Abstract

We theoretically study the infrared (IR)-dressed photoionization of atoms excited by extreme ultraviolet attosecond pulse trains above ionization threshold. The initial state of atoms is treated perturbatively by the IR field, and the continuum states are considered as Coulomb–Volkov (CV) waves. CV waves can much reduce the gauge difference calculated with Volkov waves, and, in general, the contribution of ground-state perturbation to the photoelectron spectrum is negligible. Our calculations show qualitative agreement with the experimental results [Phys. Rev. Lett. 95, 013001 (2005) [CrossRef]  ]. An evident dependence of the photoelectron spectrum on the delay phase between the IR field and the attosecond pulse train is exhibited in both helium and argon. The angular distribution of photoelectrons with various IR polarizations and the corresponding photoelectron spectra are presented. The linearly polarized IR fields are shown to have a higher controlling capability of the spectrum via IR delay phases than the circularly polarized fields. On the other hand, the circularly polarized IR fields have a fruitful angular dependence of photoelectrons with various IR delay phases.

© 2012 Optical Society of America

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  1. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
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  4. Y. Mairesse, A. Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taieb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540–1543 (2003).
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    [CrossRef]
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  17. C. J. Joachain, P. Francken, A. Maquet, P. Martin, and V. Veniard, “(e, 2e) collisions in the presence of a laser field,” Phys. Rev. Lett. 61, 165–168 (1988).
    [CrossRef]
  18. X. M. Tong and C. D. Lin, “Empirical formula for static field ionization rates of atoms and molecules by lasers in the barrier-suppression regime,” J. Phys. B 38, 2593–2600(2005).
    [CrossRef]
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    [CrossRef]
  23. A. Bayliss, A. Class, and B. J. Matkowsky, J. Comput. Phys. 116, 380–383 (1995).
    [CrossRef]
  24. H. Friedrich, Theoretical Atomic Physics (Springer, 1998), p. 29 and p. 219.
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    [CrossRef]

2011 (1)

F. Kelkensberg, W. Siu, J. F. Pérez-Torres, F. Morales, G. Gademann, A. Rouzée, P. Johnsson, M. Lucchini, F. Calegari, J. L. Sanz-Vicario, F. Martín, and M. J. Vrakking, “Attosecond control in photoionization of hydrogen molecules,” Phys. Rev. Lett. 107, 043002 (2011).
[CrossRef]

2010 (2)

X. M. Tong, P. Ranitovic, C. L. Cocke, and N. Toshima, “Mechanisms of infrared-laser-assisted atomic ionization by attosecond pulses,” Phys. Rev. A 81, 021404(R) (2010).
[CrossRef]

J. Mauritsson, T. Remetter, M. Swoboda, K. Klünder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lépine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, “Attosecond electron spectroscopy using a novel interferometric pump-probe technique,” Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef]

2009 (1)

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
[CrossRef]

2008 (1)

L. Y. Peng, E. A. Pronin, and A. F. Starace, “Attosecond pulse carrier-envelope phase effects on ionized electron momentum and energy distributions: roles of frequency, intensity and additional IR pulse,” New J. Phys. 10, 025030 (2008).
[CrossRef]

2007 (4)

P. Johnsson, J. Mauritsson, T. Remetter, A. L’Huillier, and K. J. Schafer, “Attosecond control of ionization by wave-packet interference,” Phys. Rev. Lett. 99, 233001 (2007).
[CrossRef]

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3, 381–387 (2007).
[CrossRef]

A. Maquet and R. Taïeb, “Two-colour IR+XUV spectroscopies: the ‘soft-photon approximation’,” J. Mod. Opt. 54, 1847–1857 (2007).
[CrossRef]

J. Zhang and T. Nakajima, “Coulomb effects in photoionization of H atoms irradiated by intense laser fields,” Phys. Rev. A 75, 043403 (2007).
[CrossRef]

2006 (2)

T. Remetter, P. Johnsson, J. Mauritsson, K. Varjú, Y. Ni, F. Lépine, E. Gustafsson, M. Kling, J. Khan, R. López-Martens, K. J. Schafer, M. J. J. Vrakking, and A. L’Huillier, “Attosecond electron wave packet interferometry,” Nat. Phys. 2, 323–326 (2006).
[CrossRef]

