Abstract

Recently observed momentum distribution of doubly charged recoil-ions of atoms produced by femtosecond infrared laser pulses is analyzed using the so-called intense-field many-body S-matrix theory. Observed characteristics of the momentum distributions, parallel and perpendicular to the polarization axis, are reproduced by the theory. It is shown that correlated energy-sharing between the two electrons in the intermediate state and their ‘Volkov-dressing’ in the final state, can explain the origin of these characteristics.

© Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Doerner, "Recoil-ion momentum distribution for single and double ionization of helium in strong laser fields," Phys. Rev. Lett. 84, 443-446 (2000).
    [CrossRef] [PubMed]
  2. R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schroeder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, W. Sandner "Momentum distribution of Ne^n+ ions created by an intense ultrashort laser pulse," Phys. Rev. Lett. 84, 447-450 (2000).
    [CrossRef] [PubMed]
  3. B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer and K.C. Kulander "Precision measurement od strong field double ionization of helium," Phys. Rev. Lett. 73, 1227-1230 (1994).
    [CrossRef] [PubMed]
  4. S. Larochelle, A. Talebpour and S.L. Chin, "Non-sequential multiple ionization or rare gas atoms in a Ti:sapphire laser field," J. Phys. B 31, 1201-1214 (1998).
    [CrossRef]
  5. J.S. Parker, K.T. Taylor, C.W. Clark and S. Blodgett-Ford, "Intense-field mutliphoton ionisation of a two-electron atom," J. Phys. B 29, L33-L42 (1996).
    [CrossRef]
  6. E.S. Smyth, J.S. Parker and K.T. Taylor, "Numerical integration of the time-depedent Schroedinger equation for laser-driven helium," Comp. Phys. Comm. 114, 1-14 (1998).
    [CrossRef]
  7. J.S. Parker, L.R.Moore, K.J. Mehring, D.Dundas and K.T. Taylor, "Double-electron above threshold ionization of helium,' J. Phys. B 34, L69-L78 (2001).
    [CrossRef]
  8. F.H.M. Faisal and A. Becker, "'Intense-Field Many-Body S-Matrix Theory' and mechanism of laser induced double ionization of Helium," in Selected Topics on Electron Physics, D.H. Campbell and H. Kleinpoppen, eds. (Plenum Press, New York, 1996) pp. 397-410.
    [CrossRef]
  9. F.H.M. Faisal and A. Becker, "Effect of rescattering on ATI and e-e correlation on double ionization in intense laser fields" in Multiphoton Processes 1996, P. Lambropoulos and H. Walther, eds., Int. Nat. Conf. Ser. No. 154 (IOP: Bristol, 1997) pp. 118-131.
  10. F.H.M. Faisal, A. Becker and J. Muth-Boehm, "Intense-Field Many-Body S-Matrix Theory: Applications to processes in intense laser fields," Laser Phys. 9, 115-123 (1999).
  11. A. Becker and F.H.M. Faisal, "Mechanism of laser-induced double ionization of helium," J. Phys. B 29, L197-L202 (1996).
    [CrossRef]
  12. F.H.M. Faisal and A. Becker, "Non-sequential double ionization: Mechanism and model formula," Laser Phys. 7, 684-689 (1997).
  13. A. Becker and F.H.M. Faisal, "Interplay of electron correlation and intense field dynamics in double ionization of helium," Phys. Rev. A 59, R1742-R1745 (1999).
    [CrossRef]
  14. A. Becker and F.H.M. Faisal, "Production of high charge states of Xe in a femtosecond laser pulse," Phys. Rev. A 59, R3182-R3185 (1999).
    [CrossRef]
  15. A. Becker and F.H.M. Faisal, "S-matrix analysis of ionization yields of noble gas atoms at the focus of Ti:sapphire laser pulses," J. Phys. B 32, L335-L343 (1999).
    [CrossRef]
  16. A. Becker and F.H.M. Faisal, "Interpretation of momentum distribution of recoil ions from laser induced nonsequential double ionization," Phys. Rev. Lett. 84, 3546-3549 (2000).
    [CrossRef] [PubMed]
  17. F.H.M. Faisal, "Exact Solution of the Schroedinger Equation of Two Electrons Interacting with an Intense Electromagnetic Field," Phys. Lett. A 187, 180-184 (1994).
    [CrossRef]
  18. A. Becker and F.H.M. Faisal, "Correlated Keldysh-Faisal-Reiss theory of above-threshold double ionization of He in intense laser fields," Phys. Rev. A 50, 3256-3264 (1994).
    [CrossRef] [PubMed]
  19. F.H.M. Faisal, Theory of Multiphoton Processes (Plenum Press: New York, 1987).
  20. C. Joachain, Quantum Collision Theory, 3rd edn., (North-Holland, Amsterdam, 1983).
  21. H.R. Reiss, "Effect of an intense electromagnetic field on weakly bound system," Phys. Rev. A 22, 1786-1813 (1980).
    [CrossRef]
  22. L.V. Keldysh, "Ionization in the field of a strong electromagnetic wave," Sov. Phys. JETP 20, 1307-1314 (1965) [Zh. Eksp. Teor. Fiz. 47, 1945-1957 (1964)]
  23. F.H.M. Faisal, "Multiple Absorption of Laser Photons by Atoms," J. Phys. B 6, L89-92 (1973).
    [CrossRef]
  24. P. Corkum, "Plasma perspective on strong field multiphoton ionization," Phys. Rev. Lett. 71, 1994-1997 (1993).
    [CrossRef] [PubMed]
  25. D. Charalambidis, D. Xenakis, C.J.G.J. Uiterwaal, P. Maragakis, Jian Zhang, H. Schroeder, O. Faucher, and P. Lambropoulos "Multiphoton ionisation saturation intensities and generalized cross sections from ATI spectra," J. Phys. B 30, 1467-1480 (1997).
    [CrossRef]
  26. A. Erd'elyi (Ed.), Higher Transcendental Functions, Vol. 2, (New York: McGraw-Hill, 1953).
  27. The uncertainty in the intensity measurement is $approx$ 15 - 30, and that of momentum resolution $approx$ 0.2 - 0.4 a.u. [R. Doerner, and H. Rottke (private communication)].
  28. W. Lotz, "Electron-Impact Ionization Cross Sections and Ionization Rate Coefficients for Atoms and Ions from Hydrogen to Calcium," Zeit. f. Phys. 216, 241-247 (1968).
    [CrossRef]

