Abstract

Tunneling photoionization by a bichromatic field consisting of the coherent superposition of the fundamental laser field frequency and its second harmonic is studied theoretically within the framework of the adiabatic Landau–Dykhne approach applied to the process of negative-ion photodetachment. Analytical expressions for the probability of photodetachment were derived at two fixed specified values of relative phase shift, Φ=0 and Φ=π/2, between the harmonics of the incident bichromatic field. The derived expressions are thoroughly analyzed for two possible limiting cases of tunneling and multiphoton ionization and are demonstrated to be different from the respective expressions for the monochromatic case because of the presence of an effective field strength, which is a function that strongly depends on the parameters of the incident bichromatic field.

© 2002 Optical Society of America

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  1. M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997).
    [CrossRef]
  2. F. Ehlotzky, “Atomic phenomena in bichromatic laser fields,” Phys. Rep. 345, 175–264 (2001).
    [CrossRef]
  3. H. G. Muller, P. H. Bucksbaum, D. W. Schumacher, and A. Zavriev, “Above-threshold ionisation with a two-colour laser field,” J. Phys. B 23, 2761–2769 (1990).
    [CrossRef]
  4. Y. Yin, C. Chen, and D. S. Elliott, “Asymmetric photoelectron angular distributions from interfering photoionization processes,” Phys. Rev. Lett. 69, 2353–2356 (1992).
    [CrossRef] [PubMed]
  5. D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: a study using two colors,” Phys. Rev. Lett. 73, 1344–1347 (1994).
    [CrossRef] [PubMed]
  6. S. Watanabe, K. Kondo, Y. Nabekawa, A. Sagisaka, and Y. Kobayashi, “Two-color phase control in tunneling ionization and harmonic generation by a strong laser field and its third harmonic,” Phys. Rev. Lett. 73, 2692–2695 (1994).
    [CrossRef] [PubMed]
  7. S. Watanabe, K. Kondo, Y. Nabekawa, A. Sagisaka, and Y. Kobayashi, “Tunneling ionization and harmonic generation in two-color fields,” J. Opt. Soc. Am. B 13, 424–428 (1996).
    [CrossRef]
  8. K. J. Schafer and K. C. Kulander, “Phase-dependent effects in multiphoton ionization induced by a laser field and its second harmonic,” Phys. Rev. A 45, 8026–8033 (1992).
    [CrossRef] [PubMed]
  9. R. M. Potvliege and P. H. G. Smith, “Two-colour multiphoton ionization of hydrogen by an intense laser field and one of its harmonics,” J. Phys. B 25, 2501–2516 (1992).
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  10. V. A. Pazdzersky and V. A. Yurovsky, “Photoionization by a bichromatic field: Adiabatic theory,” Phys. Rev. A 51, 632–640 (1995).
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  11. R. A. Blank and M. Shapiro, “Phase and intensity control of integral and differential above-threshold ionization rates,” Phys. Rev. A 52, 4278–4281 (1995).
    [CrossRef] [PubMed]
  12. V. A. Pazdzersky, V. I. Usachenko, and A. V. Ushnurtsev, “The asymmetry of negative ion photodetachment in a bichromatic laser field,” J. Phys. B 32, 4805–4821 (1999).
    [CrossRef]
  13. N. B. Baranova, H. R. Reiss, and B. Ya. Zel’dovich, “Multiphoton and tunnel ionization by an optical field with polar symmetry,” Phys. Rev. A 48, 1497–1505 (1993).
    [CrossRef] [PubMed]
  14. V. A. Pazdzersky, V. I. Usachenko, and A. A. Chernov, “Tunneling photoionization in a strong bichromatic laser field,” J. Phys. B 34, 363–368 (2001).
    [CrossRef]
  15. V. A. Pazdzersky, V. I. Usachenko, and A. V. Ushnurtsev, “On angular coherent control of photocurrent caused by photoionization in a bichromatic laser field,” J. Phys. B 34, 3513–3526 (2001).
    [CrossRef]
  16. M. Yu. Kuchiev and V. N. Ostrovsky, “Electron detachment from negative ions in a bichromatic laser field,” J. Phys. B 31, 2525–2538 (1998).
    [CrossRef]
  17. G. F. Gribakin and M. Yu. Kuchiev, “Multiphoton detachment of electrons from negative ions,” Phys. Rev. A 55, 3760–3771 (1997).
    [CrossRef]
  18. N. B. Delone and V. P. Krainov, Atoms in Strong Light Fields, Vol. 28 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1985).
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  19. The atomic system of units is used here and elsewhere throughout this paper unless otherwise stated.
  20. This implies the zero value of the initial kinetic momentum (or velocity) of the photoelectron at the moment of its appearance in the continuum and is quite a conventional supposition for a tunneling regime of photoionization.21 In this context, however, see also quite a different, but more natural, supposition about this value22 and related consequences.
  21. G. G. Paulus, W. Becker, and H. Walther, “Classical rescattering effects in two-color above-threshold ionization,” Phys. Rev. A 52, 4043–4053 (1995).
    [CrossRef] [PubMed]
  22. R. Kopold, W. Becker, and M. Kleber, “Quantum-path analysis of high-order above-threshold ionization,” Opt. Commun. 179, 39–50 (2000).
    [CrossRef]
  23. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Zh. Eksp. Teor. Fiz. 47, 1945–1957 (1964) [ Sov. Phys. JETP 20, 1307–1314 (1965)].
  24. G. Manfray and C. Manus, “Multiphoton ionization of atoms,” Rep. Prog. Phys. 54, 1333–1372 (1991).
    [CrossRef]
  25. H. R. Reiss, “Theoretical methods in quantum optics: S-matrix and Keldysh techniques for strong-field processes,” Prog. Quantum Electron. 16, 1–71 (1992).
    [CrossRef]
  26. V. A. Pazdzersky and V. I. Usachenko, “On the influence of intercontinuum electromagnetic transitions on photoionisation probabilities,” Laser Phys. 5, 1137–1140 (1995).
  27. A. I. Baz’, Ya. B. Zel’dovich and A. M. Perelomov, Rasseiyanie, Reaktzii i Raspady v Nerelyativistskoi Kvantovoi Mekhanike (Scattering, Reactions and Decay in NonRelativistic Quantum Mechanics) (Nauka, Moscow, 1971; in Russian).

