1. Xiao Min Tong and Chii Dong Lin
Above-threshold-ionization (ATI) of atoms in an intense, few-cycle laser pulse
Marlene Wickenhauser
Collaborators:
Xiao Min Tong and Chii Dong Lin

2. Schematic picture Calculation: atom laser pulse
ionization of electron
atom Ar
laser pulse
Calculation:
= 10 fs
= nm
Electron spectra
2D momentum distribution
I ~ 2 x 1014 W/cm2

3. Motivation Recent experiments: MPI Heidelberg, KSU e- P (a.u.) atom
A. Rudenko et al. J. Phys. B 37 L407 (2004)
P|| (a.u.)
P (a.u.)
atom
5 x 1014 W/cm2
800 nm
Low energy spectra: -lots of structure even in tunneling regime

4. Multiphoton ionization
Introduction
Tunneling ionization
Multiphoton ionization
Above-threshold-ionization (ATI)
Keldysh parameter:

5. Typical ATI spectrum ħω ATI peaks Absorbed Photons 12 14 16 18 20 22
P. H. Bucksbaum PRA (1988) ħω ħω
ATI peaks
Ionization potential
ponderomotive energy
Electrons/eV
Energy (eV)
Helium I= 2.3 x 1014 W/cm2
= 8 ps, nm

6. Outline Theory Energy Spectra 2D electron-momentum distribution
Projection on parallel momentum

7. Theory 1) Numerical solution of TDSE
-Single active electron approximation
-grid
-Split operator method for time propagation
2) Strong field approximation (SFA)
Neglect: -Coulomb field on ionized electrons
-Depletion of ground state
-Other bound states
Dipole transition moment
Laser-dressed energy

8. Energy spectrum SFA TDSE Argon I ~ 1.7 x 1014 W/cm2 = 400 nm 10 fs
Energy (eV)

9. Electron spectra from a short pulse
No well defined frequency & intensity
time
P (arb. unit)
Energy (eV)

10. Redefined Volkov phase
Laser-dressed energy:
energy shift: average=Up
electron-field coupling
Energy (eV)
-No subpeaks
-ATI peaks shifted

11. 2D momentum Distribution - SFA
Argon
I ~ 1.7 x 1014 W/cm2
= 400 nm
10 fs
P (a.u.)
P|| (a.u.)
ATI peaks
Subpeaks
Parity
Angular momentum
Energy (eV)

12. Comparison with TDSE P (a.u.) P|| (a.u.) SFA TDSE 0 0.3 0.6 0 0.3 0.6
P (a.u.)
TDSE
P|| (a.u.)

13. Intensity dependence Ar 400 nm
Ip + Up
threshold
Channel closing:
6 ħω
Ar: Ip = eV
1.7 x 1014 W/cm2: Up= 2.55 eV Ip
6 ħω
intensity
P (a.u.)
1.7 x 1014 W/cm2
3.2 x 1014 W/cm2
2.4 x 1014 W/cm2
3.9 x 1014 W/cm2
P|| (a.u.)

14. Momentum projection e- Interesting points: atom P (arb. unit)
Ne: 25 fs, 800 nm, I = 4 x 1014 W/cm2
Rudenko et al. J. Phys. B 37 L407 (2004)
P (arb. unit)
P|| (a.u.)
atom
Interesting points:
Dip in contrast to ADK
Neon, Helium: dip
Argon: peak
~ 0.6

15. Explanation for dip in literature
Rescattering: J. Chen et al, PRA (R) (2000)
Coulomb potential: K. Dimitriou et al, PRA (R) (2004)
Position of ATI peaks: (in tunneling regime) F. H. M. Faisal et al, J. Phys. B 38 L223 (2005)
Freeman Resonance: A. Rudenko et al, J. Phys. B 37 L407 (2004)

16. Argon 400 nm 10 fs dip peak Multiphoton P|| (a.u.) P|| (a.u.)
I = 1.7 x 1014 W/cm2
I = 3.9 x 1014 W/cm2
g ~ 1.76
g ~ 1.13
P|| (a.u.)
P|| (a.u.)
P|| (a.u.)

17. Argon 800 nm 10 fs dip peak Tunneling P|| (a.u.) P|| (a.u.)
I = 1.65 x 1014 W/cm2
I = 1.8 x 1014 W/cm2
g ~ 0.89
g ~ 0.85
P|| (a.u.)
P|| (a.u.)

18. Conclusion Subpeaks in ATI spectra from short pulses
Explained structures in 2D momentum distribution
Dip in parallel momentum:
-Tunneling regime: ATI peaks
-Multiphoton regime: Parity of first ATI peak
-Coulomb effect not relevant
-Longer pulses: Freeman resonances