Abstract

We investigate the long-term evolution of D2 + nuclear wave-packet after interacting with a 5fs, 800nm laser pulse at an intensity of 0.5•1014W/cm2. The nuclear wave-packet evolves in field-free condition for very long time after the laser pulse. The collapse and revival of nuclear wave-packet is studied. The scale of the classical time (~25fs), the revival time (~580fs) and the super-revival time (~12ps) are determined from the simulation as well as the calculation. The constituents of long-standing nuclear wave-packet are also analyzed.

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  1. A. H. Zewail, “Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond,” J. Phys. Chem. 104, 5660–5694 (2000).
    [CrossRef]
  2. A. Zavriyev, P. H. Bucksbaum, J. Squier, and F. Saline, “Light-induced vibrational states in H2+ and D2+ in intense laser fields,” Phys. Rev. Lett. 70(8), 1077–1080 (1993).
    [CrossRef] [PubMed]
  3. L. J. Frasinski, J. H. Posthumus, J. Plumridge, and K. Codling, “Manipulation of Bond Hardening in H2+ by Chirping of Intense Femtosecond Laser Pulses,” Phys. Rev. Lett. 83(18), 3625–3628 (1999).
    [CrossRef]
  4. D. S. Murphy, J. McKenna, C. R. Calvert, I. D. Williams, and J. F. McCann, “Ultrafast coherent control and quantum encoding of molecular vibrations in D+2 using intense laser pulses,” N. J. Phys. 9(8), 260 (2007).
    [CrossRef]
  5. Ch. Ellert, H. Stapelfeldt, E. Constant, H. Sakai, J. Wright, D. M. Rayner, and P. B. Corkum, “Observing Molecular Dynamics with Timed Coulomb Explosion Imaging,” Phil. Trans. R. Soc. A 356, 329 (1998).
    [CrossRef]
  6. J. H. Posthumus, J. Plumridge, P. F. Taday, J. H. Sanderson, A. J. Langley, K. Codling, and W. A. Bryan, “Sub-pulselength time resolution of bond softening and Coulomb explosion using polarization control of laser-induced alignment,” J. Phys. B 32(5), 029 (1999).
    [CrossRef]
  7. A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
    [CrossRef] [PubMed]
  8. J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. P. H. Schmidt, and H. Schmidt-Böcking, “Recoil-ion and electron momentum spectroscopy: reaction-microscopes,” Rep. Prog. Phys. 66(9), 1463–1545 (2003).
    [CrossRef]
  9. Th. Ergler, A. Rudenko, B. Feuerstein, K. Zrost, C. D. Schröter, R. Moshammer, and J. Ullrich, “Spatiotemporal Imaging of Ultrafast Molecular Motion: Collapse and Revival of the D2+ Nuclear Wave Packet,” Phys. Rev. Lett. 97(19), 193001 (2006).
    [CrossRef] [PubMed]
  10. B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schröter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, “Complete characterization of molecular dynamics in ultrashort laser fields,” Phys. Rev. Lett. 99(15), 153002 (2007).
    [CrossRef] [PubMed]
  11. S. Chelkowski, A. D. Bandrauk, and P. B. Corkum, “Efficient molecular dissociation by a chirped ultrashort infrared laser pulse,” Phys. Rev. Lett. 65(19), 2355–2358 (1990).
    [CrossRef] [PubMed]
  12. J. Manz, H. Naundorf, K. Yamashita, and Y. Zhao, “Quantum Model Simulation of Complete S0 → S1 Population Transfer by Means of Intense Laser Pulses with Opposite Chirp,” J. Chem. Phys. 113(20), 8969–8980 (2000).
    [CrossRef]
  13. P. Král, I. Thanopulos, and M. Shapiro, “Colloquium: Coherently controlled adiabatic passage,” Rev. Mod. Phys. 79(1), 53–77 (2007).
    [CrossRef]
  14. B. Feuerstein and U. Thumm, “Mapping of coherent and decohering nuclear wave-packet dynamics in D2+ with ultrashort laser pulses,” Phys. Rev. A 67(6), 063408 (2003).
    [CrossRef]
  15. Th. Niederhausen and U. Thumm, “Controlled vibrational quenching of nuclear wave packets in D2+,” Phys. Rev. A 77(1), 013407 (2008).
    [CrossRef]
  16. J. Vala, O. Dulieu, F. Masnou–Seeuws, P. Pillet, and R. Kosloff, “Coherent control of cold-molecule formation through photoassociation using a chirped-pulsed-laser field,” Phys. Rev. A 63(1), 013412 (2000).
    [CrossRef]
  17. C. Trump, H. Rottke, and W. Sandner, “Strong-field photoionization of vibrational ground-state H2+ and D2+ molecules,” Phys. Rev. A 59, 2858–2863 (1999).
    [CrossRef]
  18. J. M. Papanikolas, R. M. Williams, and S. R. Leone, “Manipulation of rovibrational wave packet composition in the Li2E(1Σg+) shelf state using intermediate state selection and shaped femtosecond laser pulses,” J. Chem. Phys. 107(11), 4172–4178 (1997).
    [CrossRef]
  19. S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilǎ, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing Proton Dynamics in Molecules on an attosecond time scale,” Science 312(5772), 424–427 (2006).
    [CrossRef] [PubMed]
  20. H. Niikura, D. M. Villeneuve, and P. B. Corkum, “Stopping a vibrational wave packet with laser-induced dipole forces,” Phys. Rev. Lett. 92(13), 133002 (2004).
    [CrossRef] [PubMed]
  21. R. W. Robinett, “Quantum wave packet revivals,” Phys. Rep. 392(1-2), 1–119 (2004).
    [CrossRef]
  22. J. Crank, P. Nicolson, and D. R. Hartree, “A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type,” Proc. Camb. Philos. Soc. 43(01), 50–67 (1947).
    [CrossRef]
  23. G. Hunter, A. W. Yau, and H. O. Pritchard, “Rotation-vibration level energies of the hydrogen and deuterium molecule-ions,” At. Data Nucl. Data Tables 14, 11–20 (1974).
    [CrossRef]