Other

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Doerner, "Recoil-ion momentum distribution for single and double ionization of helium in strong laser fields," Phys. Rev. Lett. 84, 443-446 (2000).
[CrossRef] [PubMed]

R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schroeder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, W. Sandner "Momentum distribution of Ne^n+ ions created by an intense ultrashort laser pulse," Phys. Rev. Lett. 84, 447-450 (2000).
[CrossRef] [PubMed]

B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer and K.C. Kulander "Precision measurement od strong field double ionization of helium," Phys. Rev. Lett. 73, 1227-1230 (1994).
[CrossRef] [PubMed]

S. Larochelle, A. Talebpour and S.L. Chin, "Non-sequential multiple ionization or rare gas atoms in a Ti:sapphire laser field," J. Phys. B 31, 1201-1214 (1998).
[CrossRef]

J.S. Parker, K.T. Taylor, C.W. Clark and S. Blodgett-Ford, "Intense-field mutliphoton ionisation of a two-electron atom," J. Phys. B 29, L33-L42 (1996).
[CrossRef]

E.S. Smyth, J.S. Parker and K.T. Taylor, "Numerical integration of the time-depedent Schroedinger equation for laser-driven helium," Comp. Phys. Comm. 114, 1-14 (1998).
[CrossRef]

J.S. Parker, L.R.Moore, K.J. Mehring, D.Dundas and K.T. Taylor, "Double-electron above threshold ionization of helium,' J. Phys. B 34, L69-L78 (2001).
[CrossRef]

F.H.M. Faisal and A. Becker, "'Intense-Field Many-Body S-Matrix Theory' and mechanism of laser induced double ionization of Helium," in Selected Topics on Electron Physics, D.H. Campbell and H. Kleinpoppen, eds. (Plenum Press, New York, 1996) pp. 397-410.
[CrossRef]

F.H.M. Faisal and A. Becker, "Effect of rescattering on ATI and e-e correlation on double ionization in intense laser fields" in Multiphoton Processes 1996, P. Lambropoulos and H. Walther, eds., Int. Nat. Conf. Ser. No. 154 (IOP: Bristol, 1997) pp. 118-131.

F.H.M. Faisal, A. Becker and J. Muth-Boehm, "Intense-Field Many-Body S-Matrix Theory: Applications to processes in intense laser fields," Laser Phys. 9, 115-123 (1999).

A. Becker and F.H.M. Faisal, "Mechanism of laser-induced double ionization of helium," J. Phys. B 29, L197-L202 (1996).
[CrossRef]

F.H.M. Faisal and A. Becker, "Non-sequential double ionization: Mechanism and model formula," Laser Phys. 7, 684-689 (1997).

