Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

Takeshi Sato (佐藤健) http://ishiken.free.fr/english/lecture.html http://www.atto.t.u-tokyo.ac.jp/report/lecture/sato_takeshi-lecture.html [email protected]

Advanced Plasma and Laser Science
 プラズマ・レーザー特論E
 


Attosecond Science
 アト秒科学 2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

femtosecond, attosecond ミリ

m

10-3

マイクロ

μ

10-6

ナノ

n

10-9

ピコ

p

10-12

フェムト

f

10-15

アト

a

10-18

Light propagates during 30 fs …

3 × 10 (m/s) × 30 × 10 8

−15

(s) = 9 × 10

−6

(m) = 9 µm 2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

Why so short pulses?

necessary shutter speed snapping ultrafast motion 3

for

2016/5/24

Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

Attosecond science Electron

atomic unit of time = 24 attoseconds Orbital period of the Bohr electron Nucleus

2⇡ T = = 2⇡ !

r

2 e 1 2 mω r = 4πϵ0 r2

4⇡✏0 mr3 = 152 as = 2⇡ a.u. 2 e

real-time observation and time-domain control of atomic-scale electron dynamics 2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

1. Strong field approximation (SFA) 2. Attosecond streaking experiment (1)Direct measurement of light waves (2)Delay in photoemission (overview) (3)Auger dynamics (overview)

3. Molecular orbital tomography 4. Ultrafast hole migration

2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

1 Strong field approximation (SFA) Lewenstein model

M. Lewenstein et al., Phys. Rev. A 49(3), 2117

Time-dependent Schrödinger equation i

(r, t) = t

1 2

2

+ V (r) + − zE(t)

(r, t),

Strong-field approximation (SPA)

• The contribution of all the excited bound states can be neglected. • The effect of the atomic potential on the motion of the continuum electron can be neglected. • The depletion of the ground state can be neglected.

2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

2-1 Direct measurement of light waves Light is an electromagnetic wave

光は電磁波である

Maxwell

1864年 ∇ · D = ρ

∇·B=0 ∂B =0 ∇×E+ ∂t ∇×H=J …しかし、一体誰が光の電界が波 打つのを見たことがあるのか？ But who ever saw a light field oscillate?

2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

2-1 Direct measurement of light waves Attosecond streaking

Pump

Probe

高調波とレーザー光を遅 延時間を持たせて照射 Irradiate an atom with an attosecond pulse and laser pulse with delay 2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

2-1 Direct measurement of light waves

高調波とレーザー光を遅延 時間を持たせて照射し、光 電子スペクトルを測定。 Irradiate an atom with an attosecond pulse and laser p u l s e w i t h d e l a y, a n d measure a photoelectron spectrum

Classical model E(t) = E0 (t) cos(ωt + φ)

Newton equation

dv dp =m = −eE(t) dt dt

ionization at

ニュートン方程式

t = tr で電離

Initial momentum 初速度（運動量） 2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

2-1 Direct measurement of light waves

高調波とレーザー光を遅延 時間を持たせて照射し、光 電子スペクトルを測定。 Irradiate an atom with an attosecond pulse and laser p u l s e w i t h d e l a y, a n d measure a photoelectron spectrum

Classical model Momentum at the detector

p=

e

Z

1 tr

p = p0 + ∆p

! p0 = 2m(¯hωX − Ip )

E(t)dt =

eA(tr )

検出器での運動量

A(t) =

Z

E(t)dt

Momentum change is directly related with the electron ejection time 2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

2-1 Direct measurement of light waves

高調波とレーザー光を遅延 時間を持たせて照射し、光 電子スペクトルを測定。 Irradiate an atom with an attosecond pulse and laser p u l s e w i t h d e l a y, a n d measure a photoelectron spectrum

