Attosecond dynamics of intense-laser induced atomic processes

W. BeckerMax-Born Institut, Berlin, Germany

D. B. MilosevicUniversity of Sarajevo, Bosnia and Hercegovina

395th Wilhelm und Else Heraeus Seminar„Time-dependent Phenomena in Quantum Mechanics“

Blaubeuren, Sept.12 – 16, 2007

supported in part by VolkswagenStiftung

Collaborators

G. G. Paulus, Texas A & M, U. Jena

E. Hasovic, M. Busuladzic, A. Gazibegovic-Busuladzic, U. Sarajevo, Bosnia and Hervegovina

M. Kleber, T. U. Munich

C. Figueira de Morisson Faria, University College, London

X. Liu, Chinese Academy of Sciences, Wuhan

Above-threshold ionization

the effects observedare single-atom effects(no collective effects)

but low counts

electrons have attosecond time structure just like HHG

Rescattering: „ears“ or „lobes“ and the plateau

Yang, Schafer, Walker, Kulander, Agostini, and DiMauro, PRL 71, 3770 (1993)

Paulus, Nicklich, Xu, Lambropoulos, and Walther,PRL 72, 2851 (1994)

Few-cycle pulses

E(t) = E0(t) cos(t + )

= carrier-envelope relative phase

A few-cycle pulse breaks the back-forward (left-right) symmetryof effects caused by a long pulse

Tunneling ionization

atomic binding potential V(r)

interaction erE(t) with the laser field

combined effective potential V+erE(t)

ground-state energy

v(t0)=0 at the exit of the tunnel

rate of tunneling ~

|)(|3

24exp

0

3

tEe

mIp is highly nonlinear

in the field E(t)

Tunneling is a valid picture if 12

p

p

U

I

N.B.: Tunneling takes place at some specific time t0

Kinematics in a laser field

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.

mv(t) = p – eA(t)

<A(t)>t = 0

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 = 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)

E. Goulielmakis et al., Science 305, 1267 (2004)

(mv02/2 = – IP)

An old experiment redone

The classical electron double-slit experiment C. Jönsson, Zs. Phys. 161, 454 (1961)

„The most beautiful experiment in physics“ according to a poll of the readers of Physics World (Sept. 2002)

5

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 A(t) = A0 ex cos2( t/nT) sin(t -)

= 0 „cosine“ pulse

„sine“ pulse

one window in eitherdirection

one window in the positivedirection,two windows in the negativedirection

A(t)

t

A(t)

p=eA(t)

t

Theory vs. experiment:

solution of the TDSE including the Coulomb field

„simple-man“ model ignoring the Coulomb field

The Coulomb field IS important

F. Lindner et al.PRL 95, 040401 (2005)

Quantum-mechanical description:

The Strong-Field Approximation (KFR)Keldysh (1964), Faisal (1973), Reiss (1980)

neglects, in brief,the Coulomb interaction in the final (continuum) statethe interaction with the laser field in the initial (bound) state

Vp0 = <p-eA(t)|V|0>

cont. next page

n

Tn

nTdtdt)1(

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

One cycle vs many cycles

energy

One member of a pair of orbits experiences the Coulomb potential more than the other

Two solutions per cycle for given p

Interference of the two solutions from within one cycle

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

F-

= 1500 nm

High-energy electrons through re(back-)scattering

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

F-

= 1500 nm

rescattering

Recollisions

Recollision: one additional interaction with the atomic potential

responsible for high-order harmonic generation,nonsequential double and multiple ionizationhigh-order above-threshold ionization (HATI)....

Formal description of rescattering

Mechanism of nonsequential double ionization: Recollision of a first-ionized electron with the ion

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

time

position in thelaser-field direction

Quantum orbits in space and time

ionization time = t´ t = recollision time

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)

Few-cycle high-energy ATI spectra as a function of the CE phase

very pronouncedleft-right(backward-forward)asymmetry

employed todetermine theCE phase

Paulus et al. PRL 93, 253004 (2003)

Nonsequential double and multiple ionization

Sequential vs. nonsequential ionization: the total rate

the „knee“

B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer, K.C. Kulander, PRL 73, 1227 (1994)

nonsequential = not sequential

first observation and identificationof a nonsequential channel:A. L‘Huillier, L.A. Lompre, G. Mainfray, C. Manus,PRA 27, 2503 (1983)

The mechanism is, essentially,rescattering, like for high-order ATI and HHG

SAEA

NB: the effect disappears forcircular polarization

Nonsequential double ionization:the ion momentum

neon

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)

ion-momentumdistribution isdouble-peaked

laser field polarization

S-matrix element for nonsequential double ionization(rescattering scenario)

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)

time

V12

V(r,r‘) = V12 =electron-electroninteraction

V(r‘‘) = binding potentialof the first electron

= Volkovstate

S-matrix element for nonsequential double ionization(rescattering scenario)

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)

time

V12

V(r,r‘) = V12 =(effective)electron-electroninteraction

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 abovethreshold,the classical model works as well as the full quantummodel

Triple ionization

Assume it takes the time t for the electrons to thermalize

time

NB: one internal propagator 4 additional integrations

Nonsequential N-fold ionization via a thermalizedN-electron ensemble

Ion-momentum distribution:

fully differential N-electron distribution:

integrate over unobserved momentum components

= mv(t+t)

t = „thermalization time“

Ne3+

Ne3+

Ne4+

Comparison with Ne3+ MBI—MPI-HD data

experiment: 1.5 x 1015 Wcm-2

Moshammer et al., PRL (2000)MPI-HD –- MBI collaboration

classical statistical modelat 1.0 x 1015 Wcm-2

t = 0

t = 0.17T

X. Liu, C. Faria, W. Becker, P.B. Corkum, JPB 39, L305 (2006)

Quantum effects of long quantum orbits

alternatively: Wigner-Baz threshold effects(Manakov, Starace)

cf. poster by D. B. Milosevic

Intensity-dependent enhancements of groups of ATI peaks

Constructive interference of long orbits at a channel closing, Ip + Up = (integer) x

experiment: Hertlein, Bucksbaum,Muller, JPB 30, L197 (1997)

theory: Kopold, Becker, Kleber, Paulus, JPB 35, 217 (2002)

intensityincreasesby ~ 5%

Quantummechanical energies: Ep = n – Up - Ip

at a channel closing, Up + Ip = Nhence Ep = 0 for N = n

the electron can revisit the ion infinitely often

„Long orbits“ or „late returns“

interference of different pathways into the same final state

calculated ATI spectrum

No. of orbits

108642

long vs.short

„longerorbits“4 and more

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 quantumorbits included in the calculation

a few orbits aresufficient toreproduce thespectrum,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 quantumorbits included in the calculation

a few orbits aresufficient toreproduce thespectrum,except near CCs

Constructive interference of many long orbits

Conclusions

|out> = S|in>

S

The black box of S-matrix theory ...

|p>|0>

... has been made transparent

|0>|p>