Abstract

By solving the time-dependent Schrödinger equation for the Cs atom, we find that, as long as the spectral bandwidth is sufficiently broad, the asymmetry of photoelectron ejection is strongly phase dependent and persists even when the chirped pulse duration becomes more than several cycles. The asymmetry survives even after the angle integration over the hemisphere, implying that the detection efficiency can be significantly improved. This counterintuitive and robust finding provides a simple way to measure the phase for both transform-limited and chirped pulses.

© 2007 Optical Society of America

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References

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2006 (3)

T. Nakajima and S. Watanabe, Phys. Rev. Lett. 96, 213001 (2006).
[CrossRef] [PubMed]

T. Nakajima and S. Watanabe, Opt. Lett. 31, 1920 (2006).
[CrossRef] [PubMed]

G. L. Yudin, A. D. Bandrauk, and P. B. Corkum, Phys. Rev. Lett. 96, 063002 (2006).
[CrossRef] [PubMed]

2004 (2)

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Nature 427, 817 (2004).
[CrossRef] [PubMed]

S. Adachi, P. Kumbhakar, and T. Kobayashi, Opt. Lett. 29, 1150 (2004).
[CrossRef] [PubMed]

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

2002 (1)

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

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]

Eur. Phys. J. D (1)

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

Nature (2)

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]

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, Nature 427, 817 (2004).
[CrossRef] [PubMed]

Opt. Lett. (6)

Phys. Rev. Lett. (5)

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

G. L. Yudin, A. D. Bandrauk, and P. B. Corkum, Phys. Rev. Lett. 96, 063002 (2006).
[CrossRef] [PubMed]

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

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

T. Nakajima and S. Watanabe, Phys. Rev. Lett. 96, 213001 (2006).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

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

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Figures (4)

Fig. 1
Fig. 1

(a) Angle-integrated photoelectron energy spectra at the CEPs, which give maximum (solid) and minimum (dashed) ionization yield for the transform-limited two-cycle pulse. Since the difference is extremely small, it is not visible in this graph. (b) Angle-resolved photoelectron energy spectra to the upward direction ( θ = 0 ) for four different CEPs, ϕ = 0 (solid), π 2 (dashed), π (long-dashed), and 3 π 2 (dot-dashed).

Fig. 2
Fig. 2

Asymmetry factor, A, as a function of CEP for five different photoelectron energies, ϵ = 0.2 eV (solid), 0.8 eV (dotted), 1.4 eV (dashed), 1.8 eV (long-dashed), and 2.2 eV (dot-dashed).

Fig. 3
Fig. 3

Photoelectron angular distribution for four different CEPs, ϕ = 0 (solid), π 2 (dashed), π (long-dashed), and 3 π 2 (dot-dashed), with five different chirp rates, (a) ξ = 3 , (b) 1.25 , (c) 0, (d) 1.25 , and (e) 3.

Fig. 4
Fig. 4

Asymmetry factor, A Ω , integrated over the hemisphere, as a function of photoelectron energy for four different CEPs, ϕ = 0 (solid), π 2 (dashed), π (long-dashed), and 3 π 2 (dot-dashed), with five different chirp rates, (a) ξ = 3 , (b) 1.25 , (c) 0, (d) 1.25 , and (e) 3.

Equations (5)

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Ψ ( r , t ) = n , l , m b n l m ( t ) ϕ n l m ( r ) ,
i Ψ ( r , t ) t = [ H 0 + V ( t ) ] Ψ ( r , t ) ,
A ( t ) = z ̂ A 0 exp [ i ( ω t + ϕ ) 4 ln 2 ( t τ T L ) 2 ( 1 1 i ξ ) ] ,
d P d ϵ ϵ = ϵ e = n ( ϵ = ϵ e ) l m b n l m ( t ) 2 ,
S ( θ , ϵ ) = l m ( 1 ) l e i δ l ( ϵ ) 2 l + 1 P l ( cos θ ) b n l m ( t ) 2 ,

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