atomic processes in strong laser fields dejan b....
TRANSCRIPT
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ATOMIC PROCESSES IN STRONG LASER FIELDS
DEJAN B. MILOŠEVIĆ
Faculty of ScienceDepartment of PhysicsUniversity of Sarajevo
Bosnia and Herzegovina
Attosecond Science Workshop, KITP, UCSB, August 16, 2006
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• Laser-assisted vs. laser-induced processes• Theory: S-matrix formalism – Feynman’s path integral –Strong-field approximation – Quantum-orbit theory• Examples• ATI by few-cycle pulses• Numerical simulations• ATI of diatomic molecules
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Collaboration• B. Piraux, Ph. Antoine, A. de Bohan, UCL, LLN, Belgium (1995-1998)• Fritz Ehlotzky, University of Innsbruck, Austria (1996-)• Anthony Starace, The University of Nebraska, Lincoln, USA (1998-)• Wilhelm Becker, Max-Born-Institute, Berlin (1999-):
Alexander von Humboldt, Volkswagenstiftung• Gerhard Paulus,Texas A&M University, MPI Garching (2000-)• Dieter Bauer, MPI, Heilderberg (2004-)• Misha Ivanov (Canada) NSERC• Marc Vrakking (AMOLF, Amsterdam)• Since 2000: Research group in Sarajevo
M.Sc. Postgraduate studentsAzra Gazibegović-Busuladžić Elvedin HasovićAner Čerkić Adnan MašićSenad Odžak Aida KramoMustafa Busuladžić
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• W. Becker, F. Grasbon, R. Kopold, D.B. Milošević, G.G. Paulus, and H. Walther Above-threshold ionization: from classical features to quantum effectsAdv. At. Mol. Opt. Phys. 48, 35-98 (2002)
• D.B. Milošević and F. EhlotzkyScattering and reaction processes in powerful laser fieldsAdv. At. Mol. Opt. Phys. 49, 373-532 (2003)
• D.B. Milošević, G.G. Paulus, D. Bauer, and W. BeckerAbove-threshold ionization by few-cycle pulsesJ. Phys. B 39, R203-R262 (2006)
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ATOMIC PROCESSES IN A STRONG LASER FIELD
• Laser-assisted processes
- Electron-atom scattering
(Weingartshofer et al. 1977)
- X-ray-atom scattering
- Electron-ion recombination
• Laser-induced processes
- Above-threshold ionization (ATI)
(Agostini et al. 1979)
- Above-threshold detachment
- High-order harmonic generation
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High-order ATI
(Paulus et al 1994)
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High Harmonics
3 ,5 ,7 ,ω ω ω …14 210 W/cm , I ω>
Strong Laser Field
Ar
High-order harmonic generation (1987)
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Three-step model
E
1
23
0z
nΩ ω=
( )fz t
( )iz t
KE
PI−
max 3.17P Pn I Uω = +
2/PU I ω∼
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X-ray – atom scattering
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DBM, F. Ehlotzky, PRA 58, 2319 (1998); Adv. AMOP 49, 373 (2003)
DBM, A. Starace, PRL 81, 5097 (1998); PRA 60, 3943 (1999); Laser Phys. 10, 278 (2000)
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Electron – atom scattering
A. Čerkić, DBM, PRA 65, 053402 (2004)
Laser Phys. 15, 268 (2005)
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DBM and F. Ehlotzky, PRA 65, 042504 (2002)
JMO 50, 657 (2003); Adv. AMOP 49, 373 (2003)
Electron – ion recombination
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The black box of S-matrix theory
S|out> |in>
( ) ( ) ( ),
ˆ ,limfi f it t
M t U t t tψ ψ′→∞ →−∞
′ ′=
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FEYNMAN’s PATH INTEGRAL
ix fx
it
ft
x
t
( )1x t
( )2x t( )clx t
i
f( )
fi
/eiS x tM ⎡ ⎤⎣ ⎦∝ ∑all paths
from i to f
( ) ( )( )f
i
, ,t
t
S dt L x t x t t= ∫
, 0S Sδ>> =Classical limit : Hamilton principle :
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( ) ⇒SFA Strong Field Approximation
( ) ( )fi f, ;L3
fi f i f f fi i i/
et iS t t p
M dt d p dt H U Hψ ψ∞
−∞ −∞
∝ ∫ ∫ ∫
( ) ⇒SPM Saddle Point Method
i f
0 S S St p t
∂ ∂ ∂= = = ⇒
∂ ∂ ∂ i f, ,t t p∈
( )fi fi fiexps sM A iΦ∝ ∑relevant paths:quantum orbits s
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( )
( )2
1i2
21
i i2
: HHG, HATI, HATD, NSDI: XSCA
: LAR, LAS
P
PK
II p A t
p A t
ω
⎫− ⎪
⎪ ⎡ ⎤− = +⎬ ⎣ ⎦⎪
⎡ ⎤+ ⎪⎣ ⎦ ⎭
( )I
( )II( ) ( ) ( ) ( )f
if i f i
t
tt t p A d r t r tτ τ− = ⇔ =∫
( ) ( )
( )
2 21 1
f f f2 2
21
f f 221,2
: HHG( ), LAR( ), XSCA( )
: HATI, LAS
: NSDI
P K K
j Pj
X I n
p A t p A t
p A t I
ω ω ω ′
=
⎧−⎪
⎪⎪⎡ ⎤ ⎡ ⎤+ = +⎨⎣ ⎦ ⎣ ⎦⎪
⎡ ⎤⎪ + +⎣ ⎦⎪⎩∑
( )III
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S-th QUANTUM ORBIT:
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
R
i
R
f
R R i i R f
R R f f R f
Re Re
Re (HATI)
s
s
t
ns s s s st
t
s s st
r t t t p d A t t t
r t t t p d A t t
τ τ
τ τ
= − + ≤ ≤
= − + ≥
∫