K. Varjú, P. Johnsson, J. Mauritsson, T. Remetter, T. Ruchon, Y. Ni, F. Lépine, M. Kling, J. Khan, K. J. Schafer, M. J. J. Vrakking, and A. L’Huillier, “Angularly resolved electron wave packet interferences,” J. Phys. B 39, 3983–3991 (2006).
[CrossRef]

2005 (2)

P. Johnsson, R. López-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varjú, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salières, P. Balcou, K. J. Schafer, and A. L’Huillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett. 95, 013001 (2005).
[CrossRef]

X. M. Tong and C. D. Lin, “Empirical formula for static field ionization rates of atoms and molecules by lasers in the barrier-suppression regime,” J. Phys. B 38, 2593–2600(2005).
[CrossRef]

2003 (1)

Y. Mairesse, A. Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taieb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540–1543 (2003).
[CrossRef]

2002 (1)

H. G. Muller, “Reconstruction of attosecond harmonic beating by interference of two-photon transitions,” Appl. Phys. B 74, S17–S21 (2002).
[CrossRef]

2001 (1)

F. Ehlotzky, “Atomic phenomena in bichromatic laser fields,” Phys. Rep. 345, 175–264 (2001).
[CrossRef]

1999 (1)

D. A. Telnov and S. I. Chu, “Multiphoton detachment of H− near the one-photon threshold: exterior complex scaling generalized pseudospectral method for complex quasienergy resonances,” Phys. Rev. A 59, 2864–2874 (1999).
[CrossRef]

1998 (1)

D. B. Milošević and F. Ehlotzky, “X-ray photoionization in the presence of bichromatic laser field,” Phys. Rev. A 57, 2859–2866 (1998).
[CrossRef]

1995 (1)

A. Bayliss, A. Class, and B. J. Matkowsky, J. Comput. Phys. 116, 380–383 (1995).
[CrossRef]

1993 (1)

A. Cionga, V. Florescu, A. Maquet, and R. Taïeb, “Target dressing effects in laser-assisted x-ray photoionization,” Phys. Rev. A 47, 1830–1840 (1993).
[CrossRef]

1988 (1)

C. J. Joachain, P. Francken, A. Maquet, P. Martin, and V. Veniard, “(e, 2e) collisions in the presence of a laser field,” Phys. Rev. Lett. 61, 165–168 (1988).
[CrossRef]

1955 (1)

A. Dalgarno and J. T. Lewis, “Exact calculation of long-range forces between atoms by perturbation theory,” Proc. R. Soc. London Ser. A 233, 70–74 (1955).
[CrossRef]

Agostini, P.

Y. Mairesse, A. Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taieb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540–1543 (2003).
[CrossRef]

Balcou, P.

P. Johnsson, R. López-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varjú, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salières, P. Balcou, K. J. Schafer, and A. L’Huillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett. 95, 013001 (2005).
[CrossRef]

Bayliss, A.

A. Bayliss, A. Class, and B. J. Matkowsky, J. Comput. Phys. 116, 380–383 (1995).
[CrossRef]

Benedetti, E.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klünder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lépine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, “Attosecond electron spectroscopy using a novel interferometric pump-probe technique,” Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef]

Bohan, A.

Y. Mairesse, A. Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taieb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540–1543 (2003).
[CrossRef]

Breger, P.

Y. Mairesse, A. Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taieb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540–1543 (2003).
[CrossRef]

Calegari, F.

F. Kelkensberg, W. Siu, J. F. Pérez-Torres, F. Morales, G. Gademann, A. Rouzée, P. Johnsson, M. Lucchini, F. Calegari, J. L. Sanz-Vicario, F. Martín, and M. J. Vrakking, “Attosecond control in photoionization of hydrogen molecules,” Phys. Rev. Lett. 107, 043002 (2011).
[CrossRef]

Canuto, C.

C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics (Springer-Verlag, 1988).

Carré, B.

Y. Mairesse, A. Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taieb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540–1543 (2003).
[CrossRef]

Chu, S. I.