2008

Th. Niederhausen and U. Thumm, “Controlled vibrational quenching of nuclear wave packets in D2+,” Phys. Rev. A 77(1), 013407 (2008).
[CrossRef]

2007

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schröter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, “Complete characterization of molecular dynamics in ultrashort laser fields,” Phys. Rev. Lett. 99(15), 153002 (2007).
[CrossRef] [PubMed]

D. S. Murphy, J. McKenna, C. R. Calvert, I. D. Williams, and J. F. McCann, “Ultrafast coherent control and quantum encoding of molecular vibrations in D+2 using intense laser pulses,” N. J. Phys. 9(8), 260 (2007).
[CrossRef]

P. Král, I. Thanopulos, and M. Shapiro, “Colloquium: Coherently controlled adiabatic passage,” Rev. Mod. Phys. 79(1), 53–77 (2007).
[CrossRef]

2006

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilǎ, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing Proton Dynamics in Molecules on an attosecond time scale,” Science 312(5772), 424–427 (2006).
[CrossRef] [PubMed]

Th. Ergler, A. Rudenko, B. Feuerstein, K. Zrost, C. D. Schröter, R. Moshammer, and J. Ullrich, “Spatiotemporal Imaging of Ultrafast Molecular Motion: Collapse and Revival of the D2+ Nuclear Wave Packet,” Phys. Rev. Lett. 97(19), 193001 (2006).
[CrossRef] [PubMed]

2004

H. Niikura, D. M. Villeneuve, and P. B. Corkum, “Stopping a vibrational wave packet with laser-induced dipole forces,” Phys. Rev. Lett. 92(13), 133002 (2004).
[CrossRef] [PubMed]

R. W. Robinett, “Quantum wave packet revivals,” Phys. Rep. 392(1-2), 1–119 (2004).
[CrossRef]

2003

B. Feuerstein and U. Thumm, “Mapping of coherent and decohering nuclear wave-packet dynamics in D2+ with ultrashort laser pulses,” Phys. Rev. A 67(6), 063408 (2003).
[CrossRef]

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. P. H. Schmidt, and H. Schmidt-Böcking, “Recoil-ion and electron momentum spectroscopy: reaction-microscopes,” Rep. Prog. Phys. 66(9), 1463–1545 (2003).
[CrossRef]

2000

A. H. Zewail, “Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond,” J. Phys. Chem. 104, 5660–5694 (2000).
[CrossRef]

J. Manz, H. Naundorf, K. Yamashita, and Y. Zhao, “Quantum Model Simulation of Complete S0 → S1 Population Transfer by Means of Intense Laser Pulses with Opposite Chirp,” J. Chem. Phys. 113(20), 8969–8980 (2000).
[CrossRef]

J. Vala, O. Dulieu, F. Masnou–Seeuws, P. Pillet, and R. Kosloff, “Coherent control of cold-molecule formation through photoassociation using a chirped-pulsed-laser field,” Phys. Rev. A 63(1), 013412 (2000).
[CrossRef]

1999

C. Trump, H. Rottke, and W. Sandner, “Strong-field photoionization of vibrational ground-state H2+ and D2+ molecules,” Phys. Rev. A 59, 2858–2863 (1999).
[CrossRef]

L. J. Frasinski, J. H. Posthumus, J. Plumridge, and K. Codling, “Manipulation of Bond Hardening in H2+ by Chirping of Intense Femtosecond Laser Pulses,” Phys. Rev. Lett. 83(18), 3625–3628 (1999).
[CrossRef]

J. H. Posthumus, J. Plumridge, P. F. Taday, J. H. Sanderson, A. J. Langley, K. Codling, and W. A. Bryan, “Sub-pulselength time resolution of bond softening and Coulomb explosion using polarization control of laser-induced alignment,” J. Phys. B 32(5), 029 (1999).
[CrossRef]

1998

Ch. Ellert, H. Stapelfeldt, E. Constant, H. Sakai, J. Wright, D. M. Rayner, and P. B. Corkum, “Observing Molecular Dynamics with Timed Coulomb Explosion Imaging,” Phil. Trans. R. Soc. A 356, 329 (1998).
[CrossRef]

1997

J. M. Papanikolas, R. M. Williams, and S. R. Leone, “Manipulation of rovibrational wave packet composition in the Li2E(1Σg+) shelf state using intermediate state selection and shaped femtosecond laser pulses,” J. Chem. Phys. 107(11), 4172–4178 (1997).
[CrossRef]

1993

A. Zavriyev, P. H. Bucksbaum, J. Squier, and F. Saline, “Light-induced vibrational states in H2+ and D2+ in intense laser fields,” Phys. Rev. Lett. 70(8), 1077–1080 (1993).
[CrossRef] [PubMed]

1990

S. Chelkowski, A. D. Bandrauk, and P. B. Corkum, “Efficient molecular dissociation by a chirped ultrashort infrared laser pulse,” Phys. Rev. Lett. 65(19), 2355–2358 (1990).
[CrossRef] [PubMed]

1974

G. Hunter, A. W. Yau, and H. O. Pritchard, “Rotation-vibration level energies of the hydrogen and deuterium molecule-ions,” At. Data Nucl. Data Tables 14, 11–20 (1974).
[CrossRef]

1947

J. Crank, P. Nicolson, and D. R. Hartree, “A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type,” Proc. Camb. Philos. Soc. 43(01), 50–67 (1947).
[CrossRef]

Baker, S.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilǎ, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing Proton Dynamics in Molecules on an attosecond time scale,” Science 312(5772), 424–427 (2006).
[CrossRef] [PubMed]

Baltuška, A.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Bandrauk, A. D.

