intensity (arb.u.)
1.0
80
世界初
8
0
–6
−4
Light emission takes place
only once.
X-ray intensity (arbitrary units)
Photoelectron energy ( eV)
Baltuska et al. Nature 421, 611 (2003)
80
90
B
Laser electric field (arbitrary units)
単独アト秒パルス
90
A
Photoelectron energy ( eV)
,1#(/%-$ H*-22 23'#K 3' /"# 3',#/ )* I3&: J: !"# 0#1/" )* /"3,
$)0-2+/3)' 1%);30#, + ,#',3/3;# $#+,-%# )* ,+/#223/# ()'/#'/: !"#
$#+,-%#0 ,1#(/%-$ )* /"# "+%$)'3( 75%+6 1-2,# %#O#(/#0 .6 )-%
<)MP3
$-2/32+6#% H0)//#0
23'# Nature
3' /"# 3',#/ )*414,
I3&: JK ,#/,
+ ,+*#
-11#%
Hentschel
et al.
509
(2001)
D
Goulielmakis
etMagazine
© 2001 Macmillan
al.0.4
Science 320,
1614 (2008)
0.2
φ″=(1.5 ± 0
40
50
60
70 80
Photon
Attosecond (10 sec) pulse
アト秒パルス
Fig. 3. Sub-100-as XUV pulse retrieval. (A)-18
Measured ATR spectrogram com
spectra of photoelectrons launched by an XUV pulse with a bandwidth of ~28 eV
at delay settings increased in steps of 80 as. Here, a positive delay corresp
arriving before the NIR pulse. The high flux of the XUV source allows this spec
within ~30 min. (B) ATR spectrogram reconstructed after ~103 iterations of th
(C) Retrieved temporal intensity profile and spectral phase of the XUV pulse. T
34 XUV emission (Fig. 4B) is almost fully compensated by a 300-nm-thick
Zr foil i
石川顕一
アト秒パルスの応用例
時間分解オージェ電子分光
Auger effect
光電子
Auger
electron
オージェ電子
光電子
Probe…Laser
750 nm
Photoelectron
Pump…HHG soft x rays
13 nm
数フェムト秒程度の超高速過程が見える！
Ultrafast process a few fs
35
Drescher et al. Nature 419, 803 (2002)
石川顕一
アト秒パルスの応用例
DIRECT MEASUREMENT OF LIGHT WAVES
•
光の電界の直接測定に初めて成功！→光が「電磁波」である
ことの直接的な証明
Direct proof of the wave nature of light
E. Goulielmakis et al., Science 305, 1267 (2004).
36
石川顕一
rent experimental parameters, the small deviations between the electron’s exact motion and
that modeled via the CVA give rise to a 2-as
discrepancy in the relative delay.
Accepting this small discrepancy, manyelectron models were applied to investigate the
effects of electron correlation. As a first attempt,
the multiconfigurational Hartree-Fock method was
used to evaluate transition matrix elements from
the ground state of Ne to states where the electron
wave asymptotically propagated along the direction of the streaking NIR electric field. These
アト秒パルスの応用例
time for allowing us to track the history of
microscopic phenomena accurately (Fig. 1A)
calls for precise knowledge of the delay between the XUV pulse and an outgoing electron
wave packet (henceforth, absolute delay). This
can only be inferred from theory. For multielectron systems, such as Ne, physical description of the discrepancies revealed by this work
proved to be a challenge. The sensitive experimental test to which time-dependent manyelectron models can now be subjected will benefit
their development.
DELAY IN PHOTOEMISSION
WHEN DOES PHOTOEMISSION BEGIN?
The photoelectric effect is usually considered instantaneous. But ...
measure o
photoemis
lute delays
tested tim
Presently,
provide th
photoioniz
cause of lo
complex s
of the pho
streaking
atomic pho
sensitive t
ually impr
predictions
understand
and will m
atomic chr
e–
Ne
Ne+
∆t2s
Refere
1.
2.
3.
4.
5.
2p
Ne
6.
2s
7.
8.
Short light pulse
Ne
Ne+
9.
10.
11.
∆t2p
e–
Fig. 3. The relative delay between photoemission from the 2p and 2s subshells of Ne atoms, induced by
sub–200-as, near–100-eV XUV pulses. The depicted delays are extracted from measured attosecond
streaking spectrograms by fitting a spectrogram, within the strong-field approximation, with parameterized NIR and XUV fields. Our optimization procedure matches the first derivatives along the time delay
dimension of the measured and reconstructed spectrograms, thereby eliminating the influence of unstreaked background electrons [for details on the fitting algorithm, see (29)]. From the analysis of a set of
spectrograms, the measured delays and associated retrieval uncertainties are plotted against the amplitude
of the vector potential applied in the attosecond streak camera. Spectrograms measured in the presence of
a satellite attosecond pulse were found to exhibit a less accurate retrieval of the delay value. When a subset
of data (red diamonds) that represents scans with less than 3% satellite pulse content was evaluated, a
mean delay value of 21 as with a standard deviation of ~5 as was found. The green circles represent the
Schultze
Science
328,bandwidth
1658 (2010)
result of analyzing spectrograms
recorded et
withal.,
an XUV
pulse with narrower
in order to exclude
the potential influence of shakeup states contributing to the electron kinetic energy spectrum.
The 2s electron appears to come out 21 attoseconds earlier than the 2p electron!
•
•
•
Eisenbud–Wigner–Smith time delay
Continuum-continuum phase shift
Core rearrangement ??
37
Klünder et al., PRL 106, 143002 (2011)
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
H. Hertz
W. Hall
A. Einst
E. P. W
C. A. A.
83 (200
A. F. St
(Springe
S. T. Ma
M. Y. Iv
(2007).
A. Baltu
R. Kienb
M. Niso
(2009).
G. Sans
M. Schu
E. Gouli
M. Hent
A. Boris
Echeniq
A. L. Ca
A. K. Ka
177401
C. Leme
A 79, 0
J. C. Ba
043602
U. Beck
Photoio
(Plenum
A. Rude
J. Mauri
石川顕一
まとめ
•
時間領域で考えよう！
•
時間依存で考えよう！
38
石川顕一
チャレンジ
放射場を量子化して、高強度
場現象（トンネル電離、高次
高調波発生）を定式化するに
は、どうすればいいか？
39
石川顕一