Abstract

We have theoretically studied the effect of nuclear mass on electron localization in dissociating H2+ and its isotopes subjected to a few-cycle 3-μm pulse. Our results reveal an anomalous isotopic effect in which the degree of electron-directed reactivity can be even higher for heavier isotopes in the intense midinfrared field. We show, for the first time, the pronounced electron localization can be established through the interferences among the multi-photon coupling channels. Due to the relative enhancement of higher-order coupling channels with growing mass, the interference maxima at different kinetic energy of the spectra gradually become in phase, ultimately resulting in the larger dissociation asymmetries of heavier isotopes.

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    [CrossRef] [PubMed]
  27. A. Thai, M. Hemmer, P. K. Bates, O. Chalus, and J. Biegert, “Sub-250-mrad, passively carrier-envelope-phase-stable mid-infrared OPCPA source at high repetition rate,” Opt. Lett.36, 3918–3920 (2011).
    [CrossRef] [PubMed]
  28. F. Silva, D.R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nature Comm.3, 807 (2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  32. M. F. Kling, C. Siedschlag, I. Znakovskaya, A. J. Verhoef, S. Zherebtsov, F. Krausz, M. Lezius, and M. J. J. Vrakking, “Strong-field control of electron localisation during molecular dissociation,” Mol. Phys.106, 455–465 (2008).
    [CrossRef]
  33. B. Feuerstein and U. Thumm, “Fragmentation of H2+ in strong 800-nm laser pulses: Initial-vibrational-state dependence,” Phys. Rev. A67, 043405 (2003).
    [CrossRef]

2012

Y. Zhou, C. Huang, Q. Liao, and P. Lu, “Classical simulations including electron correlations for sequential double ionization,” Phys. Rev. Lett.109, 053004 (2012).
[CrossRef] [PubMed]

F. He, “Control of electron localization in the dissociation of H2+ using orthogonally polarized two-color sequential laser pulses,” Phys. Rev. A86, 063415 (2012).
[CrossRef]

I. Znakovskaya, P. von den Hoff, G. Marcus, S. Zherebtsov, B. Bergues, X. Gu, Y. Deng, M. J. J. Vrakking, R. Kienberger, F. Krausz, R. de Vivie-Riedle, and M. F. Kling, “Subcycle controlled charge-directed reactivity with few-cycle midinfrared pulses,” Phys. Rev. Lett.108, 063002 (2012).
[CrossRef] [PubMed]

P. Lan, E. J. Takahashi, and K. Midorikawa, “Efficient control of electron localization by subcycle waveform synthesis,” Phys. Rev. A86, 013418 (2012).
[CrossRef]

K. Liu, Q. Zhang, and P. Lu, “Enhancing electron localization in molecular dissociation by two-color mid- and near-infrared fields,” Phys. Rev. A86, 033410 (2012).
[CrossRef]

F. Silva, D.R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nature Comm.3, 807 (2012).
[CrossRef]

2011

2010

B. Abeln, J. V. Hernández, F. Anis, and B. D. Esry, “Comparison of theoretical analyses of intense-laser-induced molecular dissociation,” J. Phys. B43, 155005 (2010).
[CrossRef]

B. Fischer, M. Kremer, T. Pfeifer, B. Feuerstein, V. Sharma, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Steering the electron in H2+ by nuclear wave packet dynamics,” Phys. Rev. Lett.105, 223001 (2010).
[CrossRef]

K. P. Singh, F. He, P. Ranitovic, W. Cao, S. De, D. Ray, S. Chen, U. Thumm, A. Becker, M. M. Murnane, H. C. Kapteyn, I. V. Litvinyuk, and C. L. Cocke, “Control of electron localization in deuterium molecular ions using an attosecond pulse train and a many-cycle infrared pulse,” Phys. Rev. Lett.104, 023001 (2010).
[CrossRef] [PubMed]

G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
[CrossRef]

2009

E. Persson, J. Burgdörfer, and S. Gräfe, “Quantum control of electron localization in molecules driven by trains of half-cycle pulses,” New J. Phys.11, 105035 (2009).
[CrossRef]

D. Ray, F. He, S. De, W. Cao, H. Mashiko, P. Ranitovic, K. P. Singh, I. Znakovskaya, U. Thumm, G. G. Paulus, M. F. Kling, I. V. Litvinyuk, and C. L. Cocke, “Ion-energy dependence of asymmetric dissociation of D2 by a two-color laser field,” Phys. Rev. Lett.103, 223201 (2009).
[CrossRef]

J. J. Hua and B. D. Esry, “The role of mass in the carrier-envelope phase effect for H2+ dissociation,” J. Phys. B42, 085601 (2009).
[CrossRef]

M. Kremer, B. Fischer, B. Feuerstein, V. L. B. de Jesus, V. Sharma, C. Hofrichter, A. Rudenko, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Electron localization in molecular fragmentation of H2 by carrier-envelope phase stabilized laser pulses,” Phys. Rev. Lett.103, 213003 (2009).
[CrossRef]

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

2008

M. F. Kling, C. Siedschlag, I. Znakovskaya, A. J. Verhoef, S. Zherebtsov, F. Krausz, M. Lezius, and M. J. J. Vrakking, “Strong-field control of electron localisation during molecular dissociation,” Mol. Phys.106, 455–465 (2008).
[CrossRef]