∫Quantum orbits depart from
the “exit of the tunnel” real time Rt − ⇒
( ) ( )i f f0 and real r t r t t= = ≈ ⇒Orbits return almost exactly to the origin
( )RRe nsr tDBM etal, J. Mod. Opt. 53, 125 (2006)
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Quantum orbits for elliptical polarization: Experiment vs. theory
ξ = 0.36
xenon at 0.77 x 1014Wcm-2
The plateau becomesa staircase
The shortest orbits arenot always the dominantorbits
Salieres, Carre, Le Deroff, Grasbon, Paulus, Walther, Kopold, Becker, Milosevic, Sanpera, Lewenstein, Science 292, 902 (2001)
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• High-order atomic processes in strong fields can be explained using SFA and QO theory
• Quantum orbits are superposed in the fashion of Feynman’s path integral
• QO can be complex to account for the tun-neling nature of the initial step of the process
• Fast calculations- Usually, only very few orbits need to be considered- If solutions are found for one set of parameters then the solutions for
arbitrary parameters can be obtained by analytical continuation
• Future: application of quantum orbits to more complex strong-field processes, inclusion of the Coulomb effects, …
• Examples
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( ) ( ) ( )1 2ˆ ˆc.c., / 2
2ir t is tiE t E e e E e e e x iyω ω− −
+ − ±= + + = ±
Bicircular field
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( )3 1 , 1n HωΩ = ± = ±
Bicircular field
( ) ( ) ( )21 2
ˆ ˆc.c., / 22
i t i tiE t E e e E e e e x iyω ω− −+ − ±= + + = ±
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Phys. Rev. A 61, 063403 (2000)
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Phys. Rev. A 62, 011403(R) (2000)
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Stereo-ATI experiment
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Stereo-ATI experiment: Correlation technique
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Stereo-ATI experiment: Experiment vs. theory
Paulus et al., Nature 2001 Milošević et al., PRL 2002
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Stereo-HATI experiment: stable CE phase
Paulus et al., Phys. Rev. Lett. 91, 253004 (2003)
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Milošević et al., Optics Express 11, 1418 (2003); Laser Phys. Lett. 1, 93 (2004)
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HATI by bicircular ω-ω field:
Electron emission angle = CE phase / 2
Biegert, Keller
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E. Hasović and DBM, Laser Phys. Lett. 3, 200 (2006)
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He, 800 nm, 1015 W/cm2, CIR + Static (%)
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S. Odžak and DBM, Phys. Lett. A 355, 368 (2006)
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Incoherent scattering
kfATI
A A
kfHATI
ksATI
A'A
kfIS
A. Čerkić and DBM J. Phys. B submitted
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Few-cycle (H)ATI
See DBM etal, J. Phys. B 39, R203 (2006)
and talk by Wilhelm Becker at conference
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Vp0 = <p-eA(t)|V|0>
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One cycle vs many cycles
eA(t)
p
nth cycle (n+1)st cycle (n+2)nd cycle
The discreteness of the spectrum is generated by the superposition of all cycles
The envelope is generated by the super-position of the two solutions within one cycle
energy
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Examples of direct quantum orbits
One member of a pair of orbits experiences the Coulomb potential more than the other
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Interference of the two solutions from within one cycle(includes focal averaging)
F-
λ = 1500 nm
cf. M.V. Frolov, N.M. Manakov, E.A. Pronin,A.F. Starace,JPB 36, L419 (2003)
Data: I. Yu Kiyan, H. Helm, PRL 90, 183001 (2003) (1.1 x 1013 Wcm-2 )Theory: D.B. Milosevic et al., PRA 68, 070502(R) (2003) (1.3 x 1013 Wcm-2 )
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Rescattered quantum orbits in space and time
ionization time = t´ t = recollision time
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Few-cycle-pulse ATI spectrum: violation of backward-forward symmetry
Different cutoffs
Peaks vs no peaks
argon, 800 nm7-cycle durationsine square envelopecosine pulse, CEP = 01014 Wcm-2
D. B. Milosevic, G. G. Paulus, WB, PRA 71, 061404 (2005)
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Building up thespectrum fromquantum orbits
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The black box of S-matrix theory ...
