Attosecond dynamics of intense-laser

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Attosecond dynamics of intense-laser induced
atomic processes
W. Becker Max-Born Institut, Berlin, Germany D.
B. Milosevic University of Sarajevo, Bosnia and
Hercegovina
supported in part by VolkswagenStiftung
395th Wilhelm und Else Heraeus Seminar Time-depen
dent Phenomena in Quantum Mechanics Blaubeuren,
Sept.12 16, 2007
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Collaborators
G. G. Paulus, Texas A M, U. Jena
E. Hasovic, M. Busuladzic, A. Gazibegovic-Busuladz
ic, U. Sarajevo,
Bosnia and Hervegovina
C. Figueira de Morisson Faria, University
College, London
X. Liu, Chinese Academy of Sciences, Wuhan
M. Kleber, T. U. Munich
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Above-threshold ionization
the effects observed are single-atom effects (no
collective effects) but low counts
electrons have attosecond time structure just
like HHG
4
Rescattering ears or lobes and the plateau
Paulus, Nicklich, Xu, Lambropoulos, and
Walther, PRL 72, 2851 (1994)
Yang, Schafer, Walker, Kulander, Agostini, and
DiMauro, PRL 71, 3770 (1993)
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Few-cycle pulses
E(t) E0(t) cos(wt f)
f carrier-envelope relative phase
A few-cycle pulse breaks the back-forward
(left-right) symmetry of effects caused by a long
pulse
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Tunneling ionization
atomic binding potential V(r)
ground-state energy
interaction erE(t) with the laser field
combined effective potential VerE(t)
v(t0)0 at the exit of the tunnel
is highly nonlinear in the field E(t)
rate of tunneling
Tunneling is a valid picture if
N.B. Tunneling takes place at some specific time
t0
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Kinematics in a laser field
velocity in a time-dependent laser field
(long-wavelength approximation)
mv(t) p eA(t)
ltA(t)gtt 0
p drift momentum
The electron tunnels out at t t0 with v(t0) 0
p eA(t0)
The drift momentum is given by the vector
potential at the time of ionization. Conversely,
the time of ionization can be determined from the
drift momentum observed.
At the end of the laser pulse, A(t) 0
p drift momentum momentum at the detector
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The laser field provides a clock
T 2.7 fs for a TiSa laser with w 1.55 eV
Electron motion in the laser field takes place on
the scale of T
Streaking principle p eA(t0) p0
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which can be started, e.g., by an additional xuv
pulse
Electron motion in the laser field takes place on
the scale of T
Streaking principle p eA(t0) p0
10
which can be started, e.g., by an additional xuv
pulse
Electron motion in the laser field takes place on
the scale of T
Streaking principle p eA(t0) p0
11
which can be started, e.g., by an additional xuv
pulse
Electron motion in the laser field takes place on
the scale of T
Streaking principle p eA(t0) p0
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Reconstruction of the electric field with the
help of an attosecond xuv pulse
measure the momentum of an electron ionized by
the attosecond pulse at time t0
p mvo eA(t0)
(mv02/2 W IP)
E. Goulielmakis et al., Science 305, 1267 (2004)
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An old experiment redone
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The classical electron double-slit experiment
C. Jönsson, Zs. Phys. 161, 454 (1961)
5m
The most beautiful experiment in physics
according to a poll of the readers of Physics
World (Sept. 2002)
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We mention that you should NOT attempt actually
to set up this experiment (unlike those we
discussed earlier). The experiment has never
been done this way. The problem is that the
apparatus to be built would have to be
impossibly small in order to display the effect
of interest to us. We are doing a thought
experiment, which we designed so that it would
be easy to discuss. (Feynman 1965)
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From slits in space to windows in time the
attosecond double slit
one and the same atom can realize the single slit

and the double slit at the same time
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Single slit vs. double slit by variation of
the carrier-envelope phase f
A(t) A0 ex cos2(p t/nT) sin(wt - f)
A(t)
cosine pulse
f 0
t
one window in either direction
peA(t)
sine pulse
A(t)
f p /2
one window in the positive direction, two windows
in the negative direction
t
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Theory vs. experiment
The Coulomb field IS important
solution of the TDSE including the Coulomb
field
F. Lindner et al. PRL 95, 040401 (2005)
simple-man model ignoring the Coulomb field
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Quantum-mechanical description
The Strong-Field Approximation (KFR) Keldysh
(1964), Faisal (1973), Reiss (1980)
neglects, in brief, the Coulomb interaction in
the final (continuum) state the interaction with
the laser field in the initial (bound) state
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Vp0 ltp-eA(t)V0gt
cont. next page
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One cycle vs many cycles
p
eA(t)
nth cycle
(n1)st cycle
(n2)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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Two solutions per cycle for given p
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
F-
l 1500 nm
Data I. Yu Kiyan, H. Helm, PRL 90, 183001
(2003) 1.1 x 1013 Wcm-2 Theory D.B.
Milosevic et al., PRA (2003) 1.3 x
1013 Wcm-2
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High-energy electrons through re(back-)scattering
F-
l 1500 nm
rescattering
Data I. Yu Kiyan, H. Helm, PRL 90, 183001
(2003) 1.1 x 1013 Wcm-2 Theory D.B.
Milosevic et al., PRA (2003) 1.3 x
1013 Wcm-2
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Recollisions
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Recollision one additional interaction
with the atomic potential
responsible for high-order harmonic
generation, nonsequential double and multiple
ionization high-order above-threshold ionization
(HATI) ....
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Formal description of rescattering
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Mechanism of nonsequential double ionization
Recollision of a first-ionized electron with the
ion
time
position in the laser-field direction
On a revisit (the first or a later one), the
first-ionized electron can free another bound
electron (or several electrons) in an inelastic
collision
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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
argon, 800 nm 7-cycle duration sine square
envelope cosine pulse, CEP 0 1014 Wcm-2
Different cutoffs Peaks vs no peaks
D. B. Milosevic, G. G. Paulus, WB, PRA 71,
061404 (2005)
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Few-cycle high-energy ATI spectra as a function
of the CE phase
very pronounced left-right (backward-forward) asym
metry
Paulus et al. PRL 93, 253004 (2003)
employed to determine the CE phase
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Nonsequential double and multiple ionization
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Sequential vs. nonsequential ionization the
total rate
the knee
nonsequential not sequential
first observation and identification of a
nonsequential channel A. LHuillier, L.A.
Lompre, G. Mainfray, C. Manus, PRA 27, 2503
(1983)
SAEA
The mechanism is, essentially, rescattering,
like for high-order ATI and HHG
NB the effect disappears for circular
polarization
B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini,
K.J. Schafer, K.C. Kulander, PRL 73, 1227 (1994)
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Nonsequential double ionization the ion momentum
ion-momentum distribution is double-peaked
R. Moshammer, B. Feuerstein, W. Schmitt, A.
Dorn, C..D. Schröter, J. Ullrich, H. Rottke, C.
Trump, M. Wittmann, G. Korn, K. Hoffmann, W.
Sandner, PRL 84, 447 (2000)
neon
laser field polarization
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S-matrix element for nonsequential double
ionization (rescattering scenario)