A. Becker and F.H.M. Faisal, "Interplay of electron correlation and intense field dynamics in double ionization of helium," Phys. Rev. A 59, R1742-R1745 (1999).
[CrossRef]

A. Becker and F.H.M. Faisal, "Production of high charge states of Xe in a femtosecond laser pulse," Phys. Rev. A 59, R3182-R3185 (1999).
[CrossRef]

A. Becker and F.H.M. Faisal, "S-matrix analysis of ionization yields of noble gas atoms at the focus of Ti:sapphire laser pulses," J. Phys. B 32, L335-L343 (1999).
[CrossRef]

A. Becker and F.H.M. Faisal, "Interpretation of momentum distribution of recoil ions from laser induced nonsequential double ionization," Phys. Rev. Lett. 84, 3546-3549 (2000).
[CrossRef] [PubMed]

F.H.M. Faisal, "Exact Solution of the Schroedinger Equation of Two Electrons Interacting with an Intense Electromagnetic Field," Phys. Lett. A 187, 180-184 (1994).
[CrossRef]

A. Becker and F.H.M. Faisal, "Correlated Keldysh-Faisal-Reiss theory of above-threshold double ionization of He in intense laser fields," Phys. Rev. A 50, 3256-3264 (1994).
[CrossRef] [PubMed]

F.H.M. Faisal, Theory of Multiphoton Processes (Plenum Press: New York, 1987).

C. Joachain, Quantum Collision Theory, 3rd edn., (North-Holland, Amsterdam, 1983).

H.R. Reiss, "Effect of an intense electromagnetic field on weakly bound system," Phys. Rev. A 22, 1786-1813 (1980).
[CrossRef]

L.V. Keldysh, "Ionization in the field of a strong electromagnetic wave," Sov. Phys. JETP 20, 1307-1314 (1965) [Zh. Eksp. Teor. Fiz. 47, 1945-1957 (1964)]

F.H.M. Faisal, "Multiple Absorption of Laser Photons by Atoms," J. Phys. B 6, L89-92 (1973).
[CrossRef]

P. Corkum, "Plasma perspective on strong field multiphoton ionization," Phys. Rev. Lett. 71, 1994-1997 (1993).
[CrossRef] [PubMed]

D. Charalambidis, D. Xenakis, C.J.G.J. Uiterwaal, P. Maragakis, Jian Zhang, H. Schroeder, O. Faucher, and P. Lambropoulos "Multiphoton ionisation saturation intensities and generalized cross sections from ATI spectra," J. Phys. B 30, 1467-1480 (1997).
[CrossRef]

A. Erd'elyi (Ed.), Higher Transcendental Functions, Vol. 2, (New York: McGraw-Hill, 1953).

The uncertainty in the intensity measurement is $approx$ 15 - 30, and that of momentum resolution $approx$ 0.2 - 0.4 a.u. [R. Doerner, and H. Rottke (private communication)].

W. Lotz, "Electron-Impact Ionization Cross Sections and Ionization Rate Coefficients for Atoms and Ions from Hydrogen to Calcium," Zeit. f. Phys. 216, 241-247 (1968).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

‘Correlation mediated energy-sharing diagram’ for laser induced non-sequential double ionization of He. For interpretation see text.

Fig. 2.
Fig. 2.

Recoil ion momentum distribution of He2+ parallel to the polarization direction, Ppar . (experimental data, panel a, [1]) and the sum-momentum of the two outgoing electrons in opposite direction (present theory, panel b, [16]).

Fig. 3.
Fig. 3.

The same as in Fig. 2 but perpendicular to the polarization direction; panel a (experiment, [1]), panel b (theory, [16]).

Fig. 4.
Fig. 4.

Sum-momentum distributions calculated without the final state ‘Volkov dressing’ of the two outgoing electrons: (a) parallel case (theory), c.f. Fig. 2; (b) perpendicular case (theory), c.f. Fig. 3.

Fig. 5.
Fig. 5.

Results of model calculations for the yields of He++-ions at λ=780 nm and τ=160 fs assuming a collision energy equal to the rescattering energy (dashed line) and to the back-scattering energy (solid line), in comparision with experimental data [3].

Fig. 6.
Fig. 6.

e - 2e’ rates as a function of the collision energy for He+ ions, as calculated from the Lotz formula [28].

Equations (33)

Equations on this page are rendered with MathJax. Learn more.