S. Chelkowski, A. D. Bandrauk, and P. B. Corkum, “Efficient molecular dissociation by a chirped ultrashort infrared laser pulse,” Phys. Rev. Lett. 65(19), 2355–2358 (1990).
[CrossRef] [PubMed]

Bryan, W. A.

J. H. Posthumus, J. Plumridge, P. F. Taday, J. H. Sanderson, A. J. Langley, K. Codling, and W. A. Bryan, “Sub-pulselength time resolution of bond softening and Coulomb explosion using polarization control of laser-induced alignment,” J. Phys. B 32(5), 029 (1999).
[CrossRef]

Bucksbaum, P. H.

A. Zavriyev, P. H. Bucksbaum, J. Squier, and F. Saline, “Light-induced vibrational states in H2+ and D2+ in intense laser fields,” Phys. Rev. Lett. 70(8), 1077–1080 (1993).
[CrossRef] [PubMed]

Calvert, C. R.

D. S. Murphy, J. McKenna, C. R. Calvert, I. D. Williams, and J. F. McCann, “Ultrafast coherent control and quantum encoding of molecular vibrations in D+2 using intense laser pulses,” N. J. Phys. 9(8), 260 (2007).
[CrossRef]

Chelkowski, S.

S. Chelkowski, A. D. Bandrauk, and P. B. Corkum, “Efficient molecular dissociation by a chirped ultrashort infrared laser pulse,” Phys. Rev. Lett. 65(19), 2355–2358 (1990).
[CrossRef] [PubMed]

Chirila, C. C.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilǎ, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing Proton Dynamics in Molecules on an attosecond time scale,” Science 312(5772), 424–427 (2006).
[CrossRef] [PubMed]

Codling, K.

L. J. Frasinski, J. H. Posthumus, J. Plumridge, and K. Codling, “Manipulation of Bond Hardening in H2+ by Chirping of Intense Femtosecond Laser Pulses,” Phys. Rev. Lett. 83(18), 3625–3628 (1999).
[CrossRef]

J. H. Posthumus, J. Plumridge, P. F. Taday, J. H. Sanderson, A. J. Langley, K. Codling, and W. A. Bryan, “Sub-pulselength time resolution of bond softening and Coulomb explosion using polarization control of laser-induced alignment,” J. Phys. B 32(5), 029 (1999).
[CrossRef]

Constant, E.

Ch. Ellert, H. Stapelfeldt, E. Constant, H. Sakai, J. Wright, D. M. Rayner, and P. B. Corkum, “Observing Molecular Dynamics with Timed Coulomb Explosion Imaging,” Phil. Trans. R. Soc. A 356, 329 (1998).
[CrossRef]

Corkum, P. B.

H. Niikura, D. M. Villeneuve, and P. B. Corkum, “Stopping a vibrational wave packet with laser-induced dipole forces,” Phys. Rev. Lett. 92(13), 133002 (2004).
[CrossRef] [PubMed]

Ch. Ellert, H. Stapelfeldt, E. Constant, H. Sakai, J. Wright, D. M. Rayner, and P. B. Corkum, “Observing Molecular Dynamics with Timed Coulomb Explosion Imaging,” Phil. Trans. R. Soc. A 356, 329 (1998).
[CrossRef]

S. Chelkowski, A. D. Bandrauk, and P. B. Corkum, “Efficient molecular dissociation by a chirped ultrashort infrared laser pulse,” Phys. Rev. Lett. 65(19), 2355–2358 (1990).
[CrossRef] [PubMed]

Crank, J.

J. Crank, P. Nicolson, and D. R. Hartree, “A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type,” Proc. Camb. Philos. Soc. 43(01), 50–67 (1947).
[CrossRef]

Dorn, A.

J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. P. H. Schmidt, and H. Schmidt-Böcking, “Recoil-ion and electron momentum spectroscopy: reaction-microscopes,” Rep. Prog. Phys. 66(9), 1463–1545 (2003).
[CrossRef]

Dörner, R.

J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. P. H. Schmidt, and H. Schmidt-Böcking, “Recoil-ion and electron momentum spectroscopy: reaction-microscopes,” Rep. Prog. Phys. 66(9), 1463–1545 (2003).
[CrossRef]

Dulieu, O.

J. Vala, O. Dulieu, F. Masnou–Seeuws, P. Pillet, and R. Kosloff, “Coherent control of cold-molecule formation through photoassociation using a chirped-pulsed-laser field,” Phys. Rev. A 63(1), 013412 (2000).
[CrossRef]

Ellert, Ch.

Ch. Ellert, H. Stapelfeldt, E. Constant, H. Sakai, J. Wright, D. M. Rayner, and P. B. Corkum, “Observing Molecular Dynamics with Timed Coulomb Explosion Imaging,” Phil. Trans. R. Soc. A 356, 329 (1998).
[CrossRef]

Ergler, T.

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schröter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, “Complete characterization of molecular dynamics in ultrashort laser fields,” Phys. Rev. Lett. 99(15), 153002 (2007).
[CrossRef] [PubMed]

Ergler, Th.

Th. Ergler, A. Rudenko, B. Feuerstein, K. Zrost, C. D. Schröter, R. Moshammer, and J. Ullrich, “Spatiotemporal Imaging of Ultrafast Molecular Motion: Collapse and Revival of the D2+ Nuclear Wave Packet,” Phys. Rev. Lett. 97(19), 193001 (2006).
[CrossRef] [PubMed]

Feuerstein, B.

