Abstract

The combination of high-order harmonic generation (HHG) with resonant XUV excitation of a core electron into the transient valence vacancy that is created in the course of the HHG process is investigated theoretically. In this setup, the first electron performs a HHG three-step process, whereas the second electron Rabi flops between the core and the valence vacancy. The modified HHG spectrum due to recombination with the valence and the core is determined and analyzed for krypton on the 3d4p resonance in the ion. We assume an 800nm laser with an intensity of about 1014Wcm2 and XUV radiation from the Free Electron Laser in Hamburg (FLASH) with an intensity in the range 10131016Wcm2. Our prediction opens perspectives for nonlinear XUV physics, attosecond x rays, and HHG-based spectroscopy involving core orbitals.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  17. R. Trebino, Frequency-Resolved Optical Gating: the Measurement of Ultrashort Laser Pulses (Kluwer, 2000).
  18. T. Morishita, A.-T. Le, Z. Chen, and C. D. Lin, Phys. Rev. Lett. 100, 013903 (2008).
    [CrossRef] [PubMed]

2010

E. A. Schneidmiller and M. V. Yurkov, Phys. Rev. ST Accel. Beams 13, 110701 (2010).
[CrossRef]

2008

T. Morishita, A.-T. Le, Z. Chen, and C. D. Lin, Phys. Rev. Lett. 100, 013903 (2008).
[CrossRef] [PubMed]

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

A. Fleischer, Phys. Rev. A 78, 053413 (2008).
[CrossRef]

2007

P. Koval, F. Wilken, D. Bauer, and C. H. Keitel, Phys. Rev. Lett. 98, 043904 (2007).
[CrossRef] [PubMed]

2004

P. Agostini and L. F. DiMauro, Rep. Prog. Phys. 67, 813 (2004).
[CrossRef]

2003

K. Ishikawa, Phys. Rev. Lett. 91, 043002 (2003).
[CrossRef] [PubMed]

2001

M. Jurvansuu, A. Kivimäki, and S. Aksela, Phys. Rev. A 64, 012502 (2001).
[CrossRef]

1997

1994

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[CrossRef] [PubMed]

S. Yoon and W. L. Glab, J. Phys. B 27, 4133 (1994).
[CrossRef]

1993

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, Phys. Rev. Lett. 70, 1599 (1993).
[CrossRef] [PubMed]

P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993).
[CrossRef] [PubMed]

Agostini, P.

P. Agostini and L. F. DiMauro, Rep. Prog. Phys. 67, 813 (2004).
[CrossRef]

Aksela, S.

M. Jurvansuu, A. Kivimäki, and S. Aksela, Phys. Rev. A 64, 012502 (2001).
[CrossRef]

Aquila, A. L.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Attwood, D. T.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Balcou, P.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[CrossRef] [PubMed]

Bauer, D.

P. Koval, F. Wilken, D. Bauer, and C. H. Keitel, Phys. Rev. Lett. 98, 043904 (2007).
[CrossRef] [PubMed]

Buth, C.

C. Buth, M. C. Kohler, and C. H. Keitel are preparing a manuscript to be titled “High-order harmonic generation for x-ray free electron laser-induced Rabi flopping.”

Chen, Z.

T. Morishita, A.-T. Le, Z. Chen, and C. D. Lin, Phys. Rev. Lett. 100, 013903 (2008).
[CrossRef] [PubMed]

Corkum, P. B.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[CrossRef] [PubMed]

P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993).
[CrossRef] [PubMed]

Cowan, R. D.

R. D. Cowan, The Theory of Atomic Structure and Spectra, Los Alamos Series in Basic and Applied Sciences (Univ. of California, 1981).

DiMauro, L. F.

P. Agostini and L. F. DiMauro, Rep. Prog. Phys. 67, 813 (2004).
[CrossRef]

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, Phys. Rev. Lett. 70, 1599 (1993).
[CrossRef] [PubMed]

Fleischer, A.

A. Fleischer, Phys. Rev. A 78, 053413 (2008).
[CrossRef]

Gagnon, J.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Glab, W. L.