|out> = S|in>
S|p>
|0>
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... has been made transparent
|p>|0>
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ATI simulation
• S-matrix theory• SFA (1BA) with rescattering (2BA)• Physical interpretation via Quantum Orbits• Focal averaging + saturation effects• Gauge aspects are important (see WB)• Choice of the ground-state wave function• Coulomb effects for ATI (not included yet)
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QM transition amplitude
( ) ( ) ( ) ( )0
lim ,t
pi p itM i dt t U t t r E t tψ ψ
→∞′ ′ ′ ′= − ⋅∫Exact:
( ) ( )0 1pi pi piM M M= + +SFA:
( ) ( ) ( ) ( ) ( )0 00 0 0 0
0
exppT
pi i pM i dt p A t r E t iS tψ ⎡ ⎤= − + ⋅ ⎣ ⎦∫
( ) ( ) ( )
( ) ( ) ( ) ( )0
1 30 1 1 1
0
10 0 0 1 exp , ,
pT
pit
i p
M dt dt d k p A t V k A t
k A t r E t iS t t kψ
∞
= − + +
⎡ ⎤× + ⋅ ⎣ ⎦
∫ ∫ ∫
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Hartree-Fock ground-state wave functions, expanded on basis set of atomic Slater orbitals:
( ) ( )10
ˆj jn ri j j l
j
r C N r e Y rςψ −= ∑
Independent-particle-model optimized potential, represented by the double Yukawa potential:
( ) ( )/
/ 0.41 1 , r D
Hr DZ eV r H e H DZH r
−−⎡ ⎤= − + − =⎣ ⎦
He (1s, Z=2), Ne, Ar, Kr, Xe (5p, Z=54)
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He, 1015 W/cm2, 760 nm
Xe, 8.05x1013 W/cm2, 760 nm
( )1 21 lpiT M M∝ + −
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SPM for HATI and QO theory
Classification of saddle-point solutions: αβm
The uniform approximation
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Semiclassical analysis. Cutoff lawBusuladzic et al, Laser Phys. , 289 (2006)16 max 10.007 0.538p p pE U I= +
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• Enhancement of HATI at channel closings
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Gaussian focal averagingKopold et al, J. Phys. B 35, 217 (2002)
( ) ( )max 1/ 2
max
0
lnI
pi pi p p pn
IdIw w n E I U nI I
δ ω⎛ ⎞∝ + + −⎜ ⎟⎝ ⎠
∑∫
Improved algorithm which includes saturation effects – important for new Br- ATD experiments
( )
( )( ) ( )( )
20
,4
; , exp ' , '
plm p pn
t
plm lm
I tw d dt E I n
w n I t dt w I t
ρρρ δ ω
ω
ρ ρ
∞ ∞
−∞
−∞
⎛ ⎞∝ + + −⎜ ⎟⎜ ⎟
⎝ ⎠⎛ ⎞
× −⎜ ⎟⎝ ⎠
∑∫ ∫
∫
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No averaging Focal averaging
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24p pIE n Iωω
= − − ( )p cE n n ω= −c p pn I Uω = +nc-photon channel is closed
• Resonant-like enhancement at particular I• Channel-closing effect in HATI• Near channel closing Ep is low• Many QO interfere constructively• All intensities from I=0 to I=Imax contribute to the focal-averaged electron yield• Channel-closing intensities are:
( ) 2
,min ,min ,max
,min ,max max
4
, 1, ,
/ 1,
c c p
c c c c
c p c
I n I
n n n n
n I I I
ω ω
ω
= −
= +
⎡ ⎤= + ≤⎣ ⎦
…
enhancement regions – a series of rounded tops in the envelope of the electron spectra
,max ,min 1c cn n− +
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Intensity-dependent enhancements
intensityincreasesby 6%
Hertlein, Bucksbaum, Muller, JPB 30, L197 (1997) Paulus et al., PRA 64, 021401 (2001)
see, also, Hansch, Walker, van Woerkom, PRA 55, R2535 (1997)
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Physical origin of the enhancements
Constructive interference of long quantum orbits
Quantum effect!!!