2001 (3)

V. A. Pazdzersky, V. I. Usachenko, and A. A. Chernov, “Tunneling photoionization in a strong bichromatic laser field,” J. Phys. B 34, 363–368 (2001).
[CrossRef]

V. A. Pazdzersky, V. I. Usachenko, and A. V. Ushnurtsev, “On angular coherent control of photocurrent caused by photoionization in a bichromatic laser field,” J. Phys. B 34, 3513–3526 (2001).
[CrossRef]

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

2000 (1)

R. Kopold, W. Becker, and M. Kleber, “Quantum-path analysis of high-order above-threshold ionization,” Opt. Commun. 179, 39–50 (2000).
[CrossRef]

1999 (1)

V. A. Pazdzersky, V. I. Usachenko, and A. V. Ushnurtsev, “The asymmetry of negative ion photodetachment in a bichromatic laser field,” J. Phys. B 32, 4805–4821 (1999).
[CrossRef]

1998 (1)

M. Yu. Kuchiev and V. N. Ostrovsky, “Electron detachment from negative ions in a bichromatic laser field,” J. Phys. B 31, 2525–2538 (1998).
[CrossRef]

1997 (2)

G. F. Gribakin and M. Yu. Kuchiev, “Multiphoton detachment of electrons from negative ions,” Phys. Rev. A 55, 3760–3771 (1997).
[CrossRef]

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997).
[CrossRef]

1996 (1)

1995 (4)

V. A. Pazdzersky and V. I. Usachenko, “On the influence of intercontinuum electromagnetic transitions on photoionisation probabilities,” Laser Phys. 5, 1137–1140 (1995).