Classical model Kinetic energy at the detector

p0 p W ⇡ W0 + = W0 m

Electron kinetic energy

Ejection time

p0 eA(tr ) m

p20 W0 = 2m

検出器での 運動エネルギー photoelectron energy vs. delay 光電子のエネルギーと 遅延時間の関係

2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

2-1 Direct measurement of light waves

高調波とレーザー光を遅延 時間を持たせて照射し、光 電子スペクトルを測定。 Irradiate an atom with an attosecond pulse and laser p u l s e w i t h d e l a y, a n d measure a photoelectron spectrum

Lewenstein model a(p, ⌧ ) = i

Z

1 1

photoelectron momentum spectrum a(p, ) action 作用積分 Z 1 i i(p2 +Ip )t exp[ iS(t)]EX (t ⌧ )dp A(t) dt = i e dp A(t) EX (t ⌧ )e dt attosecond pulse electric field アト秒パルスの電場波形

S(p, t) =

+

Z ✓

◆ − A(t)]2 [p + + Ip dt 2

1

(t) = t

p · A(t ) + − A2 (t )/2 dt

2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

2-1 Direct measurement of light waves FROG-CRAB

(Frequency-Resolved Optical Gating - Complete Reconstruction of Attosecond Bursts)

photoelectron momentum spectrum

|a(p, )|2 = (t) = t

Spectrogram Principle

ei

(t)

dp+A(t) EX (t

)ei(p

2

2 /2+Ip )t

dt

p · A(t ) + A2 (t )/2 dt 2

S( , ) =

G(t)E(t

)ei t dt

! = p2 /2 + Ip

If a spectrogram 2

S( , ) =

G(t)E(t

)ei t dt

is measured for different values of delay , the field E(t) and gate G(t) can be reconstructed (principal component generalized projections algorithm). widely used to analyze laser pulses 2016/5/24

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Photo

1 60 use Advanced Plasma and Laser Science (Takeshi SATO) for internal only (Univ. of Tokyo)

A

C

2-1 Direct measurement of light waves 70

50

60

40

40

1

0

0

Electron counts (arb. u.)

Photoelectron energy (eV)

FROG-CRAB 50

ϕ = 70°

20 40 60 80 100 120 140 160 1 Carrier-envelope phase (deg)

D ϕ = 130° (Frequency-Resolved Optical Gating - Complete Reconstruction of Attosecond Bursts) Fig. 2. Control of bandpass-filtered XUV emission wit

e60i (t) dp+A(t) EX (t

t

)e

50 40

(t) =

p · A(t ) + A2 (t )/2 dt 0

90

dt

1

E

ϕ = 170°

A

1

80

0 30

20 40 60 80 100 120 140 16070 Carrier-envelope phase (deg)

40 50 60 70 Photoelectron energy (eV)

60

90

80

80 70

60

2 emission with the waveform of monocycle light. Mea Fig. 2. Control of bandpass-filtered XUV 50 50 RAPID COMMUNICATIONS i t 2 (A) and simulated (B) (17) photoelectron spectra versus CE phase, with the delay increased in ste S( , ) = G(t)E(t )e dt = psetting /2 closest + Ipto the values select40 40 ! CE phase ~11° ( p/ 16 rad). (C to E) Spectra measured at the

PHYSICAL REVIEW A 71, 011401#R$ #2005$

Fig. 1A. The zero of the CE phase scale in (A) was 30 set to yield the best agreement with the mo 30 spectra in (B).

80 70 60 50 40 30

0.8

0.8

80

0.6

2

4

4 τx= 80 ± 5 as

70

3

60

0.4

50

0.2

40

C

−2

0 Delay (fs)

2

4

-300

2 1

-200

−4

-100

0

100

200

−2 2 Time (as)0 Delay (fs)

300

4

Fig. 3. Sub-100-as XUV pulse retrieval. (A) Measured spectra of photoelectrons launched by an XUV pulse with 1.0 D at delay settings increased 2016/5/24 in steps of 80 as. Here, a 14 4 arriving before the NIR pulse. The high flux of the XUV

Goulielmakis et al. (2008) arb.u.)

.u.)

