Abstract

We theoretically study the dependence of atomic excitation and ionization on the carrier envelope phase of few-cycle laser pulses in the multiphoton ionization regime. Our theoretical results for the hydrogen atom based on the solution of the 3D time-dependent Schrödinger equation show that the strong phase dependence can be seen in not only total ionization, but also bound-state population under the weak laser intensity regime.

© 2006 Optical Society of America

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  1. M. Nisoli, S. De Silvestri, O. Svelto, R. Szipcs, K. Ferencz, Ch. Spielmann, S. Sartania, and F. Krausz, Opt. Lett. 22, 522 (1997).
    [CrossRef] [PubMed]
  2. T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
    [CrossRef]
  3. S. Adachi, P. Kumbhakar, and T. Kobayashi, Opt. Lett. 29, 1150 (2004).
    [CrossRef] [PubMed]
  4. K. Yamane, Z. G. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, Opt. Lett. 28, 2258 (2003).
    [CrossRef] [PubMed]
  5. E. Cormier and P. Lambropoulos, Eur. Phys. J. D 2, 15 (1998).
    [CrossRef]
  6. I. P. Christov, Opt. Lett. 24, 1425 (1999).
    [CrossRef]
  7. P. Dietrich, F. Krausz, and P. B. Corkum, Opt. Lett. 25, 16 (2000).
    [CrossRef]
  8. D. B. Milosevic, G. G. Paulus, and W. Becker, Phys. Rev. Lett. 89, 153001 (2002).
    [CrossRef] [PubMed]
  9. S. Chelkowski and A. D. Bandrauk, Phys. Rev. A 65, 061802(R) (2002).
    [CrossRef]
  10. G. G. Paulus, F. Grabson, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
    [CrossRef] [PubMed]
  11. G. G. Paulus, F. Lindncr, H. Walther, A. Baltsuka, E. Gouliclmakis, M. Lczius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
    [CrossRef]
  12. X. Tang, H. Rudolph, and P. Lambropoulos, Phys. Rev. Lett. 65, 3269 (1990).
    [CrossRef] [PubMed]
  13. T. Nakajima and S. Watanabe ''Effects of the carrier-envelope phase in the multiphoton ionization regime,'' (submitted for publication).

2004 (1)

2003 (2)

K. Yamane, Z. G. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, Opt. Lett. 28, 2258 (2003).
[CrossRef] [PubMed]

G. G. Paulus, F. Lindncr, H. Walther, A. Baltsuka, E. Gouliclmakis, M. Lczius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

2002 (2)

D. B. Milosevic, G. G. Paulus, and W. Becker, Phys. Rev. Lett. 89, 153001 (2002).
[CrossRef] [PubMed]

S. Chelkowski and A. D. Bandrauk, Phys. Rev. A 65, 061802(R) (2002).
[CrossRef]

2001 (1)

G. G. Paulus, F. Grabson, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

2000 (2)

1999 (1)

1998 (1)

E. Cormier and P. Lambropoulos, Eur. Phys. J. D 2, 15 (1998).
[CrossRef]

1997 (1)

1990 (1)

X. Tang, H. Rudolph, and P. Lambropoulos, Phys. Rev. Lett. 65, 3269 (1990).
[CrossRef] [PubMed]

Adachi, S.

Baltsuka, A.

G. G. Paulus, F. Lindncr, H. Walther, A. Baltsuka, E. Gouliclmakis, M. Lczius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

Bandrauk, A. D.

S. Chelkowski and A. D. Bandrauk, Phys. Rev. A 65, 061802(R) (2002).
[CrossRef]

Becker, W.

D. B. Milosevic, G. G. Paulus, and W. Becker, Phys. Rev. Lett. 89, 153001 (2002).
[CrossRef] [PubMed]

Brabec, T.

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Chelkowski, S.

S. Chelkowski and A. D. Bandrauk, Phys. Rev. A 65, 061802(R) (2002).
[CrossRef]

Christov, I. P.

Corkum, P. B.

Cormier, E.

E. Cormier and P. Lambropoulos, Eur. Phys. J. D 2, 15 (1998).
[CrossRef]

De Silvestri, S.

G. G. Paulus, F. Grabson, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

M. Nisoli, S. De Silvestri, O. Svelto, R. Szipcs, K. Ferencz, Ch. Spielmann, S. Sartania, and F. Krausz, Opt. Lett. 22, 522 (1997).
[CrossRef] [PubMed]

Dietrich, P.

Ferencz, K.

Gouliclmakis, E.

G. G. Paulus, F. Lindncr, H. Walther, A. Baltsuka, E. Gouliclmakis, M. Lczius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

Grabson, F.

G. G. Paulus, F. Grabson, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Kobayashi, T.

Krausz, F.

G. G. Paulus, F. Lindncr, H. Walther, A. Baltsuka, E. Gouliclmakis, M. Lczius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

P. Dietrich, F. Krausz, and P. B. Corkum, Opt. Lett. 25, 16 (2000).
[CrossRef]

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

M. Nisoli, S. De Silvestri, O. Svelto, R. Szipcs, K. Ferencz, Ch. Spielmann, S. Sartania, and F. Krausz, Opt. Lett. 22, 522 (1997).
[CrossRef] [PubMed]

Kumbhakar, P.

Lambropoulos, P.