J. McKenna, A. M. Sayler, F. Anis, B. Gaire, N. G. Johnson, E. Parke, J. J. Hua, H. Mashiko, C. M. Nakamura, E. Moon, Z. Chang, K. D. Carnes, B. D. Esry, and I. Ben-Itzhak, “Enhancing high-order above-threshold dissociation of H2+ beams with few-cycle laser pulses,” Phys. Rev. Lett100, 133001 (2008).
[CrossRef] [PubMed]

2007

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Isolated sub-100-as pulse generation via controlling electron dynamics,” Phys. Rev. A,76, 011402 (2007).
[CrossRef]

X. M. Tong and C. D. Lin, “Dynamics of light-field control of molecular dissociation at the few-cycle limit,” Phys. Rev. Lett.98, 123002 (2007).
[CrossRef] [PubMed]

S. Gräfe and M. Y. Ivanov, “Effective fields in laser-driven electron recollision and charge localization,” Phys. Rev. Lett.99, 163603 (2007).
[CrossRef] [PubMed]

F. He, C. Ruiz, and A. Becker, “Control of electron excitation and localization in the dissociation of H2+ and its isotopes using two sequential ultrashort laser pulses,” Phys. Rev. Lett.99, 083002 (2007).
[CrossRef] [PubMed]

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

2006

M. F. Kling, C. Siedschlag, A. J. Verhoef, J. I. Khan, M. Schultze, T. Uphues, Y. Ni, M. Uiberacker, M. Drescher, F. Krausz, and M. J. J. Vrakking, “Control of electron localization in molecular dissociation,” Science312, 246–248 (2006).
[CrossRef] [PubMed]

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smit, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science312, 424–427 (2006).
[CrossRef] [PubMed]

P. Q. Wang, A. M. Sayler, K. D. Carnes, J. F. Xia, M. A. Smith, B. D. Esry, and I. Ben-Itzhak, “Dissociation of H2+ in intense femtosecond laser fields studied by coincidence three-dimensional momentum imaging,” Phys. Rev. A74, 043411 (2006).
[CrossRef]

2005

M. Lein, “Attosecond probing of vibrational dynamics with high-harmonic generation” Phys. Rev. Lett94, 053004 (2005).
[CrossRef] [PubMed]

2004

J. H. Posthumus, “The dynamics of small molecules in intense laser fields,” Rep. Prog. Phys.67, 623–665 (2004).
[CrossRef]

A. D. Bandrauk, S. Chelkowski, and H. S. Nguyen, “Attosecond Localization of Electrons in Molecules,” Int. J. Quant. Chem.100, 834–844 (2004).
[CrossRef]

V. Roudnev, B. D. Esry, and I. Ben-Itzhak, “Controlling HD+ and H2+ dissociation with the carrier-envelope phase difference of an intense ultrashort laser pulse,” Phys. Rev. Lett.93, 163601 (2004).
[CrossRef] [PubMed]

2003

B. Feuerstein and U. Thumm, “Fragmentation of H2+ in strong 800-nm laser pulses: Initial-vibrational-state dependence,” Phys. Rev. A67, 043405 (2003).
[CrossRef]

Abeln, B.

B. Abeln, J. V. Hernández, F. Anis, and B. D. Esry, “Comparison of theoretical analyses of intense-laser-induced molecular dissociation,” J. Phys. B43, 155005 (2010).
[CrossRef]

Anis, F.

B. Abeln, J. V. Hernández, F. Anis, and B. D. Esry, “Comparison of theoretical analyses of intense-laser-induced molecular dissociation,” J. Phys. B43, 155005 (2010).
[CrossRef]

J. McKenna, A. M. Sayler, F. Anis, B. Gaire, N. G. Johnson, E. Parke, J. J. Hua, H. Mashiko, C. M. Nakamura, E. Moon, Z. Chang, K. D. Carnes, B. D. Esry, and I. Ben-Itzhak, “Enhancing high-order above-threshold dissociation of H2+ beams with few-cycle laser pulses,” Phys. Rev. Lett100, 133001 (2008).
[CrossRef] [PubMed]

Austin, D.R.

F. Silva, D.R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nature Comm.3, 807 (2012).
[CrossRef]

Baker, S.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smit, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science312, 424–427 (2006).
[CrossRef] [PubMed]

Bandrauk, A. D.

A. D. Bandrauk, S. Chelkowski, and H. S. Nguyen, “Attosecond Localization of Electrons in Molecules,” Int. J. Quant. Chem.100, 834–844 (2004).
[CrossRef]

Bates, P. K.

Baudisch, M.

F. Silva, D.R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nature Comm.3, 807 (2012).
[CrossRef]

Becker, A.

K. P. Singh, F. He, P. Ranitovic, W. Cao, S. De, D. Ray, S. Chen, U. Thumm, A. Becker, M. M. Murnane, H. C. Kapteyn, I. V. Litvinyuk, and C. L. Cocke, “Control of electron localization in deuterium molecular ions using an attosecond pulse train and a many-cycle infrared pulse,” Phys. Rev. Lett.104, 023001 (2010).
[CrossRef] [PubMed]

F. He, C. Ruiz, and A. Becker, “Control of electron excitation and localization in the dissociation of H2+ and its isotopes using two sequential ultrashort laser pulses,” Phys. Rev. Lett.99, 083002 (2007).
[CrossRef] [PubMed]

Benedetti, E.