1.0

B C 90

0 Delay (fs)

30 −4

FIG. 1. #a$ CRAB trace of a single 315 as pulse !full width at half maximum #FWHM$ of intensity", having second- and third-

1.0

Photoelectron energy ( eV)

A XUV intensity (arb.u.)

90

−2

phase (rad)

Photoelectron energy ( eV)

−4

XUV spectral intensity (arb.u.)

Spectrogram

70

Photoelectron energy ( eV)

|a(p, )| = 2

Photoelectron energy ( eV)

photoelectron momentum spectrum

(A) and simulated (B) (17) photoelectron spectra versus ~11° ( p/ 16 rad). (C to E) Spectra measured at the CE 2 scale in (A) was set Fig. 1A. The20zero of the CE phase spectrai(p in (B)./2+Ip )t

B

0.8

Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

2-1 Direct measurement of light waves Measurement of light fields

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).

2016/5/24

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RAPID COMMUNICATIONS Spectrogram

PHYSICAL REVIEW A 71, 011401#R$ #2005$

Musical score

Most people think of acoustic waves in terms of a musical score. Intensity

pp

ff

pp

frequency

ts e y dn d. e y e it. cce ts y n re e e

Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

time

A mathematically rigorous form of a musical score is the “spectrogram.”

FIG. 1. #a$ CRAB trace of a single 315 as pulse !full width at half maximum #FWHM$ of intensity", having second- and thirdorder spectral phases #Fourier limit= 250 as$, gated by a Fourierlimited 6-fs 800 nm laser pulse, of 0.5 TW / cm2 peak intensity. The electrons are collected around % = 0 with an acceptance angle of ±30°. #b$, #c$ A comparison of the exact as pulse and the laserinduced gate phase !#t$ #full line$ with the corresponding reconstructions #dots$ obtained from the CRAB trace after 100 iterations

2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

2 Attosecond streaking experiment Attosecond streaking as a pump-probe Pump（イオン化を引き起こす）

高調波(HHG)

Probe（電子の放出時刻を測る）

レーザー光（laser）

More generally Pump: induce something Probe: measure something, with delay

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Does Photoemission Begin?

2-2 Delay in photoemission

f photoemission was one s that led to the formuantum mechanics. If an bsorbs sufficient energy ght, it can transfer that on, which is then emittoemission mainly focus e temporal or dynamic —but complex electron that will create a slight absorption and electron e delay has been poorly undamental reason: We om absorbing a photon. ollow subsequent emisthem to establish a “time t was absorbed. A practieen that the time delay is d only recently have direct feasible with the advent pulses on the attosecond ale. On page 1658 of this and co-workers present me delays between differrocesses generated by the ht pulse. This finding not studies of the timing of lso provides a new way to interactions in atoms.

More in depth @ 7/5, 12 (Multielectron)

The complex dynamics of atomic photoemission has a simple origin—the emission of a negatively charged electron changes the neutral atom into a positive ion. The energy levels of the remaining electrons are different

in the positive ion, and as the electrons adjust to their new energy levels, they release energy that is transferred to the outgoing electron. The time needed for this transfer is the origin of the small time delays.

Downloaded from www.sciencemag.org o

Ultrafast spectroscopy and multielectron Advanced Plasma and Laser Science (Takeshi SATO)electron for internal use only (Univ. of Tokyo) calculations reveal complex dynamics occurring just before an atom emits a photoelectron.

When Does Photoemission Begin? The photoelectric effect is usually considered instantaneous.

ic, Molecular, and Optical Physics, d Physics, Queen’s University BelE-mail: [email protected]

e– Ne

Ne+ ∆t2s

2p

Ne 2s

Short light pulse

Ne

Ne+ ∆t2p e–

Electron hesitation. Schematic diagram of a photoemission process for Ne. An incoming photon of an ultrashort light pulse is absorbed by either a 2s (top row) or a 2p (bottom row) electron. After photoabsorption, the electron escapes, while the orbitals of the other electrons adjust to the new surroundings as the atom becomes an ion. This adjustment leads to a time delay ∆t in the emission of the electron, which is longer for emission of a 2p electron than for emission of a 2s electron.