V(r,r) V12 electron-electron interaction
V12
V(r) binding potential of the first electron
Volkov state
time
A. Becker, F.H.M. Faisal, PRL 84, 3546 (2000) R.
Kopold, W. Becker, H. Rottke, W. Sandner, PRL
85, 3781 (2000) S.V. Popruzhenko, S. P
Goreslavski, JPB 34, L230 (2001) C. Faria, H.
Schomerus, X. Liu, W. Becker, PRA 69, 043405
(2004)
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S-matrix element for nonsequential double
ionization (rescattering scenario)

V(r,r) V12 (effective) electron-electron in
teraction
V12
time
A. Becker, F.H.M. Faisal, PRL 84, 3546 (2000) R.
Kopold, W. Becker, H. Rottke, W. Sandner, PRL
85, 3781 (2000) S.V. Popruzhenko, S. P
Goreslavski, JPB 34, L230 (2001) C. Faria, H.
Schomerus, X. Liu, W. Becker, PRA 69, 043405
(2004)
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A classical model
Injection of the electron into the continuum at
time t at the rate R(t) The rest is
classical The electron returns at time tt(t)
with energy Eret(t) Energy conservation in the
ensuing recollision

Vpk2
R(t) E(t)-1 exp-4(2mE013)1/2/(3eE(t))
highly nonlinear in the field E(t)
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A classical model
Injection of the electron into the continuum at
time t at the rate R(t) The rest is
classical The electron returns at time tt(t)
with energy Eret(t) Energy conservation in the
ensuing recollision

All phase space, no specific dynamics
Cf. statistical models in chemistry, nuclear, and
particle physics
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Comparison quantum vs classical model
quantum
sufficiently high above threshold, the classical
model works as well as the full quantum model
classical
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Triple ionization
time
Assume it takes the time Dt for the electrons
to thermalize
NB one internal propagator ? 4 additional
integrations
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Nonsequential N-fold ionization via a
thermalized N-electron ensemble

fully differential N-electron distribution
Ion-momentum distribution
mv(tDt)
integrate over unobserved momentum components
Dt thermalization time
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Ne3
Ne3
Ne4
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Comparison with Ne3 MBIMPI-HD data
Dt 0
Dt 0.17T
experiment 1.5 x 1015 Wcm-2
classical statistical model at 1.0 x 1015 Wcm-2
Moshammer et al., PRL (2000) MPI-HD - MBI
collaboration
X. Liu, C. Faria, W. Becker, P.B. Corkum, JPB 39,
L305 (2006)
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Quantum effects of long quantum orbits
cf. poster by D. B. Milosevic
alternatively Wigner-Baz threshold
effects (Manakov, Starace)
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Intensity-dependent enhancements of groups of ATI
peaks
Constructive interference of long orbits at a
channel closing, Ip Up (integer) x w
intensity increases by 5
experiment Hertlein, Bucksbaum, Muller, JPB 30,
L197 (1997)
theory Kopold, Becker, Kleber, Paulus, JPB 35,
217 (2002)
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Long orbits or late returns
Quantummechanical energies Ep nw Up - Ip
at a channel closing, Up Ip Nw hence Ep 0
for N n
the electron can revisit the ion infinitely often
interference of different pathways into the same
final state
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calculated ATI spectrum
longer orbits 4 and more
No. of orbits
10 8 6 4 2
long vs. short
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ATI channel-closing (CC) enhancements
electron energy 199 eV, TiSa laser, He, 1.04 x
1015 Wcm-2 lt I lt 1.16 x 1015 Wcm-2
number of quantum orbits included in the
calculation
a few orbits are sufficient to reproduce
the spectrum, except near CCs
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ATI channel-closing (CC) enhancements
electron energy 199 eV, TiSa laser, He, 1.04 x
1015 Wcm-2 lt I lt 1.16 x 1015 Wcm-2
number of quantum orbits included in the
calculation
a few orbits are sufficient to reproduce
the spectrum, except near CCs
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Constructive interference of many long orbits

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Conclusions
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The black box of S-matrix theory ...
outgt Singt
pgt
0gt
S
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... has been made transparent
pgt
0gt