G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
[CrossRef]

Ben-Itzhak, I.

J. McKenna, A. M. Sayler, F. Anis, B. Gaire, N. G. Johnson, E. Parke, J. J. Hua, H. Mashiko, C. M. Nakamura, E. Moon, Z. Chang, K. D. Carnes, B. D. Esry, and I. Ben-Itzhak, “Enhancing high-order above-threshold dissociation of H2+ beams with few-cycle laser pulses,” Phys. Rev. Lett100, 133001 (2008).
[CrossRef] [PubMed]

P. Q. Wang, A. M. Sayler, K. D. Carnes, J. F. Xia, M. A. Smith, B. D. Esry, and I. Ben-Itzhak, “Dissociation of H2+ in intense femtosecond laser fields studied by coincidence three-dimensional momentum imaging,” Phys. Rev. A74, 043411 (2006).
[CrossRef]

V. Roudnev, B. D. Esry, and I. Ben-Itzhak, “Controlling HD+ and H2+ dissociation with the carrier-envelope phase difference of an intense ultrashort laser pulse,” Phys. Rev. Lett.93, 163601 (2004).
[CrossRef] [PubMed]

Bergues, B.

I. Znakovskaya, P. von den Hoff, G. Marcus, S. Zherebtsov, B. Bergues, X. Gu, Y. Deng, M. J. J. Vrakking, R. Kienberger, F. Krausz, R. de Vivie-Riedle, and M. F. Kling, “Subcycle controlled charge-directed reactivity with few-cycle midinfrared pulses,” Phys. Rev. Lett.108, 063002 (2012).
[CrossRef] [PubMed]

Biegert, J.

F. Silva, D.R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nature Comm.3, 807 (2012).
[CrossRef]

A. Thai, M. Hemmer, P. K. Bates, O. Chalus, and J. Biegert, “Sub-250-mrad, passively carrier-envelope-phase-stable mid-infrared OPCPA source at high repetition rate,” Opt. Lett.36, 3918–3920 (2011).
[CrossRef] [PubMed]

Burgdörfer, J.

E. Persson, J. Burgdörfer, and S. Gräfe, “Quantum control of electron localization in molecules driven by trains of half-cycle pulses,” New J. Phys.11, 105035 (2009).
[CrossRef]

Cao, W.

K. P. Singh, F. He, P. Ranitovic, W. Cao, S. De, D. Ray, S. Chen, U. Thumm, A. Becker, M. M. Murnane, H. C. Kapteyn, I. V. Litvinyuk, and C. L. Cocke, “Control of electron localization in deuterium molecular ions using an attosecond pulse train and a many-cycle infrared pulse,” Phys. Rev. Lett.104, 023001 (2010).
[CrossRef] [PubMed]

D. Ray, F. He, S. De, W. Cao, H. Mashiko, P. Ranitovic, K. P. Singh, I. Znakovskaya, U. Thumm, G. G. Paulus, M. F. Kling, I. V. Litvinyuk, and C. L. Cocke, “Ion-energy dependence of asymmetric dissociation of D2 by a two-color laser field,” Phys. Rev. Lett.103, 223201 (2009).
[CrossRef]

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Isolated sub-100-as pulse generation via controlling electron dynamics,” Phys. Rev. A,76, 011402 (2007).
[CrossRef]

Carnes, K. D.

J. McKenna, A. M. Sayler, F. Anis, B. Gaire, N. G. Johnson, E. Parke, J. J. Hua, H. Mashiko, C. M. Nakamura, E. Moon, Z. Chang, K. D. Carnes, B. D. Esry, and I. Ben-Itzhak, “Enhancing high-order above-threshold dissociation of H2+ beams with few-cycle laser pulses,” Phys. Rev. Lett100, 133001 (2008).
[CrossRef] [PubMed]

P. Q. Wang, A. M. Sayler, K. D. Carnes, J. F. Xia, M. A. Smith, B. D. Esry, and I. Ben-Itzhak, “Dissociation of H2+ in intense femtosecond laser fields studied by coincidence three-dimensional momentum imaging,” Phys. Rev. A74, 043411 (2006).
[CrossRef]

Chalus, O.

Chang, Z.

J. McKenna, A. M. Sayler, F. Anis, B. Gaire, N. G. Johnson, E. Parke, J. J. Hua, H. Mashiko, C. M. Nakamura, E. Moon, Z. Chang, K. D. Carnes, B. D. Esry, and I. Ben-Itzhak, “Enhancing high-order above-threshold dissociation of H2+ beams with few-cycle laser pulses,” Phys. Rev. Lett100, 133001 (2008).
[CrossRef] [PubMed]

Chelkowski, S.

A. D. Bandrauk, S. Chelkowski, and H. S. Nguyen, “Attosecond Localization of Electrons in Molecules,” Int. J. Quant. Chem.100, 834–844 (2004).
[CrossRef]

Chen, S.