2016/5/24

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nucleus. Further- parameters, the measured delay of ~20 as cannot be explained distance of less than 1 Å from the function cðeÞ describes properties of rent experimental thefully small devia- thetime for allowing us to track the history of measure o screening played a dominant role, the by a delayed onset of streaking, whichAdvanced was the more, ifPlasma the wave packet. this representation, a delay Dtphenomena and Laser Science (Takeshi SATO) internal use only (Univ. photoemis tions between the electron’s exact In motion and for microscopic accurately (Fig.of 1A)Tokyo) dominant effect in (17). The streaking NIR faster 2p electrons would be exposed to the in photoemission, shown as a shift of the electhat modeled via the CVA give rise to a 2-as calls for precise knowledge of the delay be- lute delays field may be significantly screened by bound streaking field earlier than the slower 2s ones, tron’s trajectory in Fig. 1B, adds eℏ Dt to the phase discrepancy in the relative delay. tween the XUV pulse and an outgoing electron tested tim electrons at small distances from the nucleus. whereas measurements and quantum simulations of cðeÞ. It is therefore meaningful to define the Accepting small delay discrepancy, manywave packet first. this group After the absorption of an XUV photon, it takes show that the slower electron is emitted of the outgoing electron wave pack-(henceforth, absolute delay). This Presently, models were to investigate theworkcan Now we turn our attentionelectron to the quantumthe positive-energy electron a finite time to leave et,applied in accordance with earlier (4, only 5, 25),beas inferred from theory. For multi- provide th dAs a first attempt, of electron systems, such as Ne, physical descrip- photoioniz of all, we need a correlation. this screened volume, and this time interval may mechanical description. First effects aðeÞ ¼ ℏ de arg½cðeÞ%. Analyzingelectron our simulathedelay. multiconfigurational Hartree-Fock was the tion of the discrepancies revealed by this work cause of lo Consider tions, be different for electrons originating from dif- definition for the photoemission we averagemethod aðeÞover bandwidth of to created evaluate matrix proved jyðtÞ〉 bytransition ferent orbitals. However, for an atom, this dif- a photoelectron wave functionused the XUV pulseelements (29) andfrom denote the resulttoasbe a. a challenge. The sensitive exper- complex s the ground state of Ne to states where the electron imental test ference cannot exceed a few attoseconds. The an XUV pulse centered at t ¼ 0. The motion of As the first and most important task, we val-to which time-dependent many- of the pho is conve- idate characteristic scales can be extracted from the the wave packet after photoionization the experimental Intuitively, wave asymptotically propagated along the methodology. direc- electron models can now be subjected will benefit streaking continuum states one classical trajectories shown in Fig. 1B. If we as- niently described in a basis oftion expects thatfield. a delay in the formation of a atomic pho of the streaking NIR electric These their development. sume that the 2s and 2p electrons are set in je〉, each of which has a well-defined energy e wave packet causes a corresponding temporal sensitive t motion at the same moment, their classical and describes a wave that propagates in the di- shift of the streaking spectrogram. This holds true ually impr

2-2 Delay in photoemission More in depth @ 7/5, 12 (Multielectron)

The 2s electron appears to come out 21 attoseconds earlier than the 2p electron! Downloaded from www.sciencemag.org on June 21, 2011

predictions understand and will m atomic chr

Refere 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Fig. 3. The relative delay between photoemission from the 2p and 2s subshells of Ne atoms, induced by Schultze et al.,sub–200-as, Science 328, 1658 (2010) 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 result of analyzing spectrograms recorded with an XUV pulse with narrower bandwidth in order to exclude the potential influence of shakeup states contributing to the electron kinetic energy spectrum.