E. Cormier and P. Lambropoulos, Eur. Phys. J. D 2, 15 (1998).
[CrossRef]

X. Tang, H. Rudolph, and P. Lambropoulos, Phys. Rev. Lett. 65, 3269 (1990).
[CrossRef] [PubMed]

Lczius, M.

G. G. Paulus, F. Lindncr, H. Walther, A. Baltsuka, E. Gouliclmakis, M. Lczius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

Lindncr, F.

G. G. Paulus, F. Lindncr, H. Walther, A. Baltsuka, E. Gouliclmakis, M. Lczius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

Milosevic, D. B.

D. B. Milosevic, G. G. Paulus, and W. Becker, Phys. Rev. Lett. 89, 153001 (2002).
[CrossRef] [PubMed]

Morita, R.

Nakajima, T.

T. Nakajima and S. Watanabe ''Effects of the carrier-envelope phase in the multiphoton ionization regime,'' (submitted for publication).

Nisoli, M.

G. G. Paulus, F. Grabson, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

M. Nisoli, S. De Silvestri, O. Svelto, R. Szipcs, K. Ferencz, Ch. Spielmann, S. Sartania, and F. Krausz, Opt. Lett. 22, 522 (1997).
[CrossRef] [PubMed]

Oka, K.

Paulus, G. G.

G. G. Paulus, F. Lindncr, H. Walther, A. Baltsuka, E. Gouliclmakis, M. Lczius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

D. B. Milosevic, G. G. Paulus, and W. Becker, Phys. Rev. Lett. 89, 153001 (2002).
[CrossRef] [PubMed]

G. G. Paulus, F. Grabson, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Priori, E.

G. G. Paulus, F. Grabson, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Rudolph, H.

X. Tang, H. Rudolph, and P. Lambropoulos, Phys. Rev. Lett. 65, 3269 (1990).
[CrossRef] [PubMed]

Sartania, S.

Spielmann, Ch.

Stagira, S.

G. G. Paulus, F. Grabson, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Suguro, A.

Svelto, O.

Szipcs, R.

Tang, X.

X. Tang, H. Rudolph, and P. Lambropoulos, Phys. Rev. Lett. 65, 3269 (1990).
[CrossRef] [PubMed]

Villoresi, P.

G. G. Paulus, F. Grabson, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Walther, H.

G. G. Paulus, F. Lindncr, H. Walther, A. Baltsuka, E. Gouliclmakis, M. Lczius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

G. G. Paulus, F. Grabson, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Watanabe, S.

T. Nakajima and S. Watanabe ''Effects of the carrier-envelope phase in the multiphoton ionization regime,'' (submitted for publication).

Yamane, K.

Yamashita, M.

Zhang, Z. G.

Eur. Phys. J. D (1)

E. Cormier and P. Lambropoulos, Eur. Phys. J. D 2, 15 (1998).
[CrossRef]

Nature (1)

G. G. Paulus, F. Grabson, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Opt. Lett. (5)

Phys. Rev. A (1)

S. Chelkowski and A. D. Bandrauk, Phys. Rev. A 65, 061802(R) (2002).
[CrossRef]

Phys. Rev. Lett. (3)

D. B. Milosevic, G. G. Paulus, and W. Becker, Phys. Rev. Lett. 89, 153001 (2002).
[CrossRef] [PubMed]

G. G. Paulus, F. Lindncr, H. Walther, A. Baltsuka, E. Gouliclmakis, M. Lczius, and F. Krausz, Phys. Rev. Lett. 91, 253004 (2003).
[CrossRef]

X. Tang, H. Rudolph, and P. Lambropoulos, Phys. Rev. Lett. 65, 3269 (1990).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Other (1)

T. Nakajima and S. Watanabe ''Effects of the carrier-envelope phase in the multiphoton ionization regime,'' (submitted for publication).

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Figures (4)

Fig. 1
Fig. 1

(a) Phase dependence of the total ionization yield. Total (thick solid curve) and partial (thin solid, dotted, dashed, long-dashed, and dot-dashed curves) photoelectron spectra at the CEP, (b) ϕ = ϕ max , and (c) ϕ = ϕ min , that give the maximum–minimum total ionization yield. Number of cycles is N = 1 .

Fig. 2
Fig. 2

Photoelectron energy spectra at the phases that give the ionization maximum and minimum for four different numbers of cycles, (a) N = 1 , (b) N = 1.5 , (c) N = 2 , and (d) N = 3 .

Fig. 3
Fig. 3

Phase dependence of the bound-state populations for the number of cycle of N = 1 . All graphs are plotted in arbitrary units for convenience. In the absolute scale, the range of the vertical scales for 2 s , 3 p , and 4 p , for example, are from 0 to 2 × 10 11 , 10 11 , and 2 × 10 11 , respectively.

Fig. 4
Fig. 4

Depth of modulation, M, as a function of the laser intensity for the pulse of N = 1 (solid curve), N = 1.5 (dashed curve), and N = 2 (dot-dashed curve). Thin solid, dashed, and dot-dashed curves represent the corresponding results without bound states during the time propagation.

Equations (2)

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i Ψ ( r , t ) t = [ H 0 + V ( t ) ] Ψ ( r , t ) ,
Ψ ( r , t ) = n , l , m b n l m ( t ) ϕ n l m ( r ) ,

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