K. P. Singh, F. He, P. Ranitovic, W. Cao, S. De, D. Ray, S. Chen, U. Thumm, A. Becker, M. M. Murnane, H. C. Kapteyn, I. V. Litvinyuk, and C. L. Cocke, “Control of electron localization in deuterium molecular ions using an attosecond pulse train and a many-cycle infrared pulse,” Phys. Rev. Lett.104, 023001 (2010).
[CrossRef] [PubMed]

Chirila, C. C.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smit, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science312, 424–427 (2006).
[CrossRef] [PubMed]

Cocke, C. L.

K. P. Singh, F. He, P. Ranitovic, W. Cao, S. De, D. Ray, S. Chen, U. Thumm, A. Becker, M. M. Murnane, H. C. Kapteyn, I. V. Litvinyuk, and C. L. Cocke, “Control of electron localization in deuterium molecular ions using an attosecond pulse train and a many-cycle infrared pulse,” Phys. Rev. Lett.104, 023001 (2010).
[CrossRef] [PubMed]

D. Ray, F. He, S. De, W. Cao, H. Mashiko, P. Ranitovic, K. P. Singh, I. Znakovskaya, U. Thumm, G. G. Paulus, M. F. Kling, I. V. Litvinyuk, and C. L. Cocke, “Ion-energy dependence of asymmetric dissociation of D2 by a two-color laser field,” Phys. Rev. Lett.103, 223201 (2009).
[CrossRef]

Corkum, P. B.

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

Couairon, A.

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P. Q. Wang, A. M. Sayler, K. D. Carnes, J. F. Xia, M. A. Smith, B. D. Esry, and I. Ben-Itzhak, “Dissociation of H2+ in intense femtosecond laser fields studied by coincidence three-dimensional momentum imaging,” Phys. Rev. A74, 043411 (2006).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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B. Fischer, M. Kremer, T. Pfeifer, B. Feuerstein, V. Sharma, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Steering the electron in H2+ by nuclear wave packet dynamics,” Phys. Rev. Lett.105, 223001 (2010).
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M. Kremer, B. Fischer, B. Feuerstein, V. L. B. de Jesus, V. Sharma, C. Hofrichter, A. Rudenko, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Electron localization in molecular fragmentation of H2 by carrier-envelope phase stabilized laser pulses,” Phys. Rev. Lett.103, 213003 (2009).
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J. McKenna, A. M. Sayler, F. Anis, B. Gaire, N. G. Johnson, E. Parke, J. J. Hua, H. Mashiko, C. M. Nakamura, E. Moon, Z. Chang, K. D. Carnes, B. D. Esry, and I. Ben-Itzhak, “Enhancing high-order above-threshold dissociation of H2+ beams with few-cycle laser pulses,” Phys. Rev. Lett100, 133001 (2008).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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D. Ray, F. He, S. De, W. Cao, H. Mashiko, P. Ranitovic, K. P. Singh, I. Znakovskaya, U. Thumm, G. G. Paulus, M. F. Kling, I. V. Litvinyuk, and C. L. Cocke, “Ion-energy dependence of asymmetric dissociation of D2 by a two-color laser field,” Phys. Rev. Lett.103, 223201 (2009).
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F. Silva, D.R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nature Comm.3, 807 (2012).
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M. Kremer, B. Fischer, B. Feuerstein, V. L. B. de Jesus, V. Sharma, C. Hofrichter, A. Rudenko, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Electron localization in molecular fragmentation of H2 by carrier-envelope phase stabilized laser pulses,” Phys. Rev. Lett.103, 213003 (2009).
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Hua, J. J.