Eisenbud‒Wigner‒Smith time delay Coulomb-laser coupling

laser-induced initial- and final-state distortion

2016/5/24

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

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

2-3 Auger dynamics

More in depth @ 7/5, 12 (Multielectron)

Auger effect Photoelectron 光電子 Auger electron オージェ電子 Photoelectron 光電子

Ejection of a core electron

内殻電子が電離（光電効果） Instantaneous Core-excited ion

内殻励起状態のイオン ~ a few fs Ejection of a valence electron

特性Ｘ線を放出するかわり に軌道電子を放出 Observation of the ejection of Auger electrons →Ionizing X rays < a few fs
 →Attosecond pulse 2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

2-3 Auger dynamics

More in depth @ 7/5, 12 (Multielectron)

Auger effect Photoelectron 光電子 Auger electron オージェ電子 Photoelectron 光電子

Auger electron

Probe…Laser 750 nm

Pump… HHG soft x ray 13 nm Photoelectron

10フェムト秒程度の超高速過程が見える！ Ultrafast process 10 fs

2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

3 Molecular orbital tomography Matter is made up of molecules.

Hydrogen atom (H)

Carbon atom (C)

Oxygen atom (O)

A molecule is made up of atoms.

But how do atoms link to each other at all? What is chemical bond?

Hydrogen molecules (H2)

Water (H2O)

Oxygen molecules (O2)

Carbon dioxide (CO2)

Methane (CH4)

2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

3 Molecular orbital tomography

Bonds in general are a mixing or sharing of the electrons from different atoms. Nitrogen atom (N)

Nitrogen molecule (N2)

In atoms and molecules, electrons are not point particles but spread out like a cloud or wave...

How the electron wave is shared by atoms is described by molecular orbital (wave function). Theory first developed in late 1920s, Nobel prize in 1966 Now, basis for the understanding of molecular structures and chemical reaction. But, how do the molecular orbital really looks?

2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

3 Molecular orbital tomography Molecular orbital tomography

Not just the electron density Experiment

| (r)|

2

But the wave function itself

(r)

Theory

Nitrogen molecule (N2)

is measured. The wave function can be measured!

Jiro Itatani et al., Nature (2004) 2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

3 Molecular orbital tomography Classical model Laser field E(t) = E0 cos ωt レーザー電場 recombination 再結合→ 発光 photon emission (HHG) electron 電子

トンネル 電離 tunneling ionization

電場中の古典 的運動

Semiclassical electron motion

Quantum mechanical theory

2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

3 Molecular orbital tomography Lewenstein model Time-dependent dipole moment

(r, t) | z | (r, t)

x(t)

transition dipole matrix element x(t) = i

t

dt

d3 p d (p + A(t)) · exp[ iS(p, t, t )] · E(t )d(p + A(t )) + c.c.

recombination

Semiclassical action 作用積分 exp[ iS(p, t, t )]

propagation t

S(p, t, t ) =

dt t

ionization

[p + A(t )]2 + Ip 2

phase of a path (in the spirit of path integral) 経路の位相（ファインマンの経路積分に関連）

Clear physical picture corresponding to the three-step model

2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

3 Molecular orbital tomography Time-dependent dipole moment x(t) = i

t

x(t)

(r, t) | z | (r, t)

d3 p d (p + A(t)) · exp[ iS(p, t, t )] · E(t )d(p + A(t )) + c.c.

dt

recombination

propagation

ionization

Fourier transform フーリエ変換 x ˆ(

h)

=i

t

dt

dt

d3 p d (p + A(t)) · exp[i

iS(p, t, t )] · E(t )d(p + A(t )) + c.c..

ht

4

10

Harmonic spectrum

|ˆ x(

2 h )|

2

10

0

10

-2

10

-4

10

-6

10

-8

10

-10

10

-12

10

-14

10

0

20

40

60 80 100 Harmonic order

120

140

2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

3 Molecular orbital tomography From another viewpoint 別の視点から t

x(t) = i

d3 p d (p + A(t)) · exp[ iS(p, t, t )] · E(t )d(p + A(t )) + c.c.