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schröter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, “Complete characterization of molecular dynamics in ultrashort laser fields,” Phys. Rev. Lett. 99(15), 153002 (2007).
[CrossRef] [PubMed]

Th. Ergler, A. Rudenko, B. Feuerstein, K. Zrost, C. D. Schröter, R. Moshammer, and J. Ullrich, “Spatiotemporal Imaging of Ultrafast Molecular Motion: Collapse and Revival of the D2+ Nuclear Wave Packet,” Phys. Rev. Lett. 97(19), 193001 (2006).
[CrossRef] [PubMed]

B. Feuerstein and U. Thumm, “Mapping of coherent and decohering nuclear wave-packet dynamics in D2+ with ultrashort laser pulses,” Phys. Rev. A 67(6), 063408 (2003).
[CrossRef]

Frasinski, L. J.

L. J. Frasinski, J. H. Posthumus, J. Plumridge, and K. Codling, “Manipulation of Bond Hardening in H2+ by Chirping of Intense Femtosecond Laser Pulses,” Phys. Rev. Lett. 83(18), 3625–3628 (1999).
[CrossRef]

Gohle, Ch.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Goulielmakis, E.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Hänsch, T. W.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Hartree, D. R.

J. Crank, P. Nicolson, and D. R. Hartree, “A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type,” Proc. Camb. Philos. Soc. 43(01), 50–67 (1947).
[CrossRef]

Haworth, C. A.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilǎ, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing Proton Dynamics in Molecules on an attosecond time scale,” Science 312(5772), 424–427 (2006).
[CrossRef] [PubMed]

Hentschel, M.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Holzwarth, R.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Hunter, G.

G. Hunter, A. W. Yau, and H. O. Pritchard, “Rotation-vibration level energies of the hydrogen and deuterium molecule-ions,” At. Data Nucl. Data Tables 14, 11–20 (1974).
[CrossRef]

Kosloff, R.

J. Vala, O. Dulieu, F. Masnou–Seeuws, P. Pillet, and R. Kosloff, “Coherent control of cold-molecule formation through photoassociation using a chirped-pulsed-laser field,” Phys. Rev. A 63(1), 013412 (2000).
[CrossRef]

Král, P.

P. Král, I. Thanopulos, and M. Shapiro, “Colloquium: Coherently controlled adiabatic passage,” Rev. Mod. Phys. 79(1), 53–77 (2007).
[CrossRef]

Krausz, F.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Langley, A. J.

J. H. Posthumus, J. Plumridge, P. F. Taday, J. H. Sanderson, A. J. Langley, K. Codling, and W. A. Bryan, “Sub-pulselength time resolution of bond softening and Coulomb explosion using polarization control of laser-induced alignment,” J. Phys. B 32(5), 029 (1999).
[CrossRef]

Lein, M.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilǎ, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing Proton Dynamics in Molecules on an attosecond time scale,” Science 312(5772), 424–427 (2006).
[CrossRef] [PubMed]

Leone, S. R.

J. M. Papanikolas, R. M. Williams, and S. R. Leone, “Manipulation of rovibrational wave packet composition in the Li2E(1Σg+) shelf state using intermediate state selection and shaped femtosecond laser pulses,” J. Chem. Phys. 107(11), 4172–4178 (1997).
[CrossRef]

Manz, J.

J. Manz, H. Naundorf, K. Yamashita, and Y. Zhao, “Quantum Model Simulation of Complete S0 → S1 Population Transfer by Means of Intense Laser Pulses with Opposite Chirp,” J. Chem. Phys. 113(20), 8969–8980 (2000).
[CrossRef]

Marangos, J. P.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilǎ, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing Proton Dynamics in Molecules on an attosecond time scale,” Science 312(5772), 424–427 (2006).
[CrossRef] [PubMed]

Masnou–Seeuws, F.

J. Vala, O. Dulieu, F. Masnou–Seeuws, P. Pillet, and R. Kosloff, “Coherent control of cold-molecule formation through photoassociation using a chirped-pulsed-laser field,” Phys. Rev. A 63(1), 013412 (2000).
[CrossRef]

McCann, J. F.

D. S. Murphy, J. McKenna, C. R. Calvert, I. D. Williams, and J. F. McCann, “Ultrafast coherent control and quantum encoding of molecular vibrations in D+2 using intense laser pulses,” N. J. Phys. 9(8), 260 (2007).
[CrossRef]

McKenna, J.

D. S. Murphy, J. McKenna, C. R. Calvert, I. D. Williams, and J. F. McCann, “Ultrafast coherent control and quantum encoding of molecular vibrations in D+2 using intense laser pulses,” N. J. Phys. 9(8), 260 (2007).
[CrossRef]

Moshammer, R.

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schröter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, “Complete characterization of molecular dynamics in ultrashort laser fields,” Phys. Rev. Lett. 99(15), 153002 (2007).
[CrossRef] [PubMed]

Th. Ergler, A. Rudenko, B. Feuerstein, K. Zrost, C. D. Schröter, R. Moshammer, and J. Ullrich, “Spatiotemporal Imaging of Ultrafast Molecular Motion: Collapse and Revival of the D2+ Nuclear Wave Packet,” Phys. Rev. Lett. 97(19), 193001 (2006).
[CrossRef] [PubMed]

J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. P. H. Schmidt, and H. Schmidt-Böcking, “Recoil-ion and electron momentum spectroscopy: reaction-microscopes,” Rep. Prog. Phys. 66(9), 1463–1545 (2003).
[CrossRef]

Murphy, D. S.