D. A. Telnov and S. I. Chu, “Multiphoton detachment of H− near the one-photon threshold: exterior complex scaling generalized pseudospectral method for complex quasienergy resonances,” Phys. Rev. A 59, 2864–2874 (1999).
[CrossRef]

Cionga, A.

A. Cionga, V. Florescu, A. Maquet, and R. Taïeb, “Target dressing effects in laser-assisted x-ray photoionization,” Phys. Rev. A 47, 1830–1840 (1993).
[CrossRef]

Class, A.

A. Bayliss, A. Class, and B. J. Matkowsky, J. Comput. Phys. 116, 380–383 (1995).
[CrossRef]

Cocke, C. L.

X. M. Tong, P. Ranitovic, C. L. Cocke, and N. Toshima, “Mechanisms of infrared-laser-assisted atomic ionization by attosecond pulses,” Phys. Rev. A 81, 021404(R) (2010).
[CrossRef]

Corkum, P. B.

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3, 381–387 (2007).
[CrossRef]

Dalgarno, A.

A. Dalgarno and J. T. Lewis, “Exact calculation of long-range forces between atoms by perturbation theory,” Proc. R. Soc. London Ser. A 233, 70–74 (1955).
[CrossRef]

Dinu, L. C.

Y. Mairesse, A. Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taieb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540–1543 (2003).
[CrossRef]

Ehlotzky, F.

F. Ehlotzky, “Atomic phenomena in bichromatic laser fields,” Phys. Rep. 345, 175–264 (2001).
[CrossRef]

D. B. Milošević and F. Ehlotzky, “X-ray photoionization in the presence of bichromatic laser field,” Phys. Rev. A 57, 2859–2866 (1998).
[CrossRef]

Ferrari, F.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klünder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lépine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, “Attosecond electron spectroscopy using a novel interferometric pump-probe technique,” Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef]

Florescu, V.

A. Cionga, V. Florescu, A. Maquet, and R. Taïeb, “Target dressing effects in laser-assisted x-ray photoionization,” Phys. Rev. A 47, 1830–1840 (1993).
[CrossRef]

Francken, P.

C. J. Joachain, P. Francken, A. Maquet, P. Martin, and V. Veniard, “(e, 2e) collisions in the presence of a laser field,” Phys. Rev. Lett. 61, 165–168 (1988).
[CrossRef]

Frasinski, L. J.

Y. Mairesse, A. Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taieb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540–1543 (2003).
[CrossRef]

Friedrich, H.

H. Friedrich, Theoretical Atomic Physics (Springer, 1998), p. 29 and p. 219.

Gaarde, M. B.

P. Johnsson, R. López-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varjú, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salières, P. Balcou, K. J. Schafer, and A. L’Huillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett. 95, 013001 (2005).
[CrossRef]

Gademann, G.

F. Kelkensberg, W. Siu, J. F. Pérez-Torres, F. Morales, G. Gademann, A. Rouzée, P. Johnsson, M. Lucchini, F. Calegari, J. L. Sanz-Vicario, F. Martín, and M. J. Vrakking, “Attosecond control in photoionization of hydrogen molecules,” Phys. Rev. Lett. 107, 043002 (2011).
[CrossRef]

Ghafur, O.

J. Mauritsson, T. Remetter, M. Swoboda, K. Klünder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lépine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, “Attosecond electron spectroscopy using a novel interferometric pump-probe technique,” Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef]

Gustafsson, E.

T. Remetter, P. Johnsson, J. Mauritsson, K. Varjú, Y. Ni, F. Lépine, E. Gustafsson, M. Kling, J. Khan, R. López-Martens, K. J. Schafer, M. J. J. Vrakking, and A. L’Huillier, “Attosecond electron wave packet interferometry,” Nat. Phys. 2, 323–326 (2006).
[CrossRef]

Hussaini, M. Y.

C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics (Springer-Verlag, 1988).

Ivanov, M.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
[CrossRef]

Joachain, C. J.

C. J. Joachain, P. Francken, A. Maquet, P. Martin, and V. Veniard, “(e, 2e) collisions in the presence of a laser field,” Phys. Rev. Lett. 61, 165–168 (1988).
[CrossRef]

C. J. Joachain, “The Coulomb potential,” in Quantum Collision Theory (North-Holland, 1975), pp. 134–160.

Johnsson, P.