dt

=

= a(k, t) amplitude of the recolliding wave ground state 基底状態 packet 再結合電子波

g (r) | r | e

k = p + A(t) x ˆ(

h)

a(k)

g (r)

g (r)

|ˆ x(

2 )| h

|r|e

|r|e

|

ik·r

束の振幅 a(k, t)e

ik·r

ik·r

=i

2 ˆ (k)| k g

k

ik·r

ˆ (k) g

electron 電子

The harmonic spectrum contains the information of the spatial Fourier transform of the ground-state wave function 高次高調波スペクトルは、原 子や分子の波動関数の空間フーリエ変換の情報を含んでいる。 2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

3 Molecular orbital tomography |ˆ x( Molecular axis 分子軸

k

2 )| h

|

2 ˆ (k)| k g

Laser polarization レーザーの偏光方向

1. Align molecules (Pump) 2. Measure harmonic spectrum (Probe) 3. Repeat for different alignment angles

4

10

2

10

0

10

-2

10

-4

10

-6

10

-8

10

-10

10

-12

10

-14

10

0

20

40

60 80 100 Harmonic order

120

140

Reconstruction of

g (r) 2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

3 Molecular orbital tomography Computed tomography (CT)

X-ray absorption measurement from different angles. 様々な 方向からエックス線を照 射し、吸収測定 Reconstruction 再構成

3D image 三次元画像が得られる。

2016/5/24

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Advanced Plasma

Calibrating the continuum wave packet

dimensional Fourier transform F of the object. This is the basis of computed tomography based on the inverse Radon transform. Our and Laser Science (Takeshi SATO) for internal dipole is the Fourier transform of a projection of the wavefunction, and so can be inverted. We describe the mathematical details of the tomographic reconstruction in the Methods section. This procedure can reconstruct orbital shapes with symmetries such as jg, pg and pu, using harmonics 17–51 of an 800-nm laser field and 25 angles from 08 to 1808 (fewer angles are needed for symmetric molecules). A complete inversion of a general orbital requires knowledge of the relative phase and amplitude of each harmonic for two ortho-

use only (Univ. of Tokyo)

3 Molecular orbital tomography

As discussed above, the harmonic spectrum is an experimental evaluation of the dipole, d(q). If we could evaluate the plane-wave amplitude a[k(q)] independently, then our measurement would R determine w g(r)(er)exp[ik(q)x]dr — that is, the spatial Fourier components of rw g(r). One way to do this is to perform the same experiment with a reference atom. Argon is very similar to N2 in its response to strong laser fields, having nearly the same ionization potential and intensity-dependent ionization probability6. This is confirmed by the dependence of the instantaneous ionization rates29 for atoms, and for different orientations of N2 (ref. 30). That means that the first, critical, step in the three-step high harmonic generation process is the same. Because the laser field dominates wave packet motion in the direction of the laser field, the second step, which determines the chirp of the re-colliding wave packets seen by Ar or N2, will be the same. Thus, a[k(q)] will be the same. The continuum wave packet will also be similar for Ar and N2. The narrow saddle point through which the electron tunnels acts as a spatial filter that removes much of the structure of the orbital from the continuum wave packet. This can be seen in numerical simulations31. By measuring the ellipticity dependence of the high harmonic signal24 produced by N2 and argon, we confirmed that the lateral spread of the wave packets is similar. The ionization rate of N2 is angle-dependent30,32, but is readily measured from the ion yield, and varies only by 25% for N2 (ref. 33). This variation is almost cancelled by the angular dependence of the wave-packet

|ˆ x(

2 )| h

|

2 ˆ (k)| k g

k

Experiment

Theory (Hartree-Fock)

Reconstruction 再構成

Nitrogen molecule (N2)

Jiro Itatani et al., Nature (2004)

Figure 3 High harmonic spectra were recorded for N2 molecules aligned at 19 different angles between 0 and 908 relative to the polarization axis of the laser. For clarity, only some of the angles have been plotted above. The high harmonic spectrum from argon is also shown; argon is used as the reference atom. Clearly the spectra depend on both the

Figure 4 Molecular orbital wavefunction of N2. a, Reconstructed wavefunction of the HOMO of N2. The reconstruction is from a tomographic inversion of the high harmonic spectra taken at 19 projection angles. Both positive and negative values are present, so this is a wavefunction, not the square of the wavefunction, up to an arbitrary phase. b, The shape of the N2 2p jg orbital from an ab initio calculation. The colour scales are the same for both images. c, Cuts along the internuclear axis for the reconstructed (dashed) and

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

3 Molecular orbital tomography

Wave function can be measured! 波動関数は測定できる！ Experiment

Wave function is measured!