H ( t ) = H i 0 + V i ( t ) ,
[ ( i d dt H i 0 ) V i ( t ) ] Ψ ( t ) > = 0
Ψ ( t ) > = ϕ i ( t ) > + t i t dt 1 G ( t , t 1 ) V i ( t 1 ) ϕ i ( t 1 ) > ,
[ i d dt H ( t ) ] G ( t , t ) = δ ( t t ) .
[ i d dt H i 0 ] ϕ i ( t ) > = 0 .
V i ( t ) = j = 1 , 2 [ 1 c p j · A ( t ) + 1 2 c 2 A 2 ( t ) ] .
H ( t ) = H f 0 ( t ) + V f ( t ) ,
[ i d dt H f 0 ( t ) ] G f 0 ( t , t ) = δ ( t t ) .
G ( t , t ) = G f 0 ( t , t ) + t i t d t 1 G f 0 ( t , t 1 ) V f ( t 1 ) G ( t 1 , t )
Ψ ( t ) > = ϕ i ( t ) > + t i t d t 1 G f 0 ( t , t 1 ) V i ( t 1 ) ϕ i ( t 1 ) >
+ t i t t i t 2 d t 2 d t 1 G f 0 ( t , t 2 ) V f ( t 2 ) G ( t 2 , t 1 ) V i ( t 1 ) ϕ i ( t 1 ) > .
( S 1 ) f i ( t ) = i [ t i t d t 1 < ϕ f ( t 1 ) V i ( t 1 ) ϕ i ( t 1 ) >
+ t i t t i t 2 d t 2 d t 1 < ϕ f ( t 2 ) V f ( t 2 ) G ( t 2 , t 1 ) V i ( t 1 ) ϕ i ( t 1 ) > ] .
H ( t ) = H 0 ( t ) + V 0 ( t ) ,
H 0 ( t ) = [ p 1 A ( t ) c ] 2 2 + [ p 2 2 2 m Z r 2 ] ; ( Z = 2 , for He ) .
G 0 ( t , t ) = i θ ( t t ) j 1 ( 2 π ) 3 d k k ϕ j + ( 2 ) >
× e i t t { [ ( k e A ( τ ) c ] 2 2 + E j } d τ < k ϕ j + ( 2 )
G ( t , t ) = G 0 ( t , t ) + t i t d t 1 G 0 ( t , t 1 ) V 0 ( t 1 ) G 0 ( t 1 , t ) + ,
( S 1 ) f i ( t ) = j = 1 S f i ( j ) ( t )
S f i ( 1 ) ( t ) = t i t d t 1 < ϕ f ( t 1 ) V i ( t 1 ) ϕ i ( t 1 ) >
S f i ( 2 ) ( t ) = t i t t i t 2 d t 2 d t 1 < ϕ f ( t 2 ) V f ( t 2 ) G 0 ( t 2 , t 1 ) V i ( t 1 ) ϕ i ( t 1 ) >
S f i ( 3 ) ( t ) = t i t t i t 3 t i t 2 d t 3 d t 2 d t 1 < ϕ f ( t 3 ) V f ( t 3 ) G 0 ( t 3 , t 2 ) V 0 ( t 2 ) V 0 ( t 2 )
× G 0 ( t 2 , t 1 ) V i ( t 1 ) | ϕ i ( t 1 ) >
S f i ( 2 ) ( t f , t i ) N S = i t i t f d t 2 < ϕ f V ( k a , k b ; r 1 , r 2 ; t 2 ) V corr ( t 2 ) Ψ i ( r 1 , r 2 ; t 2 ) >
Ψ i ( r 1 , r 2 ; t 2 ) = t i t 2 d t 1 G 0 ( r 1 , r 2 , t 2 ; r 1 , r 2 , t 1 ) V ATI ( t 1 ) ϕ 1 S ( r 1 , r 2 ; t 1 ) >
= i t i t 2 d t 1 j 1 ( 2 π ) 3 d k ϕ V ( k ; r 1 ; t 2 ) ϕ j + ( r 2 ; t 2 ) >
× < ϕ j + ( r 2 ; t 1 ) ϕ V ( k ; r 1 ; t 1 ) V ATI ( t 1 ) ϕ 1 S ( r 1 , r 2 ; t 1 ) >
S f i ( 2 ) ( , ) N S = 2 π i N δ ( k a 2 2 + k b 2 2 + E B + 2 U p N ω ) T ( N ) ( k a , k b ) ,
T ( N ) ( k a , k b ) = n j 1 ( 2 π ) 3 d k < ϕ 0 ( k a , r 1 ) ϕ 0 ( k b , r 2 ) 1 r 12 ϕ j + ( r 2 ) ϕ 0 ( k , r 1 ) >
× J N n ( α 0 · ( k a + k b k ) ; U p 2 ω ) J n ( α 0 · k ; U p 2 ω ) k 2 2 E j + E B + U p n ω + i 0
× ( E j E B k 2 2 ) < ϕ j + ( r 2 ) ϕ 0 ( k , r 1 ) ϕ 1 S ( r 1 , r 2 ) > ,
d Γ ( N ) d k a d k b = 2 π δ ( k a 2 2 + k b 2 2 + E B + 2 U p N ω ) T ( N ) ( k a , k b ) 2 .
P par . cut off ( k a ) par . + ( k b ) par . cut off Re ( 4 U p + ( 8 U p E B ) ) ,

Metrics