G. G. Paulus, W. Becker, and H. Walther, “Classical rescattering effects in two-color above-threshold ionization,” Phys. Rev. A 52, 4043–4053 (1995).
[CrossRef] [PubMed]

V. A. Pazdzersky and V. A. Yurovsky, “Photoionization by a bichromatic field: Adiabatic theory,” Phys. Rev. A 51, 632–640 (1995).
[CrossRef] [PubMed]

R. A. Blank and M. Shapiro, “Phase and intensity control of integral and differential above-threshold ionization rates,” Phys. Rev. A 52, 4278–4281 (1995).
[CrossRef] [PubMed]

1994 (2)

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: a study using two colors,” Phys. Rev. Lett. 73, 1344–1347 (1994).
[CrossRef] [PubMed]

S. Watanabe, K. Kondo, Y. Nabekawa, A. Sagisaka, and Y. Kobayashi, “Two-color phase control in tunneling ionization and harmonic generation by a strong laser field and its third harmonic,” Phys. Rev. Lett. 73, 2692–2695 (1994).
[CrossRef] [PubMed]

1993 (1)

N. B. Baranova, H. R. Reiss, and B. Ya. Zel’dovich, “Multiphoton and tunnel ionization by an optical field with polar symmetry,” Phys. Rev. A 48, 1497–1505 (1993).
[CrossRef] [PubMed]

1992 (4)

H. R. Reiss, “Theoretical methods in quantum optics: S-matrix and Keldysh techniques for strong-field processes,” Prog. Quantum Electron. 16, 1–71 (1992).
[CrossRef]

K. J. Schafer and K. C. Kulander, “Phase-dependent effects in multiphoton ionization induced by a laser field and its second harmonic,” Phys. Rev. A 45, 8026–8033 (1992).
[CrossRef] [PubMed]

R. M. Potvliege and P. H. G. Smith, “Two-colour multiphoton ionization of hydrogen by an intense laser field and one of its harmonics,” J. Phys. B 25, 2501–2516 (1992).
[CrossRef]

Y. Yin, C. Chen, and D. S. Elliott, “Asymmetric photoelectron angular distributions from interfering photoionization processes,” Phys. Rev. Lett. 69, 2353–2356 (1992).
[CrossRef] [PubMed]

1991 (1)

G. Manfray and C. Manus, “Multiphoton ionization of atoms,” Rep. Prog. Phys. 54, 1333–1372 (1991).
[CrossRef]

1990 (1)

H. G. Muller, P. H. Bucksbaum, D. W. Schumacher, and A. Zavriev, “Above-threshold ionisation with a two-colour laser field,” J. Phys. B 23, 2761–2769 (1990).
[CrossRef]

1965 (1)

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

Baranova, N. B.

N. B. Baranova, H. R. Reiss, and B. Ya. Zel’dovich, “Multiphoton and tunnel ionization by an optical field with polar symmetry,” Phys. Rev. A 48, 1497–1505 (1993).
[CrossRef] [PubMed]

Becker, W.

R. Kopold, W. Becker, and M. Kleber, “Quantum-path analysis of high-order above-threshold ionization,” Opt. Commun. 179, 39–50 (2000).
[CrossRef]

G. G. Paulus, W. Becker, and H. Walther, “Classical rescattering effects in two-color above-threshold ionization,” Phys. Rev. A 52, 4043–4053 (1995).
[CrossRef] [PubMed]

Blank, R. A.

R. A. Blank and M. Shapiro, “Phase and intensity control of integral and differential above-threshold ionization rates,” Phys. Rev. A 52, 4278–4281 (1995).
[CrossRef] [PubMed]

Bucksbaum, P. H.