= | | exp(i ) Theory (Hartree-Fock)

Nitrogen molecule (N2)

Jiro Itatani et al., Nature (2004)

X-ray diffraction, electron microscope, STM etc. measures just electron density. 2

=| |

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

3 Molecular orbital tomography MO tomography as a pump-probe Pump（alignment）

Relatively weak laser

Probe（HHG => Molecular orbital）

Strong laser

More generally Pump: induce something Probe: measure something, with delay

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produced a doubly charged molecular fragment ation of isolated attosecond pulses in 2002 ical reaction in a D2 molecule (13). Although the Advanced Plasma and Laser Science (Takeshi SATO) for of internal onlyand (Univ. ofmiTokyo) by ejection a seconduse electron, charge study of more complex molecules is challenging, This demonstration was then followed by gration manifested itself as a sub-4.5-fs oscillaa formative measurement of the amino acid er important experimental results in the field tion in the yield of this fragment as a function phenylalanine has shown that ionization by a ultrafast atomic physics, such as the real-time of pump-probe delay. Numerical simulations of short APT leads to dynamics on a temporal scale ervation of electron tunneling (3) and the the temporal evolution of the electronic wave of a few tens of femtoseconds. This has been inasurement of temporal delays of the order of packet created by the attosecond pulse strongly terpreted as the possible signature of ultrafast w tens of attoseconds in the photoemission support the interpretation of the experimental electron transfer inside the molecule (14). lectrons from different atomic orbitals of neon フェニルアラニン data in terms of charge migration resulting from The application of attosecond techniques to and argon (5). The unprecedented time resoultrafast electron dynamics preceding nuclear molecules offers the possibility of investigating on offered by attosecond pulses has also alrearrangement. primary relaxation processes, which involve eleced quantum mechanical electron motion and The a-amino acids consist of a central carbon tronic and nuclear degrees of freedom and their degree of coherence to be measured in atoms atom (a carbon) linked to an amine (-NH2) coupling. In the case of large molecules (e.g., biusing attosecond transient absorption specgroup, a carboxylic group (-COOH), a hydrogen ologically relevant molecules), prompt ionizascopy (6). Attosecond techniques have been amino acid lied in the field of ultrafast solid-state physwith the measurement of delays in electron アミノ酸 otoemission from crystalline solids (7) and Fig. 1. Three-dimensional investigation of the ultrafast field-induced structure of phenylalanine. ulator-to-conductor state transition in a diMolecular structure of the most ctric (8). In the past few years, attosecond abundant conformer of the ses have also been used to measure ultrafast aromatic amino acid phenylalanine. ctronic processes in simple molecules (9). SubDark gray spheres represent mtosecond electron localization after attocarbon atoms; light gray spheres, ond excitation has been observed in H2 and D2 hydrogen atoms; blue sphere,

4. Ultrafast hole migration

Ultrafast electron dynamics in phenylalanine initiated through ionization by attosecond pulses Calegari et al., Science 346, 336-339 (2014)

N

O

biological effect of ionizing radiation

itute of Photonics and Nanotechnologies (IFN)–Consiglio onale delle Ricerche (CNR), Piazza Leonardo da 32, 20133 Milano, Italy. 2Departamento de Química, ulo 13, Universidad Autónoma de Madrid, Cantoblanco 49 Madrid, Spain. 3Department of Physics, Politecnico di no, Piazza Leonardo da Vinci 32, 20133 Milano, Italy. tre for Plasma Physics, School of Maths and Physics, en’s University, Belfast BT7 1NN, UK. 5IFN-CNR, Via ea 7, 35131 Padova, Italy. 6Dipartimento di Scienze miche e Farmaceutiche, Università di Trieste and –Istituto Officina dei Materiali, 34127 Trieste, Italy. ituto Madrileño de Estudios Avanzados en Nanociencia, oblanco, 28049 Madrid, Spain.

nitrogen; and red spheres, oxygen. The molecular geometry has been optimized by using density functional theory (DFT) with a B3LYP functional.