S. Yoon and W. L. Glab, J. Phys. B 27, 4133 (1994).
[CrossRef]

Goulielmakis, E.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Gullikson, E. M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Hofstetter, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Ishikawa, K.

K. Ishikawa, Phys. Rev. Lett. 91, 043002 (2003).
[CrossRef] [PubMed]

Ivanov, M. Y.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[CrossRef] [PubMed]

Jurvansuu, M.

M. Jurvansuu, A. Kivimäki, and S. Aksela, Phys. Rev. A 64, 012502 (2001).
[CrossRef]

Keitel, C. H.

P. Koval, F. Wilken, D. Bauer, and C. H. Keitel, Phys. Rev. Lett. 98, 043904 (2007).
[CrossRef] [PubMed]

C. Buth, M. C. Kohler, and C. H. Keitel are preparing a manuscript to be titled “High-order harmonic generation for x-ray free electron laser-induced Rabi flopping.”

Kienberger, R.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Kivimäki, A.

M. Jurvansuu, A. Kivimäki, and S. Aksela, Phys. Rev. A 64, 012502 (2001).
[CrossRef]

Kleineberg, U.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Kohler, M. C.

C. Buth, M. C. Kohler, and C. H. Keitel are preparing a manuscript to be titled “High-order harmonic generation for x-ray free electron laser-induced Rabi flopping.”

Koval, P.

P. Koval, F. Wilken, D. Bauer, and C. H. Keitel, Phys. Rev. Lett. 98, 043904 (2007).
[CrossRef] [PubMed]

Krainov, V. P.

Krausz, F.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Kulander, K. C.

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, Phys. Rev. Lett. 70, 1599 (1993).
[CrossRef] [PubMed]

L’Huillier, A.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[CrossRef] [PubMed]

Le, A.-T.

T. Morishita, A.-T. Le, Z. Chen, and C. D. Lin, Phys. Rev. Lett. 100, 013903 (2008).
[CrossRef] [PubMed]

Lewenstein, M.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[CrossRef] [PubMed]

Lin, C. D.

T. Morishita, A.-T. Le, Z. Chen, and C. D. Lin, Phys. Rev. Lett. 100, 013903 (2008).
[CrossRef] [PubMed]

Meystre, P.

P. Meystre and M. Sargent, III, Elements of Quantum Optics, 3rd ed. (Springer, 1999).

Morishita, T.

T. Morishita, A.-T. Le, Z. Chen, and C. D. Lin, Phys. Rev. Lett. 100, 013903 (2008).
[CrossRef] [PubMed]

Sargent, M.

P. Meystre and M. Sargent, III, Elements of Quantum Optics, 3rd ed. (Springer, 1999).

Schafer, K. J.

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, Phys. Rev. Lett. 70, 1599 (1993).
[CrossRef] [PubMed]

Schneidmiller, E. A.

E. A. Schneidmiller and M. V. Yurkov, Phys. Rev. ST Accel. Beams 13, 110701 (2010).
[CrossRef]

Schultze, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Trebino, R.

R. Trebino, Frequency-Resolved Optical Gating: the Measurement of Ultrashort Laser Pulses (Kluwer, 2000).

Uiberacker, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Wilken, F.

P. Koval, F. Wilken, D. Bauer, and C. H. Keitel, Phys. Rev. Lett. 98, 043904 (2007).
[CrossRef] [PubMed]

Yakovlev, V. S.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Yang, B.

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, Phys. Rev. Lett. 70, 1599 (1993).
[CrossRef] [PubMed]

Yoon, S.

S. Yoon and W. L. Glab, J. Phys. B 27, 4133 (1994).
[CrossRef]

Yurkov, M. V.