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: a study using two colors,” Phys. Rev. Lett. 73, 1344–1347 (1994).
[CrossRef] [PubMed]

H. G. Muller, P. H. Bucksbaum, D. W. Schumacher, and A. Zavriev, “Above-threshold ionisation with a two-colour laser field,” J. Phys. B 23, 2761–2769 (1990).
[CrossRef]

Chen, C.

Y. Yin, C. Chen, and D. S. Elliott, “Asymmetric photoelectron angular distributions from interfering photoionization processes,” Phys. Rev. Lett. 69, 2353–2356 (1992).
[CrossRef] [PubMed]

Chernov, A. A.

V. A. Pazdzersky, V. I. Usachenko, and A. A. Chernov, “Tunneling photoionization in a strong bichromatic laser field,” J. Phys. B 34, 363–368 (2001).
[CrossRef]

Ehlotzky, F.

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

Elliott, D. S.

Y. Yin, C. Chen, and D. S. Elliott, “Asymmetric photoelectron angular distributions from interfering photoionization processes,” Phys. Rev. Lett. 69, 2353–2356 (1992).
[CrossRef] [PubMed]

Gribakin, G. F.

G. F. Gribakin and M. Yu. Kuchiev, “Multiphoton detachment of electrons from negative ions,” Phys. Rev. A 55, 3760–3771 (1997).
[CrossRef]

Keitel, C. H.

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997).
[CrossRef]

Keldysh, L. V.

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

Kleber, M.

R. Kopold, W. Becker, and M. Kleber, “Quantum-path analysis of high-order above-threshold ionization,” Opt. Commun. 179, 39–50 (2000).
[CrossRef]

Knight, P. L.

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997).
[CrossRef]

Kobayashi, Y.

S. Watanabe, K. Kondo, Y. Nabekawa, A. Sagisaka, and Y. Kobayashi, “Tunneling ionization and harmonic generation in two-color fields,” J. Opt. Soc. Am. B 13, 424–428 (1996).
[CrossRef]

S. Watanabe, K. Kondo, Y. Nabekawa, A. Sagisaka, and Y. Kobayashi, “Two-color phase control in tunneling ionization and harmonic generation by a strong laser field and its third harmonic,” Phys. Rev. Lett. 73, 2692–2695 (1994).
[CrossRef] [PubMed]

Kondo, K.

S. Watanabe, K. Kondo, Y. Nabekawa, A. Sagisaka, and Y. Kobayashi, “Tunneling ionization and harmonic generation in two-color fields,” J. Opt. Soc. Am. B 13, 424–428 (1996).
[CrossRef]

S. Watanabe, K. Kondo, Y. Nabekawa, A. Sagisaka, and Y. Kobayashi, “Two-color phase control in tunneling ionization and harmonic generation by a strong laser field and its third harmonic,” Phys. Rev. Lett. 73, 2692–2695 (1994).
[CrossRef] [PubMed]

Kopold, R.

R. Kopold, W. Becker, and M. Kleber, “Quantum-path analysis of high-order above-threshold ionization,” Opt. Commun. 179, 39–50 (2000).
[CrossRef]

Kuchiev, M. Yu.

M. Yu. Kuchiev and V. N. Ostrovsky, “Electron detachment from negative ions in a bichromatic laser field,” J. Phys. B 31, 2525–2538 (1998).
[CrossRef]

G. F. Gribakin and M. Yu. Kuchiev, “Multiphoton detachment of electrons from negative ions,” Phys. Rev. A 55, 3760–3771 (1997).
[CrossRef]

Kulander, K. C.

K. J. Schafer and K. C. Kulander, “Phase-dependent effects in multiphoton ionization induced by a laser field and its second harmonic,” Phys. Rev. A 45, 8026–8033 (1992).
[CrossRef] [PubMed]

Manfray, G.

G. Manfray and C. Manus, “Multiphoton ionization of atoms,” Rep. Prog. Phys. 54, 1333–1372 (1991).
[CrossRef]

Manus, C.