D. S. Murphy, J. McKenna, C. R. Calvert, I. D. Williams, and J. F. McCann, “Ultrafast coherent control and quantum encoding of molecular vibrations in D+2 using intense laser pulses,” N. J. Phys. 9(8), 260 (2007).
[CrossRef]

Naundorf, H.

J. Manz, H. Naundorf, K. Yamashita, and Y. Zhao, “Quantum Model Simulation of Complete S0 → S1 Population Transfer by Means of Intense Laser Pulses with Opposite Chirp,” J. Chem. Phys. 113(20), 8969–8980 (2000).
[CrossRef]

Nicolson, P.

J. Crank, P. Nicolson, and D. R. Hartree, “A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type,” Proc. Camb. Philos. Soc. 43(01), 50–67 (1947).
[CrossRef]

Niederhausen, T.

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schröter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, “Complete characterization of molecular dynamics in ultrashort laser fields,” Phys. Rev. Lett. 99(15), 153002 (2007).
[CrossRef] [PubMed]

Niederhausen, Th.

Th. Niederhausen and U. Thumm, “Controlled vibrational quenching of nuclear wave packets in D2+,” Phys. Rev. A 77(1), 013407 (2008).
[CrossRef]

Niikura, H.

H. Niikura, D. M. Villeneuve, and P. B. Corkum, “Stopping a vibrational wave packet with laser-induced dipole forces,” Phys. Rev. Lett. 92(13), 133002 (2004).
[CrossRef] [PubMed]

Papanikolas, J. M.

J. M. Papanikolas, R. M. Williams, and S. R. Leone, “Manipulation of rovibrational wave packet composition in the Li2E(1Σg+) shelf state using intermediate state selection and shaped femtosecond laser pulses,” J. Chem. Phys. 107(11), 4172–4178 (1997).
[CrossRef]

Pillet, P.

J. Vala, O. Dulieu, F. Masnou–Seeuws, P. Pillet, and R. Kosloff, “Coherent control of cold-molecule formation through photoassociation using a chirped-pulsed-laser field,” Phys. Rev. A 63(1), 013412 (2000).
[CrossRef]

Plumridge, J.

L. J. Frasinski, J. H. Posthumus, J. Plumridge, and K. Codling, “Manipulation of Bond Hardening in H2+ by Chirping of Intense Femtosecond Laser Pulses,” Phys. Rev. Lett. 83(18), 3625–3628 (1999).
[CrossRef]

J. H. Posthumus, J. Plumridge, P. F. Taday, J. H. Sanderson, A. J. Langley, K. Codling, and W. A. Bryan, “Sub-pulselength time resolution of bond softening and Coulomb explosion using polarization control of laser-induced alignment,” J. Phys. B 32(5), 029 (1999).
[CrossRef]

Posthumus, J. H.

J. H. Posthumus, J. Plumridge, P. F. Taday, J. H. Sanderson, A. J. Langley, K. Codling, and W. A. Bryan, “Sub-pulselength time resolution of bond softening and Coulomb explosion using polarization control of laser-induced alignment,” J. Phys. B 32(5), 029 (1999).
[CrossRef]

L. J. Frasinski, J. H. Posthumus, J. Plumridge, and K. Codling, “Manipulation of Bond Hardening in H2+ by Chirping of Intense Femtosecond Laser Pulses,” Phys. Rev. Lett. 83(18), 3625–3628 (1999).
[CrossRef]

Pritchard, H. O.

G. Hunter, A. W. Yau, and H. O. Pritchard, “Rotation-vibration level energies of the hydrogen and deuterium molecule-ions,” At. Data Nucl. Data Tables 14, 11–20 (1974).
[CrossRef]

Rayner, D. M.

Ch. Ellert, H. Stapelfeldt, E. Constant, H. Sakai, J. Wright, D. M. Rayner, and P. B. Corkum, “Observing Molecular Dynamics with Timed Coulomb Explosion Imaging,” Phil. Trans. R. Soc. A 356, 329 (1998).
[CrossRef]

Robinett, R. W.

R. W. Robinett, “Quantum wave packet revivals,” Phys. Rep. 392(1-2), 1–119 (2004).
[CrossRef]

Robinson, J. S.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilǎ, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing Proton Dynamics in Molecules on an attosecond time scale,” Science 312(5772), 424–427 (2006).
[CrossRef] [PubMed]

Rottke, H.

C. Trump, H. Rottke, and W. Sandner, “Strong-field photoionization of vibrational ground-state H2+ and D2+ molecules,” Phys. Rev. A 59, 2858–2863 (1999).
[CrossRef]

Rudenko, A.

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schröter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, “Complete characterization of molecular dynamics in ultrashort laser fields,” Phys. Rev. Lett. 99(15), 153002 (2007).
[CrossRef] [PubMed]

Th. Ergler, A. Rudenko, B. Feuerstein, K. Zrost, C. D. Schröter, R. Moshammer, and J. Ullrich, “Spatiotemporal Imaging of Ultrafast Molecular Motion: Collapse and Revival of the D2+ Nuclear Wave Packet,” Phys. Rev. Lett. 97(19), 193001 (2006).
[CrossRef] [PubMed]

Sakai, H.

Ch. Ellert, H. Stapelfeldt, E. Constant, H. Sakai, J. Wright, D. M. Rayner, and P. B. Corkum, “Observing Molecular Dynamics with Timed Coulomb Explosion Imaging,” Phil. Trans. R. Soc. A 356, 329 (1998).
[CrossRef]

Saline, F.

A. Zavriyev, P. H. Bucksbaum, J. Squier, and F. Saline, “Light-induced vibrational states in H2+ and D2+ in intense laser fields,” Phys. Rev. Lett. 70(8), 1077–1080 (1993).
[CrossRef] [PubMed]

Sanderson, J. H.

