Transcript Document

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-dependent Phenomena in Quantum Mechanics“
Blaubeuren, Sept.12 – 16, 2007
Collaborators
G. G. Paulus, Texas A & M, U. Jena
E. Hasovic, M. Busuladzic, A. Gazibegovic-Busuladzic,
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
Above-threshold ionization
the effects observed
are single-atom effects
(no collective effects)
but low counts
electrons have attosecond time structure just like HHG
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)
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
Tunneling ionization
atomic binding potential V(r)
ground-state
energy
interaction erE(t) with the laser field
combined effective potential V+erE(t)
v(t0)=0 at the exit of the tunnel
 4 2mI  is highly nonlinear

rate of tunneling ~ exp 
 in the field E(t)
 3e | E (t ) | 
3
p
0
Tunneling is a valid picture if
I

 1
2U
p
p
N.B.: Tunneling takes place at some specific time t0
Kinematics in a laser field
mv(t) = p – eA(t)
<A(t)>t = 0
velocity in a time-dependent laser field
(long-wavelength approximation)
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
The laser field provides a clock
T = 2.7 fs for a Ti:Sa 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
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
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
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
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)
An old experiment redone
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)
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)
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
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)
f= 0
„cosine“ pulse
one window in either
direction
t
p=eA(t)
„sine“ pulse
A(t)
f = p /2
t
one window in the positive
direction,
two windows in the negative
direction
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
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
Vp0 = <p-eA(t)|V|0>


 dt = 


( n 1)T
 dt
n =  nT
cont. next
page
One cycle vs many cycles
p
eA(t)
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 superposition of the two solutions within one cycle
energy
Two solutions per cycle for given p
One member of a pair of orbits experiences the Coulomb
potential more than the other
Interference of the two solutions from within one cycle
Fl = 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
High-energy electrons through re(back-)scattering
Fl = 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
Recollisions
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)
....
Formal description of rescattering
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
Quantum orbits in space and time
ionization time = t´
t = recollision time
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)
Few-cycle high-energy ATI spectra as a function of the
CE phase
very pronounced
left-right
(backward-forward)
asymmetry
Paulus et al. PRL 93,
253004 (2003)
employed to
determine the
CE phase
Nonsequential double and multiple
ionization
Sequential vs. nonsequential ionization: the total rate
the „knee“
nonsequential = not sequential
first observation and identification
of a nonsequential channel:
A. L‘Huillier, L.A. Lompre,
G. Mainfray, C. Manus,
PRA 27, 2503 (1983)
SAEA
The mechanism is, essentially,
rescattering,
like for high-order ATI and HHG
B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini,
K.J. Schafer, K.C. Kulander, PRL 73, 1227 (1994)
NB: the effect disappears for
circular polarization
Nonsequential double ionization:
the ion momentum
ion-momentum
distribution is
double-peaked
neon
laser field polarization
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)
S-matrix element for nonsequential double ionization
(rescattering scenario)
V(r,r‘) = V12 =
electron-electron
interaction
V12
= Volkov
state
time
V(r‘‘) = binding potential
of the first electron
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)
S-matrix element for nonsequential double ionization
(rescattering scenario)
V12
time
V(r,r‘) = V12 =
(effective)
electron-electron
interaction
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)
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 t=t(t‘) with energy Eret(t)
Energy conservation in the ensuing recollision
|Vpk|2
R(t‘) = |E(t‘)|-1 exp[-4(2m|E01|3)1/2/(3e|E(t‘)|)]
highly nonlinear in the field E(t‘)
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 t=t(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
Comparison: quantum vs classical model
quantum
classical
sufficiently high above
threshold,
the classical model
works as well
as the full quantum
model
Triple ionization
time
NB: one internal propagator
 4 additional integrations
Assume it takes
the time Dt for the
electrons to
thermalize
Nonsequential N-fold ionization via a thermalized
N-electron ensemble
fully differential N-electron distribution:
Ion-momentum distribution:
= mv(t+Dt)
integrate over unobserved momentum components
Dt = „thermalization time“
Ne3+
Ne3+
Ne4+
Comparison with Ne3+ MBI—MPI-HD data
Dt = 0
Dt = 0.17T
experiment: 1.5 x 1015 Wcm-2
Moshammer et al., PRL (2000)
MPI-HD –- MBI collaboration
classical statistical model
at 1.0 x 1015 Wcm-2
X. Liu, C. Faria, W. Becker, P.B. Corkum, JPB 39, L305 (2006)
Quantum effects of long quantum orbits
cf. poster by D. B. Milosevic
alternatively: Wigner-Baz threshold effects
(Manakov, Starace)
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)
„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
calculated ATI spectrum
No. of orbits
10
8
6
4
2
„longer
orbits“
4 and more
long vs.
short
ATI channel-closing (CC) enhancements
electron energy = 199 eV, Ti:Sa laser, He, 1.04 x 1015 Wcm-2 < I < 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
ATI channel-closing (CC) enhancements
electron energy = 199 eV, Ti:Sa laser, He, 1.04 x 1015 Wcm-2 < I < 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
Constructive interference of many long orbits
Conclusions
The black box of S-matrix theory ...
|out> = S|in>
|p>
|0>
S
... has been made transparent
|p>
|0>