F. Kelkensberg, W. Siu, J. F. Pérez-Torres, F. Morales, G. Gademann, A. Rouzée, P. Johnsson, M. Lucchini, F. Calegari, J. L. Sanz-Vicario, F. Martín, and M. J. Vrakking, “Attosecond control in photoionization of hydrogen molecules,” Phys. Rev. Lett. 107, 043002 (2011).
[CrossRef]

J. Mauritsson, T. Remetter, M. Swoboda, K. Klünder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lépine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, “Attosecond electron spectroscopy using a novel interferometric pump-probe technique,” Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef]

P. Johnsson, J. Mauritsson, T. Remetter, A. L’Huillier, and K. J. Schafer, “Attosecond control of ionization by wave-packet interference,” Phys. Rev. Lett. 99, 233001 (2007).
[CrossRef]

K. Varjú, P. Johnsson, J. Mauritsson, T. Remetter, T. Ruchon, Y. Ni, F. Lépine, M. Kling, J. Khan, K. J. Schafer, M. J. J. Vrakking, and A. L’Huillier, “Angularly resolved electron wave packet interferences,” J. Phys. B 39, 3983–3991 (2006).
[CrossRef]

T. Remetter, P. Johnsson, J. Mauritsson, K. Varjú, Y. Ni, F. Lépine, E. Gustafsson, M. Kling, J. Khan, R. López-Martens, K. J. Schafer, M. J. J. Vrakking, and A. L’Huillier, “Attosecond electron wave packet interferometry,” Nat. Phys. 2, 323–326 (2006).
[CrossRef]

P. Johnsson, R. López-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varjú, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salières, P. Balcou, K. J. Schafer, and A. L’Huillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett. 95, 013001 (2005).
[CrossRef]

Kazamias, S.

P. Johnsson, R. López-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varjú, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salières, P. Balcou, K. J. Schafer, and A. L’Huillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett. 95, 013001 (2005).
[CrossRef]

Kelkensberg, F.

F. Kelkensberg, W. Siu, J. F. Pérez-Torres, F. Morales, G. Gademann, A. Rouzée, P. Johnsson, M. Lucchini, F. Calegari, J. L. Sanz-Vicario, F. Martín, and M. J. Vrakking, “Attosecond control in photoionization of hydrogen molecules,” Phys. Rev. Lett. 107, 043002 (2011).
[CrossRef]

J. Mauritsson, T. Remetter, M. Swoboda, K. Klünder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lépine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, “Attosecond electron spectroscopy using a novel interferometric pump-probe technique,” Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef]

Khan, J.

K. Varjú, P. Johnsson, J. Mauritsson, T. Remetter, T. Ruchon, Y. Ni, F. Lépine, M. Kling, J. Khan, K. J. Schafer, M. J. J. Vrakking, and A. L’Huillier, “Angularly resolved electron wave packet interferences,” J. Phys. B 39, 3983–3991 (2006).
[CrossRef]

T. Remetter, P. Johnsson, J. Mauritsson, K. Varjú, Y. Ni, F. Lépine, E. Gustafsson, M. Kling, J. Khan, R. López-Martens, K. J. Schafer, M. J. J. Vrakking, and A. L’Huillier, “Attosecond electron wave packet interferometry,” Nat. Phys. 2, 323–326 (2006).
[CrossRef]

Kling, M.

T. Remetter, P. Johnsson, J. Mauritsson, K. Varjú, Y. Ni, F. Lépine, E. Gustafsson, M. Kling, J. Khan, R. López-Martens, K. J. Schafer, M. J. J. Vrakking, and A. L’Huillier, “Attosecond electron wave packet interferometry,” Nat. Phys. 2, 323–326 (2006).
[CrossRef]

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J. Mauritsson, T. Remetter, M. Swoboda, K. Klünder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lépine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, “Attosecond electron spectroscopy using a novel interferometric pump-probe technique,” Phys. Rev. Lett. 105, 053001 (2010).
[CrossRef]