J. H. Posthumus, J. Plumridge, P. F. Taday, J. H. Sanderson, A. J. Langley, K. Codling, and W. A. Bryan, “Sub-pulselength time resolution of bond softening and Coulomb explosion using polarization control of laser-induced alignment,” J. Phys. B 32(5), 029 (1999).
[CrossRef]

Sandner, W.

C. Trump, H. Rottke, and W. Sandner, “Strong-field photoionization of vibrational ground-state H2+ and D2+ molecules,” Phys. Rev. A 59, 2858–2863 (1999).
[CrossRef]

Schmidt, L. P. H.

J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. P. H. Schmidt, and H. Schmidt-Böcking, “Recoil-ion and electron momentum spectroscopy: reaction-microscopes,” Rep. Prog. Phys. 66(9), 1463–1545 (2003).
[CrossRef]

Schmidt-Böcking, H.

J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. P. H. Schmidt, and H. Schmidt-Böcking, “Recoil-ion and electron momentum spectroscopy: reaction-microscopes,” Rep. Prog. Phys. 66(9), 1463–1545 (2003).
[CrossRef]

Schröter, C. D.

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schröter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, “Complete characterization of molecular dynamics in ultrashort laser fields,” Phys. Rev. Lett. 99(15), 153002 (2007).
[CrossRef] [PubMed]

Th. Ergler, A. Rudenko, B. Feuerstein, K. Zrost, C. D. Schröter, R. Moshammer, and J. Ullrich, “Spatiotemporal Imaging of Ultrafast Molecular Motion: Collapse and Revival of the D2+ Nuclear Wave Packet,” Phys. Rev. Lett. 97(19), 193001 (2006).
[CrossRef] [PubMed]

Scrinzi, A.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Shapiro, M.

P. Král, I. Thanopulos, and M. Shapiro, “Colloquium: Coherently controlled adiabatic passage,” Rev. Mod. Phys. 79(1), 53–77 (2007).
[CrossRef]

Smith, R. A.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilǎ, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing Proton Dynamics in Molecules on an attosecond time scale,” Science 312(5772), 424–427 (2006).
[CrossRef] [PubMed]

Squier, J.

A. Zavriyev, P. H. Bucksbaum, J. Squier, and F. Saline, “Light-induced vibrational states in H2+ and D2+ in intense laser fields,” Phys. Rev. Lett. 70(8), 1077–1080 (1993).
[CrossRef] [PubMed]

Stapelfeldt, H.

Ch. Ellert, H. Stapelfeldt, E. Constant, H. Sakai, J. Wright, D. M. Rayner, and P. B. Corkum, “Observing Molecular Dynamics with Timed Coulomb Explosion Imaging,” Phil. Trans. R. Soc. A 356, 329 (1998).
[CrossRef]

Taday, P. F.

J. H. Posthumus, J. Plumridge, P. F. Taday, J. H. Sanderson, A. J. Langley, K. Codling, and W. A. Bryan, “Sub-pulselength time resolution of bond softening and Coulomb explosion using polarization control of laser-induced alignment,” J. Phys. B 32(5), 029 (1999).
[CrossRef]

Teng, H.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilǎ, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing Proton Dynamics in Molecules on an attosecond time scale,” Science 312(5772), 424–427 (2006).
[CrossRef] [PubMed]

Thanopulos, I.

P. Král, I. Thanopulos, and M. Shapiro, “Colloquium: Coherently controlled adiabatic passage,” Rev. Mod. Phys. 79(1), 53–77 (2007).
[CrossRef]

Thumm, U.

Th. Niederhausen and U. Thumm, “Controlled vibrational quenching of nuclear wave packets in D2+,” Phys. Rev. A 77(1), 013407 (2008).
[CrossRef]

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schröter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, “Complete characterization of molecular dynamics in ultrashort laser fields,” Phys. Rev. Lett. 99(15), 153002 (2007).
[CrossRef] [PubMed]

B. Feuerstein and U. Thumm, “Mapping of coherent and decohering nuclear wave-packet dynamics in D2+ with ultrashort laser pulses,” Phys. Rev. A 67(6), 063408 (2003).
[CrossRef]

Tisch, J. W. G.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilǎ, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing Proton Dynamics in Molecules on an attosecond time scale,” Science 312(5772), 424–427 (2006).
[CrossRef] [PubMed]

Trump, C.

C. Trump, H. Rottke, and W. Sandner, “Strong-field photoionization of vibrational ground-state H2+ and D2+ molecules,” Phys. Rev. A 59, 2858–2863 (1999).
[CrossRef]

Udem, Th.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Uiberacker, M.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Ullrich, J.

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schröter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, “Complete characterization of molecular dynamics in ultrashort laser fields,” Phys. Rev. Lett. 99(15), 153002 (2007).
[CrossRef] [PubMed]

Th. Ergler, A. Rudenko, B. Feuerstein, K. Zrost, C. D. Schröter, R. Moshammer, and J. Ullrich, “Spatiotemporal Imaging of Ultrafast Molecular Motion: Collapse and Revival of the D2+ Nuclear Wave Packet,” Phys. Rev. Lett. 97(19), 193001 (2006).
[CrossRef] [PubMed]

J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. P. H. Schmidt, and H. Schmidt-Böcking, “Recoil-ion and electron momentum spectroscopy: reaction-microscopes,” Rep. Prog. Phys. 66(9), 1463–1545 (2003).
[CrossRef]

Vala, J.

J. Vala, O. Dulieu, F. Masnou–Seeuws, P. Pillet, and R. Kosloff, “Coherent control of cold-molecule formation through photoassociation using a chirped-pulsed-laser field,” Phys. Rev. A 63(1), 013412 (2000).
[CrossRef]

Villeneuve, D. M.