E. A. Schneidmiller and M. V. Yurkov, Phys. Rev. ST Accel. Beams 13, 110701 (2010).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

S. Yoon and W. L. Glab, J. Phys. B 27, 4133 (1994).
[CrossRef]

Phys. Rev. A

M. Jurvansuu, A. Kivimäki, and S. Aksela, Phys. Rev. A 64, 012502 (2001).
[CrossRef]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994).
[CrossRef] [PubMed]

A. Fleischer, Phys. Rev. A 78, 053413 (2008).
[CrossRef]

Phys. Rev. Lett.

T. Morishita, A.-T. Le, Z. Chen, and C. D. Lin, Phys. Rev. Lett. 100, 013903 (2008).
[CrossRef] [PubMed]

P. Koval, F. Wilken, D. Bauer, and C. H. Keitel, Phys. Rev. Lett. 98, 043904 (2007).
[CrossRef] [PubMed]

K. Ishikawa, Phys. Rev. Lett. 91, 043002 (2003).
[CrossRef] [PubMed]

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, Phys. Rev. Lett. 70, 1599 (1993).
[CrossRef] [PubMed]

P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993).
[CrossRef] [PubMed]

Phys. Rev. ST Accel. Beams

E. A. Schneidmiller and M. V. Yurkov, Phys. Rev. ST Accel. Beams 13, 110701 (2010).
[CrossRef]

Rep. Prog. Phys.

P. Agostini and L. F. DiMauro, Rep. Prog. Phys. 67, 813 (2004).
[CrossRef]

Science

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Other

C. Buth, M. C. Kohler, and C. H. Keitel are preparing a manuscript to be titled “High-order harmonic generation for x-ray free electron laser-induced Rabi flopping.”

P. Meystre and M. Sargent, III, Elements of Quantum Optics, 3rd ed. (Springer, 1999).

R. Trebino, Frequency-Resolved Optical Gating: the Measurement of Ultrashort Laser Pulses (Kluwer, 2000).

Los Alamos National Laboratory, Atomic physics codes, http://aphysics2.lanl.gov/tempweb/lanl/.

R. D. Cowan, The Theory of Atomic Structure and Spectra, Los Alamos Series in Basic and Applied Sciences (Univ. of California, 1981).

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Figures (2)

Fig. 1
Fig. 1

Schematic of the three-step model for the HHG process augmented by XUV excitation of a core electron.

Fig. 2
Fig. 2

Photon number of the hth harmonic order for XUV intensities of (a)  10 13 W cm 2 and (b)  10 16 W cm 2 . The black solid curves show the contribution from recombination with a valence hole; the red dashed curves correspond to recombination with a core hole. The lines represent harmonic strengths obtained by integrating over peaks in the HPNS.

Equations (7)

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

| Ψ , t = a ( t ) e i 2 ( E a + E c ω X ) t + i I P t | a | c + R 3 [ b a ( k , t ) e i 2 ( E a + E c ω X ) t + i I P t | k | c + b c ( k , t ) e i 2 ( E a + E c + ω X ) t + i I P t | k | a ] d 3 k ,
d d t a ( t ) = Γ 0 2 a ( t ) i R 3 b a ( k , t ) a | h ^ L | k d 3 k .
R = ( δ i Γ a R 0 X R 0 X δ i Γ c ) .
t b ( k , t ) = i 2 ( R + ( k 2 + 2 I P ) ) b ( k , t ) + E L ( t ) × k z b ( k , t ) i a ( t ) E L ( t ) k | h ^ L | a ( 1 0 ) .
D ˜ ( Ω ) = i i { a , c } j { + , } U i j w j 0 ( 2 π i ) 3 τ 3 e i F 0 , j ( τ ) × N = i N J N ( U P ω L C ( τ ) ) e i N ω L τ × M = b M N , i ( τ ) h M , 0 , i ( Ω , τ ) d τ .
h M , N , i ( Ω , τ ) = e Γ 0 2 τ ( 1 e Γ 0 T P i ( Ω ˜ M , N , i Ω ) T P ) Γ 0 + i ( Ω ˜ M , N , i Ω ) .
d 2 P ( Ω ) d Ω d Ω S = 4 π Ω ϱ ( Ω ) | D ˜ ( Ω ) | 2 ,

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