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[CrossRef]

T. Remetter, P. Johnsson, J. Mauritsson, K. Varjú, Y. Ni, F. Lépine, E. Gustafsson, M. Kling, J. Khan, R. López-Martens, K. J. Schafer, M. J. J. Vrakking, and A. L’Huillier, “Attosecond electron wave packet interferometry,” Nat. Phys. 2, 323–326 (2006).
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P. Johnsson, R. López-Martens, S. Kazamias, J. Mauritsson, C. Valentin, T. Remetter, K. Varjú, M. B. Gaarde, Y. Mairesse, H. Wabnitz, P. Salières, P. Balcou, K. J. Schafer, and A. L’Huillier, “Attosecond electron wave packet dynamics in strong laser fields,” Phys. Rev. Lett. 95, 013001 (2005).
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[CrossRef]

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J. Mauritsson, T. Remetter, M. Swoboda, K. Klünder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lépine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, “Attosecond electron spectroscopy using a novel interferometric pump-probe technique,” Phys. Rev. Lett. 105, 053001 (2010).
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J. Mauritsson, T. Remetter, M. Swoboda, K. Klünder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S. Zherebtsov, M. F. Kling, F. Lépine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli, “Attosecond electron spectroscopy using a novel interferometric pump-probe technique,” Phys. Rev. Lett. 105, 053001 (2010).
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Figures (6)

Fig. 1.
Fig. 1.

(a) Profile and (b) frequency spectrum of APT at ω x = 23 eV (central frequency), τ x = 0.3 fs (FWHM of each burst), and T h = π / ω IR . A variation from SAP to APT by tuning τ T (FWHM of APT) is demonstrated. FWHM: full width at half-maximum.

Fig. 2.
Fig. 2.

CV and Volkov photoelectron spectra under the LG (dotted curves) and VG (solid curves) for (a) He at ϕ d = 0.5 π , (b) He at ϕ d = 0 , (c) Ar at ϕ d = 0.5 π , and (d) Ar at ϕ d = 0 . I APT = 5 × 10 13 W / cm 2 , τ x = 0.3 fs , τ T = 3 fs , and ω x = 35 eV for He, and ω x = 26 eV for Ar. I IR = 10 13 W / cm 2 and ω IR = 1.55 eV . Insets of (a) and (b) show schematic diagrams for delay phases between IR and APT electric fields. Inset of (d) shows the dipole matrix element φ k ( 0 ) | z ^ · r | ψ g ( 0 ) in Eq. (8a) for He ( l = 1 : dashed curve) and Ar ( l = 2 : solid curve; l = 0 : minor not shown). The photoelectron spectra are integrated over solid angle.

Fig. 3.
Fig. 3.

Unperturbed (dotted curve) and perturbed (solid curve) photoelectron spectra integrated over solid angle under the VG for (a) He at ϕ d = 0 and (b) Ar at ϕ d = 0 . Other optical conditions are the same as those in Fig. 2. (c) Comparison of spectra in He between the TDSE calculations (solid curve) and S -matrix results (dotted curve) of CV waves.

Fig. 4.
Fig. 4.

Angular distribution of photoelectrons for (a)–(e)  E IR E XUV , (f)–(j)  E IR E XUV , and (k)–(o) circular IR polarization in He under the LG. E z : APT’s electric field (solid curve in purple). A z : z -component IR magnetic vector potential (solid curve in red). A y : y -component IR vector potential (dashed curve in red).

Fig. 5.
Fig. 5.

Photoelectron spectra as a function of IR delay phase under the LG for (a)  E IR E APT in He, (b)  E IR E APT in He, (c) circular IR polarization in He, and (d)  E IR E APT in Ar. Other optical conditions are the same as those in Fig. 2. (e) Simulation of Ar for comparison with the experimental result of Johnsson et al. [5], where E IR E APT , I IR = 3 × 10 13 W / cm 2 , and τ x = 0.2 fs to include the IR harmonics 13 through 35, and the APT’s central frequency at harmonic 24 ( ω x = 37.2 eV ). All spectra are integrated over solid angle.

Fig. 6.
Fig. 6.