H. Niikura, D. M. Villeneuve, and P. B. Corkum, “Stopping a vibrational wave packet with laser-induced dipole forces,” Phys. Rev. Lett. 92(13), 133002 (2004).
[CrossRef] [PubMed]

Williams, I. D.

D. S. Murphy, J. McKenna, C. R. Calvert, I. D. Williams, and J. F. McCann, “Ultrafast coherent control and quantum encoding of molecular vibrations in D+2 using intense laser pulses,” N. J. Phys. 9(8), 260 (2007).
[CrossRef]

Williams, R. M.

J. M. Papanikolas, R. M. Williams, and S. R. Leone, “Manipulation of rovibrational wave packet composition in the Li2E(1Σg+) shelf state using intermediate state selection and shaped femtosecond laser pulses,” J. Chem. Phys. 107(11), 4172–4178 (1997).
[CrossRef]

Wright, J.

Ch. Ellert, H. Stapelfeldt, E. Constant, H. Sakai, J. Wright, D. M. Rayner, and P. B. Corkum, “Observing Molecular Dynamics with Timed Coulomb Explosion Imaging,” Phil. Trans. R. Soc. A 356, 329 (1998).
[CrossRef]

Yakovlev, V. S.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Yamashita, K.

J. Manz, H. Naundorf, K. Yamashita, and Y. Zhao, “Quantum Model Simulation of Complete S0 → S1 Population Transfer by Means of Intense Laser Pulses with Opposite Chirp,” J. Chem. Phys. 113(20), 8969–8980 (2000).
[CrossRef]

Yau, A. W.

G. Hunter, A. W. Yau, and H. O. Pritchard, “Rotation-vibration level energies of the hydrogen and deuterium molecule-ions,” At. Data Nucl. Data Tables 14, 11–20 (1974).
[CrossRef]

Zavriyev, A.

A. Zavriyev, P. H. Bucksbaum, J. Squier, and F. Saline, “Light-induced vibrational states in H2+ and D2+ in intense laser fields,” Phys. Rev. Lett. 70(8), 1077–1080 (1993).
[CrossRef] [PubMed]

Zewail, A. H.

A. H. Zewail, “Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond,” J. Phys. Chem. 104, 5660–5694 (2000).
[CrossRef]

Zhao, Y.

J. Manz, H. Naundorf, K. Yamashita, and Y. Zhao, “Quantum Model Simulation of Complete S0 → S1 Population Transfer by Means of Intense Laser Pulses with Opposite Chirp,” J. Chem. Phys. 113(20), 8969–8980 (2000).
[CrossRef]

Zrost, K.

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schröter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, “Complete characterization of molecular dynamics in ultrashort laser fields,” Phys. Rev. Lett. 99(15), 153002 (2007).
[CrossRef] [PubMed]

Th. Ergler, A. Rudenko, B. Feuerstein, K. Zrost, C. D. Schröter, R. Moshammer, and J. Ullrich, “Spatiotemporal Imaging of Ultrafast Molecular Motion: Collapse and Revival of the D2+ Nuclear Wave Packet,” Phys. Rev. Lett. 97(19), 193001 (2006).
[CrossRef] [PubMed]

At. Data Nucl. Data Tables

G. Hunter, A. W. Yau, and H. O. Pritchard, “Rotation-vibration level energies of the hydrogen and deuterium molecule-ions,” At. Data Nucl. Data Tables 14, 11–20 (1974).
[CrossRef]

J. Chem. Phys.

J. Manz, H. Naundorf, K. Yamashita, and Y. Zhao, “Quantum Model Simulation of Complete S0 → S1 Population Transfer by Means of Intense Laser Pulses with Opposite Chirp,” J. Chem. Phys. 113(20), 8969–8980 (2000).
[CrossRef]

J. M. Papanikolas, R. M. Williams, and S. R. Leone, “Manipulation of rovibrational wave packet composition in the Li2E(1Σg+) shelf state using intermediate state selection and shaped femtosecond laser pulses,” J. Chem. Phys. 107(11), 4172–4178 (1997).
[CrossRef]

J. Phys. B

J. H. Posthumus, J. Plumridge, P. F. Taday, J. H. Sanderson, A. J. Langley, K. Codling, and W. A. Bryan, “Sub-pulselength time resolution of bond softening and Coulomb explosion using polarization control of laser-induced alignment,” J. Phys. B 32(5), 029 (1999).
[CrossRef]

J. Phys. Chem.

A. H. Zewail, “Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond,” J. Phys. Chem. 104, 5660–5694 (2000).
[CrossRef]

N. J. Phys.

D. S. Murphy, J. McKenna, C. R. Calvert, I. D. Williams, and J. F. McCann, “Ultrafast coherent control and quantum encoding of molecular vibrations in D+2 using intense laser pulses,” N. J. Phys. 9(8), 260 (2007).
[CrossRef]

Nature

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Phil. Trans. R. Soc. A

Ch. Ellert, H. Stapelfeldt, E. Constant, H. Sakai, J. Wright, D. M. Rayner, and P. B. Corkum, “Observing Molecular Dynamics with Timed Coulomb Explosion Imaging,” Phil. Trans. R. Soc. A 356, 329 (1998).
[CrossRef]

Phys. Rep.