For zero drift momentum,p = 0, the electron revisitsinfinitely often
p2/(2m) = Nω − Ip – Up = 0
Ip + Up = Nω„Channel Closing“
Analytical proof:S.V. Popruzhenko, P.A. Korneev, S.P. Goreslavskii, WB, PRL 89, 023001 (2002)D.B. Milosevic, WB, PRA 66, 063417 (2002)
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Alternative explanations of the intensity-dependent enhancements
Threshold cusps a la Wigner/Baz:
B. Borca, M.V. Frolov, N.L. Manakov, A.F. Starace, PRL 88, 193001 (2002)
Multiphoton resonance with ponderomotively upshifted Rydberg state:
H.G. Muller, F.C. Kooiman, PRL 81, 1207 (1998)H.G. Muller, PRL 83, 3158 (1999)J. Wassaf, V. Veniard, R. Taieb, A. Maquet, PRL 90, 013003 (2003)
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Enhancements disappear for short pulses
pulse duration
enhancements disappearfor short pulses
peaks become narrower for long pulses
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Focal-averaged angular-resolved ATI energy spectrum xenon, 760 nm, 8 x 1013 Wcm-2
contains the effects of
channel closings(several)
cutoff (rainbow)enhancements
con-/destructive interferences ofpairs of quantum orbitsand/or the twomembers of each pair
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Even (odd) CC vs. s (p) ground states
Manakov and Frolov, JETP Lett. 83, 536 (2006)
Krajewska, Fabrikant, and Starace, Phys. Rev. A (submitted)
DBM etal (in preparation)
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Conclusions• Realistic choices of the initial wave function and
the rescattering potential (improved SFA)• Plateau height: direct vs. rescattering
He (6 orders), Xe, Kr (1-2 orders)• Plateau length:
Direct: s-state (2-3Up), p-state (4Up => interf.) Rescattering:
• Quantum orbits αβm, θ – dependent cutoff• Focal averaging and saturation• Qualitative change due to channel closing eff.• CC – pronounced enhancement• Agreement with experimental results
max 10.007 0.538p p pE U I= +
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Ionization of a diatomic molecule by a strong laser field
( ) ( ) ( )22 2
tot , ,2 2 2
eA Be A A B B e A B
A B e
pP PH er e R e R E t V r R RM M m
= + + − + + ⋅ +
( ) ( )Jacobi
, , , , , , , ,e A B CM tr R R r R R i r R t H r R tΦ Φ→ ∂ =→
( ) ( ) ( )2 2
,2 2 r RP pH e r e R E t V r R
mµ= + − + ⋅ +
( ) ( ) ( ) ( ), A Be A e B ABV r R V r V r V R= + +
( ) ( )CM CM lim lim ,fi f i fit tS P P M t tδ
′→∞ →−∞′= −
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( ) ( ) ( )
( ) ( ) ( )
3 3 * 3 3, , , , , ,
, ,
t
fi ft
r R i
M t t i d d r d R r R t d r d R r R U t r R
e r e R r R
τ Φ τ
Ε τ Φ τ′
′ ′ ′ ′ ′=
′ ′ ′ ′× + ⋅
∫ ∫ ∫ ∫ ∫
Neglect e-a int: F FF e ABH H h H→ = +
( ) ( ) ( )2 2
, 2 2
F Fe r AB R AB
p Ph e r E t H e R E t V Rm µ
= − ⋅ = − ⋅ +
( ) ( ) ( )* * * *SFA : , , , ABv f
f f
iE tf f ep ABvU r R t r t R eΦ Φ φ ϕ→ =
( ) ( ) ( ) ( )( )BOA : , , ; ei ABvi
i
i E R E ti ei ABvr R t r R R eΦ φ ϕ +
=
( ) ( ) ( )
( ) ( ) ( )( )
( )
0
,
1/ 20 1
MO-LCAO : ;
2HFR-STO: ,
2 !
a
a a
a a
ei Ja a JJ A B a
na n r
a J l m
a
r R c r
r r e Yn
ς
φ ψ
ςψ θ ϕ
=
+
− −
=
=
∑ ∑
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( ) ( )( ) ( )CM CM 202 / 2
f i f ffi f i v v f ABv ABv ei p fin
S i P P S p E E E R U n T nπ δ δ ω= − − + − − + −∑
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g 23 HOMO of Nσ
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g 21 HOMO of Oπ
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N2
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O2
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g 21 HOMO of Fπ g 23 HOMO of Fσ