G. Manfray and C. Manus, “Multiphoton ionization of atoms,” Rep. Prog. Phys. 54, 1333–1372 (1991).
[CrossRef]

Muller, H. G.

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: a study using two colors,” Phys. Rev. Lett. 73, 1344–1347 (1994).
[CrossRef] [PubMed]

H. G. Muller, P. H. Bucksbaum, D. W. Schumacher, and A. Zavriev, “Above-threshold ionisation with a two-colour laser field,” J. Phys. B 23, 2761–2769 (1990).
[CrossRef]

Nabekawa, Y.

S. Watanabe, K. Kondo, Y. Nabekawa, A. Sagisaka, and Y. Kobayashi, “Tunneling ionization and harmonic generation in two-color fields,” J. Opt. Soc. Am. B 13, 424–428 (1996).
[CrossRef]

S. Watanabe, K. Kondo, Y. Nabekawa, A. Sagisaka, and Y. Kobayashi, “Two-color phase control in tunneling ionization and harmonic generation by a strong laser field and its third harmonic,” Phys. Rev. Lett. 73, 2692–2695 (1994).
[CrossRef] [PubMed]

Ostrovsky, V. N.

M. Yu. Kuchiev and V. N. Ostrovsky, “Electron detachment from negative ions in a bichromatic laser field,” J. Phys. B 31, 2525–2538 (1998).
[CrossRef]

Paulus, G. G.

G. G. Paulus, W. Becker, and H. Walther, “Classical rescattering effects in two-color above-threshold ionization,” Phys. Rev. A 52, 4043–4053 (1995).
[CrossRef] [PubMed]

Pazdzersky, V. A.

V. A. Pazdzersky, V. I. Usachenko, and A. A. Chernov, “Tunneling photoionization in a strong bichromatic laser field,” J. Phys. B 34, 363–368 (2001).
[CrossRef]

V. A. Pazdzersky, V. I. Usachenko, and A. V. Ushnurtsev, “On angular coherent control of photocurrent caused by photoionization in a bichromatic laser field,” J. Phys. B 34, 3513–3526 (2001).
[CrossRef]

V. A. Pazdzersky, V. I. Usachenko, and A. V. Ushnurtsev, “The asymmetry of negative ion photodetachment in a bichromatic laser field,” J. Phys. B 32, 4805–4821 (1999).
[CrossRef]

V. A. Pazdzersky and V. I. Usachenko, “On the influence of intercontinuum electromagnetic transitions on photoionisation probabilities,” Laser Phys. 5, 1137–1140 (1995).

V. A. Pazdzersky and V. A. Yurovsky, “Photoionization by a bichromatic field: Adiabatic theory,” Phys. Rev. A 51, 632–640 (1995).
[CrossRef] [PubMed]

Potvliege, R. M.

R. M. Potvliege and P. H. G. Smith, “Two-colour multiphoton ionization of hydrogen by an intense laser field and one of its harmonics,” J. Phys. B 25, 2501–2516 (1992).
[CrossRef]

Protopapas, M.

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997).
[CrossRef]

Reiss, H. R.

N. B. Baranova, H. R. Reiss, and B. Ya. Zel’dovich, “Multiphoton and tunnel ionization by an optical field with polar symmetry,” Phys. Rev. A 48, 1497–1505 (1993).
[CrossRef] [PubMed]

H. R. Reiss, “Theoretical methods in quantum optics: S-matrix and Keldysh techniques for strong-field processes,” Prog. Quantum Electron. 16, 1–71 (1992).
[CrossRef]

Sagisaka, A.

S. Watanabe, K. Kondo, Y. Nabekawa, A. Sagisaka, and Y. Kobayashi, “Tunneling ionization and harmonic generation in two-color fields,” J. Opt. Soc. Am. B 13, 424–428 (1996).
[CrossRef]

S. Watanabe, K. Kondo, Y. Nabekawa, A. Sagisaka, and Y. Kobayashi, “Two-color phase control in tunneling ionization and harmonic generation by a strong laser field and its third harmonic,” Phys. Rev. Lett. 73, 2692–2695 (1994).
[CrossRef] [PubMed]

Schafer, K. J.