J. J. Hua and B. D. Esry, “The role of mass in the carrier-envelope phase effect for H2+ dissociation,” J. Phys. B42, 085601 (2009).
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J. McKenna, A. M. Sayler, F. Anis, B. Gaire, N. G. Johnson, E. Parke, J. J. Hua, H. Mashiko, C. M. Nakamura, E. Moon, Z. Chang, K. D. Carnes, B. D. Esry, and I. Ben-Itzhak, “Enhancing high-order above-threshold dissociation of H2+ beams with few-cycle laser pulses,” Phys. Rev. Lett100, 133001 (2008).
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Y. Zhou, C. Huang, Q. Liao, and P. Lu, “Classical simulations including electron correlations for sequential double ionization,” Phys. Rev. Lett.109, 053004 (2012).
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F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81, 163–234 (2009).
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F. Kelkensberg, G. Sansone, M. Y. Ivanov, and M. Vrakking, “A semi-classical model of attosecond electron localization in dissociative ionization of hydrogen,” Phys. Chem. Chem. Phys.13, 8647–8652 (2011).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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S. Gräfe and M. Y. Ivanov, “Effective fields in laser-driven electron recollision and charge localization,” Phys. Rev. Lett.99, 163603 (2007).
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J. McKenna, A. M. Sayler, F. Anis, B. Gaire, N. G. Johnson, E. Parke, J. J. Hua, H. Mashiko, C. M. Nakamura, E. Moon, Z. Chang, K. D. Carnes, B. D. Esry, and I. Ben-Itzhak, “Enhancing high-order above-threshold dissociation of H2+ beams with few-cycle laser pulses,” Phys. Rev. Lett100, 133001 (2008).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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K. P. Singh, F. He, P. Ranitovic, W. Cao, S. De, D. Ray, S. Chen, U. Thumm, A. Becker, M. M. Murnane, H. C. Kapteyn, I. V. Litvinyuk, and C. L. Cocke, “Control of electron localization in deuterium molecular ions using an attosecond pulse train and a many-cycle infrared pulse,” Phys. Rev. Lett.104, 023001 (2010).
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F. Kelkensberg, G. Sansone, M. Y. Ivanov, and M. Vrakking, “A semi-classical model of attosecond electron localization in dissociative ionization of hydrogen,” Phys. Chem. Chem. Phys.13, 8647–8652 (2011).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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M. F. Kling, C. Siedschlag, A. J. Verhoef, J. I. Khan, M. Schultze, T. Uphues, Y. Ni, M. Uiberacker, M. Drescher, F. Krausz, and M. J. J. Vrakking, “Control of electron localization in molecular dissociation,” Science312, 246–248 (2006).
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I. Znakovskaya, P. von den Hoff, G. Marcus, S. Zherebtsov, B. Bergues, X. Gu, Y. Deng, M. J. J. Vrakking, R. Kienberger, F. Krausz, R. de Vivie-Riedle, and M. F. Kling, “Subcycle controlled charge-directed reactivity with few-cycle midinfrared pulses,” Phys. Rev. Lett.108, 063002 (2012).
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I. Znakovskaya, P. von den Hoff, G. Marcus, S. Zherebtsov, B. Bergues, X. Gu, Y. Deng, M. J. J. Vrakking, R. Kienberger, F. Krausz, R. de Vivie-Riedle, and M. F. Kling, “Subcycle controlled charge-directed reactivity with few-cycle midinfrared pulses,” Phys. Rev. Lett.108, 063002 (2012).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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D. Ray, F. He, S. De, W. Cao, H. Mashiko, P. Ranitovic, K. P. Singh, I. Znakovskaya, U. Thumm, G. G. Paulus, M. F. Kling, I. V. Litvinyuk, and C. L. Cocke, “Ion-energy dependence of asymmetric dissociation of D2 by a two-color laser field,” Phys. Rev. Lett.103, 223201 (2009).
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M. F. Kling, C. Siedschlag, I. Znakovskaya, A. J. Verhoef, S. Zherebtsov, F. Krausz, M. Lezius, and M. J. J. Vrakking, “Strong-field control of electron localisation during molecular dissociation,” Mol. Phys.106, 455–465 (2008).
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M. F. Kling, C. Siedschlag, A. J. Verhoef, J. I. Khan, M. Schultze, T. Uphues, Y. Ni, M. Uiberacker, M. Drescher, F. Krausz, and M. J. J. Vrakking, “Control of electron localization in molecular dissociation,” Science312, 246–248 (2006).
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I. Znakovskaya, P. von den Hoff, G. Marcus, S. Zherebtsov, B. Bergues, X. Gu, Y. Deng, M. J. J. Vrakking, R. Kienberger, F. Krausz, R. de Vivie-Riedle, and M. F. Kling, “Subcycle controlled charge-directed reactivity with few-cycle midinfrared pulses,” Phys. Rev. Lett.108, 063002 (2012).
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F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81, 163–234 (2009).
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M. F. Kling, C. Siedschlag, I. Znakovskaya, A. J. Verhoef, S. Zherebtsov, F. Krausz, M. Lezius, and M. J. J. Vrakking, “Strong-field control of electron localisation during molecular dissociation,” Mol. Phys.106, 455–465 (2008).
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P. B. Corkum and F. Krausz, “Attosecond science,” Nature Phys.3, 381–387 (2007).
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M. F. Kling, C. Siedschlag, A. J. Verhoef, J. I. Khan, M. Schultze, T. Uphues, Y. Ni, M. Uiberacker, M. Drescher, F. Krausz, and M. J. J. Vrakking, “Control of electron localization in molecular dissociation,” Science312, 246–248 (2006).
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Kremer, M.

B. Fischer, M. Kremer, T. Pfeifer, B. Feuerstein, V. Sharma, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Steering the electron in H2+ by nuclear wave packet dynamics,” Phys. Rev. Lett.105, 223001 (2010).
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M. Kremer, B. Fischer, B. Feuerstein, V. L. B. de Jesus, V. Sharma, C. Hofrichter, A. Rudenko, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Electron localization in molecular fragmentation of H2 by carrier-envelope phase stabilized laser pulses,” Phys. Rev. Lett.103, 213003 (2009).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smit, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science312, 424–427 (2006).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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M. F. Kling, C. Siedschlag, I. Znakovskaya, A. J. Verhoef, S. Zherebtsov, F. Krausz, M. Lezius, and M. J. J. Vrakking, “Strong-field control of electron localisation during molecular dissociation,” Mol. Phys.106, 455–465 (2008).
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P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Isolated sub-100-as pulse generation via controlling electron dynamics,” Phys. Rev. A,76, 011402 (2007).
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Y. Zhou, C. Huang, Q. Liao, and P. Lu, “Classical simulations including electron correlations for sequential double ionization,” Phys. Rev. Lett.109, 053004 (2012).
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X. M. Tong and C. D. Lin, “Dynamics of light-field control of molecular dissociation at the few-cycle limit,” Phys. Rev. Lett.98, 123002 (2007).
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K. P. Singh, F. He, P. Ranitovic, W. Cao, S. De, D. Ray, S. Chen, U. Thumm, A. Becker, M. M. Murnane, H. C. Kapteyn, I. V. Litvinyuk, and C. L. Cocke, “Control of electron localization in deuterium molecular ions using an attosecond pulse train and a many-cycle infrared pulse,” Phys. Rev. Lett.104, 023001 (2010).
[CrossRef] [PubMed]