放射線の生物効果

responding author. E-mail: [email protected] (F.M.); [email protected] (M.N.)

6

17 OCTOBER 2014 • VOL 346 ISSUE 6207

sciencemag.org SCIENCE

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ttosecond techniques to ssibility of investigating esses, which involve elecees of freedom and their large molecules (e.g., biecules), prompt ioniza-

al nine. e most he nylalanine. sent spheres, here, s, oxygen. has density with a

data in terms of charge migration resulting from Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo) ultrafast electron dynamics preceding nuclear rearrangement. The a-amino acids consist of a central carbon atom (a carbon) linked to an amine (-NH2) group, a carboxylic group (-COOH), a hydrogen

4. Ultrafast hole migration

N

O

pump sub-300 as XUV 15-35 eV probe 4 fs VIS/NIR 1.77 eV / 700 nm

sciencemag.org SCIENCE

detect ++NH -CH-R dication 2

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only the be related to nuclear which scale. The experimental displayand a riseLaser time of Advanceddata Plasma Science (Takeshi SATO) dynamics, for internal use usually only (Univ.430 of K, Tokyo) substantially pr come into play on a longer temporal scale, ulti10 T 2 fs and an exponential decay with time mentary materi mately leading to charge localization in a parconstant of 25 T 2 fs [this longer relaxation time figuration show ticular molecular fragment. Indeed, standard constant is in agreement with earlier experiTo further inv we also varied width of the att an indium foil XUV spectrum width at half m 15 eV, followed component ext doubly charged ly visible, sugge involves relativ cation. We have gram with all th alanine generat all the states of materials). A nu states of the ca dication are po tion of just a fe cannot be acces in the case of X dium foil. In th states to the low the less probab photons. We also perfo describe the ho Fig. 2. Pump-probe measurements. (A) Yield of doubly charged immonium ion (mass/charge = 60) as second pulse si a function of pump-probe delay, measured with 3-fs temporal steps.The red line is a fitting curve with an ment. Details o exponential rise time of 10 fs and an exponential relaxation time of 25 fs. (B) Yield of doubly charged supplementary immonium ion versus pump-probe delay measured with 0.5-fs temporal steps, within the temporal central frequen 36 2016/5/24 window shown as dotted box in (A). Error bars show the standard error of the results of four measurethe pulse, a ma

4. Ultrafast hole migration

dication yield oscillates with period

4.3 fs

assigned to electron dynamics in the molecule

Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

4. Ultrafast hole migration

Time evolution of hole density (calculation) 正孔密度の時間発展

detected Create wave packet 波束の生成

Energy levels of relevant species エネルギーレベル probe: 1.77 eV / 700 nm 4 fs VIS/NIR pump: 15-35 eV sub-300 as XUV

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

4. Ultrafast hole migration

Hole migration as a pump-probe Pump（single ionization => hole）

sub-300 as XUV

Probe（further ionization & fragmentation）

4 fs VIS/NIR

More generally Pump: induce something Probe: measure something, with delay 2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

Hole density (calculation) 2016/5/24

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Advanced Plasma and Laser Science (Takeshi SATO) for internal use only (Univ. of Tokyo)

Summary

1. Strong field approximation (SFA) Lewenstein model

2. Attosecond streaking experiment Atomic time scale

3. Molecular orbital tomography Atomic length scale

4. Ultrafast hole migration Atomic time and length scales

Today within SAE & SFA approximations Multielectron phenomena & First principle theories @ 7/5, 12 2016/5/24

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