K. J. Schafer and K. C. Kulander, “Phase-dependent effects in multiphoton ionization induced by a laser field and its second harmonic,” Phys. Rev. A 45, 8026–8033 (1992).
[CrossRef] [PubMed]

Schumacher, D. W.

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: a study using two colors,” Phys. Rev. Lett. 73, 1344–1347 (1994).
[CrossRef] [PubMed]

H. G. Muller, P. H. Bucksbaum, D. W. Schumacher, and A. Zavriev, “Above-threshold ionisation with a two-colour laser field,” J. Phys. B 23, 2761–2769 (1990).
[CrossRef]

Shapiro, M.

R. A. Blank and M. Shapiro, “Phase and intensity control of integral and differential above-threshold ionization rates,” Phys. Rev. A 52, 4278–4281 (1995).
[CrossRef] [PubMed]

Smith, P. H. G.

R. M. Potvliege and P. H. G. Smith, “Two-colour multiphoton ionization of hydrogen by an intense laser field and one of its harmonics,” J. Phys. B 25, 2501–2516 (1992).
[CrossRef]

Usachenko, V. I.

V. A. Pazdzersky, V. I. Usachenko, and A. V. Ushnurtsev, “On angular coherent control of photocurrent caused by photoionization in a bichromatic laser field,” J. Phys. B 34, 3513–3526 (2001).
[CrossRef]

V. A. Pazdzersky, V. I. Usachenko, and A. A. Chernov, “Tunneling photoionization in a strong bichromatic laser field,” J. Phys. B 34, 363–368 (2001).
[CrossRef]

V. A. Pazdzersky, V. I. Usachenko, and A. V. Ushnurtsev, “The asymmetry of negative ion photodetachment in a bichromatic laser field,” J. Phys. B 32, 4805–4821 (1999).
[CrossRef]

V. A. Pazdzersky and V. I. Usachenko, “On the influence of intercontinuum electromagnetic transitions on photoionisation probabilities,” Laser Phys. 5, 1137–1140 (1995).

Ushnurtsev, A. V.

V. A. Pazdzersky, V. I. Usachenko, and A. V. Ushnurtsev, “On angular coherent control of photocurrent caused by photoionization in a bichromatic laser field,” J. Phys. B 34, 3513–3526 (2001).
[CrossRef]

V. A. Pazdzersky, V. I. Usachenko, and A. V. Ushnurtsev, “The asymmetry of negative ion photodetachment in a bichromatic laser field,” J. Phys. B 32, 4805–4821 (1999).
[CrossRef]

Walther, H.

G. G. Paulus, W. Becker, and H. Walther, “Classical rescattering effects in two-color above-threshold ionization,” Phys. Rev. A 52, 4043–4053 (1995).
[CrossRef] [PubMed]

Watanabe, S.

S. Watanabe, K. Kondo, Y. Nabekawa, A. Sagisaka, and Y. Kobayashi, “Tunneling ionization and harmonic generation in two-color fields,” J. Opt. Soc. Am. B 13, 424–428 (1996).
[CrossRef]

S. Watanabe, K. Kondo, Y. Nabekawa, A. Sagisaka, and Y. Kobayashi, “Two-color phase control in tunneling ionization and harmonic generation by a strong laser field and its third harmonic,” Phys. Rev. Lett. 73, 2692–2695 (1994).
[CrossRef] [PubMed]

Weihe, F.

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: a study using two colors,” Phys. Rev. Lett. 73, 1344–1347 (1994).
[CrossRef] [PubMed]

Yin, Y.

Y. Yin, C. Chen, and D. S. Elliott, “Asymmetric photoelectron angular distributions from interfering photoionization processes,” Phys. Rev. Lett. 69, 2353–2356 (1992).
[CrossRef] [PubMed]

Yurovsky, V. A.