R. W. Robinett, “Quantum wave packet revivals,” Phys. Rep. 392(1-2), 1–119 (2004).
[CrossRef]

Phys. Rev. A

B. Feuerstein and U. Thumm, “Mapping of coherent and decohering nuclear wave-packet dynamics in D2+ with ultrashort laser pulses,” Phys. Rev. A 67(6), 063408 (2003).
[CrossRef]

Th. Niederhausen and U. Thumm, “Controlled vibrational quenching of nuclear wave packets in D2+,” Phys. Rev. A 77(1), 013407 (2008).
[CrossRef]

J. Vala, O. Dulieu, F. Masnou–Seeuws, P. Pillet, and R. Kosloff, “Coherent control of cold-molecule formation through photoassociation using a chirped-pulsed-laser field,” Phys. Rev. A 63(1), 013412 (2000).
[CrossRef]

C. Trump, H. Rottke, and W. Sandner, “Strong-field photoionization of vibrational ground-state H2+ and D2+ molecules,” Phys. Rev. A 59, 2858–2863 (1999).
[CrossRef]

Phys. Rev. Lett.

A. Zavriyev, P. H. Bucksbaum, J. Squier, and F. Saline, “Light-induced vibrational states in H2+ and D2+ in intense laser fields,” Phys. Rev. Lett. 70(8), 1077–1080 (1993).
[CrossRef] [PubMed]

L. J. Frasinski, J. H. Posthumus, J. Plumridge, and K. Codling, “Manipulation of Bond Hardening in H2+ by Chirping of Intense Femtosecond Laser Pulses,” Phys. Rev. Lett. 83(18), 3625–3628 (1999).
[CrossRef]

Th. Ergler, A. Rudenko, B. Feuerstein, K. Zrost, C. D. Schröter, R. Moshammer, and J. Ullrich, “Spatiotemporal Imaging of Ultrafast Molecular Motion: Collapse and Revival of the D2+ Nuclear Wave Packet,” Phys. Rev. Lett. 97(19), 193001 (2006).
[CrossRef] [PubMed]

B. Feuerstein, T. Ergler, A. Rudenko, K. Zrost, C. D. Schröter, R. Moshammer, J. Ullrich, T. Niederhausen, and U. Thumm, “Complete characterization of molecular dynamics in ultrashort laser fields,” Phys. Rev. Lett. 99(15), 153002 (2007).
[CrossRef] [PubMed]

S. Chelkowski, A. D. Bandrauk, and P. B. Corkum, “Efficient molecular dissociation by a chirped ultrashort infrared laser pulse,” Phys. Rev. Lett. 65(19), 2355–2358 (1990).
[CrossRef] [PubMed]

H. Niikura, D. M. Villeneuve, and P. B. Corkum, “Stopping a vibrational wave packet with laser-induced dipole forces,” Phys. Rev. Lett. 92(13), 133002 (2004).
[CrossRef] [PubMed]

Proc. Camb. Philos. Soc.

J. Crank, P. Nicolson, and D. R. Hartree, “A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type,” Proc. Camb. Philos. Soc. 43(01), 50–67 (1947).
[CrossRef]

Rep. Prog. Phys.

J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. P. H. Schmidt, and H. Schmidt-Böcking, “Recoil-ion and electron momentum spectroscopy: reaction-microscopes,” Rep. Prog. Phys. 66(9), 1463–1545 (2003).
[CrossRef]

Rev. Mod. Phys.

P. Král, I. Thanopulos, and M. Shapiro, “Colloquium: Coherently controlled adiabatic passage,” Rev. Mod. Phys. 79(1), 53–77 (2007).
[CrossRef]

Science

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilǎ, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing Proton Dynamics in Molecules on an attosecond time scale,” Science 312(5772), 424–427 (2006).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Nuclear wave-packet propagation of D2 + in a laser pulse in (5 fs, 800nm) at the intensity of 0.5•1014W/cm2. The figure presents the time evolution of probability density | φ ( R , t ) | 2 . The subplots (a) and (b) show the half fractional revival in the time range of 200 ≤ t ≤ 400 and the fully revival in the time range of 450 ≤ t ≤ 650 respectively. The figures are plotted as logarithmic color scale.

Fig. 2
Fig. 2

The expectation inter-nuclear value R (top) and the temporal history of the auto-correlation function | φ ( t = 0 ) | φ ( t ) | (bottom) from the starting time to about 4ps.

Fig. 3
Fig. 3

The expectation inter-nuclear value R . From top to bottom, those figures give the temporal history of the expectation inter-nuclear values in three different time region. The insets (b) shows the zoom-out patterns. The inset (a) shows that the first super-revival time is about 12ps. The inset (b) shows the vibration period of the revival wave-packet is about 25fs.

Fig. 4
Fig. 4

The Fourier spectrum of the nuclear wave-packet

Equations (8)

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

H ( z , R , t ) = H 0 ( R , t ) + V ( z , t ) ,
H 0 ( R , t ) = T i + T e l + 1 / R + V e i , V ( z , t ) = z E ( t ) ,
| φ ( R , t ) | 2 = k ρ k k | ϕ k ( R ) | 2 + k m ρ k m ( t ) ϕ k ( R ) ϕ m ( R ) ,
ρ k m ( t ) = a k a m e i ω k m t ,     ω k m = ω k ω m .
E v = E ( v 0 ) + E ( v 0 ) ( v v 0 ) + E ( v 0 ) 2 ( v v 0 ) 2 + E ( v 0 ) 6 ( v v 0 ) 3 + ....
e E v t exp ( i ω 0 t 2 π i ( v v 0 ) t / T c l 2 π i ( v v 0 ) 2 t / T r e v 2 π i ( v v 0 ) 3 t / T S u p e r ... ) ,
T c l ( v ) = 2 π | 3 ω e y e ( v + 1 2 ) 2 2 ω e x e ( v + 1 2 ) + ω e | ,
          T r e v ( v ) = 2 π | 3 ω e y e ( v + 1 2 ) ω e x e | , T S u p e r ( v ) = 2 π | ω e y e | ,

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