Angular distribution of photoelectron in He under the LG for the IR circular polarization at (a)  ϕ d = 0 , (b)  ϕ d = 0.25 π , and (c)  ϕ d = 0.5 π ; and for E IR E APT at (d)  ϕ d = 0 , (e)  ϕ d = 0.25 π , and (f)  ϕ d = 0.5 π . The arrow denotes the z -axis direction. Other optical conditions are the same as those in Fig. 2.

Equations (14)

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S = i d t Ψ k ( r , t ) | H int ( t ) | Ψ g ( r , t ) ,
E APT ( t ) = z ^ ξ = 10 10 ( 1 ) ξ E x sin [ ω x ( t ξ T h ) ] exp [ 2 ln 2 ( t ξ T h τ x ) 2 ] exp [ 2 ln 2 ( t τ T ) 2 ] ,
E IR ( t ) = E IR [ z ^ cos ( Δ 2 ) sin ( ω IR t + ϕ d ) + y ^ sin ( Δ 2 ) cos ( ω IR t + ϕ d ) ] ,
Ψ g L , V ( r , t ) = e i ω g t { | ψ g ( 0 ) > + i E IR 2 [ G ( ω g ω IR ) M ^ L , V | ψ g ( 0 ) > e i ( ω IR t + ϕ d ) ± G ( ω g + ω IR ) M ^ L , V | ψ g ( 0 ) > e i ( ω IR t + ϕ d ) ] } ,
G ( Ω ) = 1 Ω H ^ 0 = n | ψ n ( 0 ) ψ n ( 0 ) | Ω E n .
Ψ k C V ( r , t ) = e i ω k t e i α IR ( t ) · k | ψ k ( 0 ) ,
Ψ k V ( r , t ) = ( 2 π ) 3 / 2 k 1 / 2 e i ω k t e i α IR ( t ) · k e i k · r ,
[ 1 2 d 2 d r 2 + l ( l + 1 ) 2 r 2 + V M ( r ) k 2 2 ] u l ( r ) = 0 ,
u l ( r ) r sin [ k r l 2 π 1 k ln ( 2 k r ) + σ l + δ l ] .
e i α IR ( t ) · k = n , m = J ˜ n , m e i ( ± n ± m ) ( ω IR t + ϕ d ) ,
S L ( 0 ) ( ω k g ) = i φ k ( 0 ) | z ^ · r | ψ g ( 0 ) n , m = J ˜ n , m e i ( ± n ± m ) ϕ d F APT [ ω k g ( ± n ± m ) ω IR ] ,
S V ( 0 ) ( ω k g ) = i φ k ( 0 ) | z ^ · r | ψ g ( 0 ) n , m = J ˜ n , m e i ( ± n ± m ) ϕ d F APT [ ω k g ( ± n ± m ) ω IR ] ω k g + ( ± n ± m ) ω IR ,
S L ( 1 ) ( ω k g ) = E IR 2 n , m = J ˜ n , m × { e i ( ± n ± m + 1 ) ϕ d F APT [ ω k g ( ± n ± m + 1 ) ω IR ] φ k ( 0 ) | z ^ · r | G ( ω g ω IR ) z ^ · r ψ g ( 0 ) + e i ( ± n ± m 1 ) ϕ d F APT [ ω k g ( ± n ± m 1 ) ω IR ] φ k ( 0 ) | z ^ · r | G ( ω g + ω IR ) z ^ · r ψ g ( 0 ) } ,
S V ( 1 ) ( ω k g ) = E IR 2 ω IR n , m = J ˜ n , m × { e i ( ± n ± m + 1 ) ϕ d F APT [ ω k g ( ± n ± m + 1 ) ω IR ] ω k g + ( ± n ± m + 1 ) ω IR φ k ( 0 ) | z ^ · r | G ( ω g ω IR ) z ^ · r ψ g ( 0 ) + e i ( ± n ± m 1 ) ϕ d F APT [ ω k g ( ± n ± m 1 ) ω IR ] ω k g + ( ± n ± m 1 ) ω IR φ k ( 0 ) | z ^ · r | G ( ω g + ω IR ) z ^ · r ψ g ( 0 ) } ,

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