V. A. Pazdzersky and V. A. Yurovsky, “Photoionization by a bichromatic field: Adiabatic theory,” Phys. Rev. A 51, 632–640 (1995).
[CrossRef] [PubMed]

Zavriev, A.

H. G. Muller, P. H. Bucksbaum, D. W. Schumacher, and A. Zavriev, “Above-threshold ionisation with a two-colour laser field,” J. Phys. B 23, 2761–2769 (1990).
[CrossRef]

Zel’dovich, B. Ya.

N. B. Baranova, H. R. Reiss, and B. Ya. Zel’dovich, “Multiphoton and tunnel ionization by an optical field with polar symmetry,” Phys. Rev. A 48, 1497–1505 (1993).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (1)

J. Phys. B (6)

H. G. Muller, P. H. Bucksbaum, D. W. Schumacher, and A. Zavriev, “Above-threshold ionisation with a two-colour laser field,” J. Phys. B 23, 2761–2769 (1990).
[CrossRef]

R. M. Potvliege and P. H. G. Smith, “Two-colour multiphoton ionization of hydrogen by an intense laser field and one of its harmonics,” J. Phys. B 25, 2501–2516 (1992).
[CrossRef]

V. A. Pazdzersky, V. I. Usachenko, and A. V. Ushnurtsev, “The asymmetry of negative ion photodetachment in a bichromatic laser field,” J. Phys. B 32, 4805–4821 (1999).
[CrossRef]

V. A. Pazdzersky, V. I. Usachenko, and A. A. Chernov, “Tunneling photoionization in a strong bichromatic laser field,” J. Phys. B 34, 363–368 (2001).
[CrossRef]

V. A. Pazdzersky, V. I. Usachenko, and A. V. Ushnurtsev, “On angular coherent control of photocurrent caused by photoionization in a bichromatic laser field,” J. Phys. B 34, 3513–3526 (2001).
[CrossRef]

M. Yu. Kuchiev and V. N. Ostrovsky, “Electron detachment from negative ions in a bichromatic laser field,” J. Phys. B 31, 2525–2538 (1998).
[CrossRef]

Laser Phys. (1)

V. A. Pazdzersky and V. I. Usachenko, “On the influence of intercontinuum electromagnetic transitions on photoionisation probabilities,” Laser Phys. 5, 1137–1140 (1995).

Opt. Commun. (1)

R. Kopold, W. Becker, and M. Kleber, “Quantum-path analysis of high-order above-threshold ionization,” Opt. Commun. 179, 39–50 (2000).
[CrossRef]

Phys. Rep. (1)

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

Phys. Rev. A (6)

K. J. Schafer and K. C. Kulander, “Phase-dependent effects in multiphoton ionization induced by a laser field and its second harmonic,” Phys. Rev. A 45, 8026–8033 (1992).
[CrossRef] [PubMed]

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The atomic system of units is used here and elsewhere throughout this paper unless otherwise stated.

This implies the zero value of the initial kinetic momentum (or velocity) of the photoelectron at the moment of its appearance in the continuum and is quite a conventional supposition for a tunneling regime of photoionization.21 In this context, however, see also quite a different, but more natural, supposition about this value22 and related consequences.

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Figures (3)

Fig. 1
Fig. 1

Ratio β(α)=Eeff(Φ=π/2)/Eeff(Φ=0)(α) [Eq. (34)] of effective field strengths {setting the character of the exponential dependence of the probability of tunneling ionization on the effective strength of the bichromatic field [Eq. (1)] for values of relative phase shift Φ} calculated as a function of parameter α.

Fig. 2
Fig. 2

Ratio λ(α)=w0,n(Φ=π/2)(α)/w0,n(Φ=0)(α) [Eq. (36)] of photodetachment probabilities {each corresponds to a multiphoton regime of ionization for a specific value of relative phase shift Φ between the bichromatic field [Eq. (1)] harmonics} calculated as a function of parameter α for three values of Keldysh parameter γ.