D. Ray, F. He, S. De, W. Cao, H. Mashiko, P. Ranitovic, K. P. Singh, I. Znakovskaya, U. Thumm, G. G. Paulus, M. F. Kling, I. V. Litvinyuk, and C. L. Cocke, “Ion-energy dependence of asymmetric dissociation of D2 by a two-color laser field,” Phys. Rev. Lett.103, 223201 (2009).
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K. Liu, Q. Zhang, and P. Lu, “Enhancing electron localization in molecular dissociation by two-color mid- and near-infrared fields,” Phys. Rev. A86, 033410 (2012).
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S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smit, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science312, 424–427 (2006).
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I. Znakovskaya, P. von den Hoff, G. Marcus, S. Zherebtsov, B. Bergues, X. Gu, Y. Deng, M. J. J. Vrakking, R. Kienberger, F. Krausz, R. de Vivie-Riedle, and M. F. Kling, “Subcycle controlled charge-directed reactivity with few-cycle midinfrared pulses,” Phys. Rev. Lett.108, 063002 (2012).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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D. Ray, F. He, S. De, W. Cao, H. Mashiko, P. Ranitovic, K. P. Singh, I. Znakovskaya, U. Thumm, G. G. Paulus, M. F. Kling, I. V. Litvinyuk, and C. L. Cocke, “Ion-energy dependence of asymmetric dissociation of D2 by a two-color laser field,” Phys. Rev. Lett.103, 223201 (2009).
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J. McKenna, A. M. Sayler, F. Anis, B. Gaire, N. G. Johnson, E. Parke, J. J. Hua, H. Mashiko, C. M. Nakamura, E. Moon, Z. Chang, K. D. Carnes, B. D. Esry, and I. Ben-Itzhak, “Enhancing high-order above-threshold dissociation of H2+ beams with few-cycle laser pulses,” Phys. Rev. Lett100, 133001 (2008).
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P. Lan, E. J. Takahashi, and K. Midorikawa, “Efficient control of electron localization by subcycle waveform synthesis,” Phys. Rev. A86, 013418 (2012).
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J. McKenna, A. M. Sayler, F. Anis, B. Gaire, N. G. Johnson, E. Parke, J. J. Hua, H. Mashiko, C. M. Nakamura, E. Moon, Z. Chang, K. D. Carnes, B. D. Esry, and I. Ben-Itzhak, “Enhancing high-order above-threshold dissociation of H2+ beams with few-cycle laser pulses,” Phys. Rev. Lett100, 133001 (2008).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
[CrossRef]

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B. Fischer, M. Kremer, T. Pfeifer, B. Feuerstein, V. Sharma, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Steering the electron in H2+ by nuclear wave packet dynamics,” Phys. Rev. Lett.105, 223001 (2010).
[CrossRef]

M. Kremer, B. Fischer, B. Feuerstein, V. L. B. de Jesus, V. Sharma, C. Hofrichter, A. Rudenko, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Electron localization in molecular fragmentation of H2 by carrier-envelope phase stabilized laser pulses,” Phys. Rev. Lett.103, 213003 (2009).
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K. P. Singh, F. He, P. Ranitovic, W. Cao, S. De, D. Ray, S. Chen, U. Thumm, A. Becker, M. M. Murnane, H. C. Kapteyn, I. V. Litvinyuk, and C. L. Cocke, “Control of electron localization in deuterium molecular ions using an attosecond pulse train and a many-cycle infrared pulse,” Phys. Rev. Lett.104, 023001 (2010).
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J. McKenna, A. M. Sayler, F. Anis, B. Gaire, N. G. Johnson, E. Parke, J. J. Hua, H. Mashiko, C. M. Nakamura, E. Moon, Z. Chang, K. D. Carnes, B. D. Esry, and I. Ben-Itzhak, “Enhancing high-order above-threshold dissociation of H2+ beams with few-cycle laser pulses,” Phys. Rev. Lett100, 133001 (2008).
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M. F. Kling, C. Siedschlag, A. J. Verhoef, J. I. Khan, M. Schultze, T. Uphues, Y. Ni, M. Uiberacker, M. Drescher, F. Krausz, and M. J. J. Vrakking, “Control of electron localization in molecular dissociation,” Science312, 246–248 (2006).
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Nisoli, M.