Fig. 3
Fig. 3

Photodetachment probability w0,n(Φ)(α) on a decimal logarithmic scale calculated for multiphoton ionization according to Eqs. (30) and (35) as a function of parameter α for two values, Φ=π/2 and Φ=0 of the relative phase shift between the harmonics of the bichromatic field [Eq. (1)] and two values of Keldysh parameter γ(γ=5,γ=10).

Equations (37)

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E(t)=e[E1 cos(ωt)+E2 cos(2ωt+Φ)],
f0n(tk)=exp[iS(tκ)],
S(tκ)=0tκ[εn(t)-ε0(t)]dt
dS(t)dtt=tκ=0;
εn(tκ)=ε0(tκ).
w0n(tκ)=exp{-2 Im[S(tκ)]}.
ε0(tκ)Ip,
εn(t)12E1ωsin(ωt)+E22ωsin(2ωt+Φ)2.
sinh(τκ)+α2sinh(2τκ+Φ)=±iγ,
S(tκ)=12E122ω2+E228ω2+κ2τκω-E124ω3sin(2τκ)-E2232ω3[sin(4τκ+2Φ)-sin(2Φ)]+E1E22ω3sin(τκ+Φ)-sin Φ-13[sin(3τκ+Φ)-sin Φ].
w(γ)=exp-κ2ωf(γ),
f(γ)=1+12γ2arcsinh(γ)-12γ1+γ2,
sin(xκ)cosh(yκ)+α2sin(2xκ)cosh(2yκ)=0,
cos(xκ)sinh(yκ)+α2cos(2xκ)sinh(2yκ)=γ.
±sinh(yκ)+α2sinh(2yκ)=γ
y1,2=ln1α[(1+4γα)1/21],
y1,2=γ/α±1.
cosh(yκ)+α cos(xκ)cosh(2yκ)=0.
x3,4=πarccos1α,y3,4=-γαα2-1.
x3,4=πarccos(1/4γα),y3,4=-ln(2y/α),
Im[S(t1)]=κ221+12γ2+α28γ2y1-14γ2sinh(2y1)-2α3γ2sinh3(y1),
sinh(y1)+(α/2)sinh(2y1)=γ.
sin(τκ)1,2=12α[1±(1+2α2-4iγα)1/2].
|yi|=γE1/Eeff=ωκ/Eeff,
Eeff(α)=E11+12α21/2(α2-1+1+2α2)0.5,
x1=arcsin12α(1+1+2α2),x2=π-x1,
yi=12ln1α2(1+ρ(α)-{2[1+ρ(α)+2α2]}1/2),
ρ(α)=[(1+2α2)2+16γ2α2]1/2.
S(tκ)=κ22ω1+12γ2+α28γ2τκ-14γ2sin(2τκ)+α232γ2sin(4τκ)+α2γ2cos(τκ)-13cos(3τκ),
w0,n(Φ=0)=exp-2κ33(E1+E2),γ1,
w0,n(Φ=0)=E2(E12+4κωE2)1/2-E1κ2/ω,γ1,
w0,n(Φ=0)=(E1/E0)κ2/ω,E0=2κω.
w0,n(Φ=0)=(E2/E0)κ2/2ω.
w0,n(Φ=π/2)(α)=exp-2κ33Eeff(α),
β(α)=Eeff(Φ=π/2)(α)Eeff(Φ=0)(α)=1+12α21/2(α2-1+1+2α2)0.51+α,
w0,n(Φ=π/2)(α)=α(1+ρ(α)-{2[1+ρ(α)+2α2]}1/2)1/2κ2/ω,
λ(α)=w0,n(Φ=π/2)(α)w0,n(Φ=0)(α)=1+4γα-1(+ρ(α)-{2[1+ρ(α)+2α2]}1/2)1/2.

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