G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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J. McKenna, A. M. Sayler, F. Anis, B. Gaire, N. G. Johnson, E. Parke, J. J. Hua, H. Mashiko, C. M. Nakamura, E. Moon, Z. Chang, K. D. Carnes, B. D. Esry, and I. Ben-Itzhak, “Enhancing high-order above-threshold dissociation of H2+ beams with few-cycle laser pulses,” Phys. Rev. Lett100, 133001 (2008).
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D. Ray, F. He, S. De, W. Cao, H. Mashiko, P. Ranitovic, K. P. Singh, I. Znakovskaya, U. Thumm, G. G. Paulus, M. F. Kling, I. V. Litvinyuk, and C. L. Cocke, “Ion-energy dependence of asymmetric dissociation of D2 by a two-color laser field,” Phys. Rev. Lett.103, 223201 (2009).
[CrossRef]

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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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E. Persson, J. Burgdörfer, and S. Gräfe, “Quantum control of electron localization in molecules driven by trains of half-cycle pulses,” New J. Phys.11, 105035 (2009).
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B. Fischer, M. Kremer, T. Pfeifer, B. Feuerstein, V. Sharma, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Steering the electron in H2+ by nuclear wave packet dynamics,” Phys. Rev. Lett.105, 223001 (2010).
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K. P. Singh, F. He, P. Ranitovic, W. Cao, S. De, D. Ray, S. Chen, U. Thumm, A. Becker, M. M. Murnane, H. C. Kapteyn, I. V. Litvinyuk, and C. L. Cocke, “Control of electron localization in deuterium molecular ions using an attosecond pulse train and a many-cycle infrared pulse,” Phys. Rev. Lett.104, 023001 (2010).
[CrossRef] [PubMed]

D. Ray, F. He, S. De, W. Cao, H. Mashiko, P. Ranitovic, K. P. Singh, I. Znakovskaya, U. Thumm, G. G. Paulus, M. F. Kling, I. V. Litvinyuk, and C. L. Cocke, “Ion-energy dependence of asymmetric dissociation of D2 by a two-color laser field,” Phys. Rev. Lett.103, 223201 (2009).
[CrossRef]

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K. P. Singh, F. He, P. Ranitovic, W. Cao, S. De, D. Ray, S. Chen, U. Thumm, A. Becker, M. M. Murnane, H. C. Kapteyn, I. V. Litvinyuk, and C. L. Cocke, “Control of electron localization in deuterium molecular ions using an attosecond pulse train and a many-cycle infrared pulse,” Phys. Rev. Lett.104, 023001 (2010).
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D. Ray, F. He, S. De, W. Cao, H. Mashiko, P. Ranitovic, K. P. Singh, I. Znakovskaya, U. Thumm, G. G. Paulus, M. F. Kling, I. V. Litvinyuk, and C. L. Cocke, “Ion-energy dependence of asymmetric dissociation of D2 by a two-color laser field,” Phys. Rev. Lett.103, 223201 (2009).
[CrossRef]

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S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smit, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science312, 424–427 (2006).
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V. Roudnev, B. D. Esry, and I. Ben-Itzhak, “Controlling HD+ and H2+ dissociation with the carrier-envelope phase difference of an intense ultrashort laser pulse,” Phys. Rev. Lett.93, 163601 (2004).
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M. Kremer, B. Fischer, B. Feuerstein, V. L. B. de Jesus, V. Sharma, C. Hofrichter, A. Rudenko, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Electron localization in molecular fragmentation of H2 by carrier-envelope phase stabilized laser pulses,” Phys. Rev. Lett.103, 213003 (2009).
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F. He, C. Ruiz, and A. Becker, “Control of electron excitation and localization in the dissociation of H2+ and its isotopes using two sequential ultrashort laser pulses,” Phys. Rev. Lett.99, 083002 (2007).
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F. Kelkensberg, G. Sansone, M. Y. Ivanov, and M. Vrakking, “A semi-classical model of attosecond electron localization in dissociative ionization of hydrogen,” Phys. Chem. Chem. Phys.13, 8647–8652 (2011).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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J. McKenna, A. M. Sayler, F. Anis, B. Gaire, N. G. Johnson, E. Parke, J. J. Hua, H. Mashiko, C. M. Nakamura, E. Moon, Z. Chang, K. D. Carnes, B. D. Esry, and I. Ben-Itzhak, “Enhancing high-order above-threshold dissociation of H2+ beams with few-cycle laser pulses,” Phys. Rev. Lett100, 133001 (2008).
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P. Q. Wang, A. M. Sayler, K. D. Carnes, J. F. Xia, M. A. Smith, B. D. Esry, and I. Ben-Itzhak, “Dissociation of H2+ in intense femtosecond laser fields studied by coincidence three-dimensional momentum imaging,” Phys. Rev. A74, 043411 (2006).
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B. Fischer, M. Kremer, T. Pfeifer, B. Feuerstein, V. Sharma, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Steering the electron in H2+ by nuclear wave packet dynamics,” Phys. Rev. Lett.105, 223001 (2010).
[CrossRef]

M. Kremer, B. Fischer, B. Feuerstein, V. L. B. de Jesus, V. Sharma, C. Hofrichter, A. Rudenko, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Electron localization in molecular fragmentation of H2 by carrier-envelope phase stabilized laser pulses,” Phys. Rev. Lett.103, 213003 (2009).
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M. F. Kling, C. Siedschlag, A. J. Verhoef, J. I. Khan, M. Schultze, T. Uphues, Y. Ni, M. Uiberacker, M. Drescher, F. Krausz, and M. J. J. Vrakking, “Control of electron localization in molecular dissociation,” Science312, 246–248 (2006).
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B. Fischer, M. Kremer, T. Pfeifer, B. Feuerstein, V. Sharma, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Steering the electron in H2+ by nuclear wave packet dynamics,” Phys. Rev. Lett.105, 223001 (2010).
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M. Kremer, B. Fischer, B. Feuerstein, V. L. B. de Jesus, V. Sharma, C. Hofrichter, A. Rudenko, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Electron localization in molecular fragmentation of H2 by carrier-envelope phase stabilized laser pulses,” Phys. Rev. Lett.103, 213003 (2009).
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M. F. Kling, C. Siedschlag, I. Znakovskaya, A. J. Verhoef, S. Zherebtsov, F. Krausz, M. Lezius, and M. J. J. Vrakking, “Strong-field control of electron localisation during molecular dissociation,” Mol. Phys.106, 455–465 (2008).
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M. F. Kling, C. Siedschlag, A. J. Verhoef, J. I. Khan, M. Schultze, T. Uphues, Y. Ni, M. Uiberacker, M. Drescher, F. Krausz, and M. J. J. Vrakking, “Control of electron localization in molecular dissociation,” Science312, 246–248 (2006).
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F. Silva, D.R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nature Comm.3, 807 (2012).
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K. P. Singh, F. He, P. Ranitovic, W. Cao, S. De, D. Ray, S. Chen, U. Thumm, A. Becker, M. M. Murnane, H. C. Kapteyn, I. V. Litvinyuk, and C. L. Cocke, “Control of electron localization in deuterium molecular ions using an attosecond pulse train and a many-cycle infrared pulse,” Phys. Rev. Lett.104, 023001 (2010).
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D. Ray, F. He, S. De, W. Cao, H. Mashiko, P. Ranitovic, K. P. Singh, I. Znakovskaya, U. Thumm, G. G. Paulus, M. F. Kling, I. V. Litvinyuk, and C. L. Cocke, “Ion-energy dependence of asymmetric dissociation of D2 by a two-color laser field,” Phys. Rev. Lett.103, 223201 (2009).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smit, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science312, 424–427 (2006).
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P. Q. Wang, A. M. Sayler, K. D. Carnes, J. F. Xia, M. A. Smith, B. D. Esry, and I. Ben-Itzhak, “Dissociation of H2+ in intense femtosecond laser fields studied by coincidence three-dimensional momentum imaging,” Phys. Rev. A74, 043411 (2006).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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P. Lan, E. J. Takahashi, and K. Midorikawa, “Efficient control of electron localization by subcycle waveform synthesis,” Phys. Rev. A86, 013418 (2012).
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S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smit, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science312, 424–427 (2006).
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F. Silva, D.R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nature Comm.3, 807 (2012).
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A. Thai, M. Hemmer, P. K. Bates, O. Chalus, and J. Biegert, “Sub-250-mrad, passively carrier-envelope-phase-stable mid-infrared OPCPA source at high repetition rate,” Opt. Lett.36, 3918–3920 (2011).
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B. Fischer, M. Kremer, T. Pfeifer, B. Feuerstein, V. Sharma, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Steering the electron in H2+ by nuclear wave packet dynamics,” Phys. Rev. Lett.105, 223001 (2010).
[CrossRef]

K. P. Singh, F. He, P. Ranitovic, W. Cao, S. De, D. Ray, S. Chen, U. Thumm, A. Becker, M. M. Murnane, H. C. Kapteyn, I. V. Litvinyuk, and C. L. Cocke, “Control of electron localization in deuterium molecular ions using an attosecond pulse train and a many-cycle infrared pulse,” Phys. Rev. Lett.104, 023001 (2010).
[CrossRef] [PubMed]

M. Kremer, B. Fischer, B. Feuerstein, V. L. B. de Jesus, V. Sharma, C. Hofrichter, A. Rudenko, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Electron localization in molecular fragmentation of H2 by carrier-envelope phase stabilized laser pulses,” Phys. Rev. Lett.103, 213003 (2009).
[CrossRef]

D. Ray, F. He, S. De, W. Cao, H. Mashiko, P. Ranitovic, K. P. Singh, I. Znakovskaya, U. Thumm, G. G. Paulus, M. F. Kling, I. V. Litvinyuk, and C. L. Cocke, “Ion-energy dependence of asymmetric dissociation of D2 by a two-color laser field,” Phys. Rev. Lett.103, 223201 (2009).
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B. Feuerstein and U. Thumm, “Fragmentation of H2+ in strong 800-nm laser pulses: Initial-vibrational-state dependence,” Phys. Rev. A67, 043405 (2003).
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S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smit, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science312, 424–427 (2006).
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X. M. Tong and C. D. Lin, “Dynamics of light-field control of molecular dissociation at the few-cycle limit,” Phys. Rev. Lett.98, 123002 (2007).
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M. F. Kling, C. Siedschlag, A. J. Verhoef, J. I. Khan, M. Schultze, T. Uphues, Y. Ni, M. Uiberacker, M. Drescher, F. Krausz, and M. J. J. Vrakking, “Control of electron localization in molecular dissociation,” Science312, 246–248 (2006).
[CrossRef] [PubMed]

Ullrich, J.

B. Fischer, M. Kremer, T. Pfeifer, B. Feuerstein, V. Sharma, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Steering the electron in H2+ by nuclear wave packet dynamics,” Phys. Rev. Lett.105, 223001 (2010).
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M. Kremer, B. Fischer, B. Feuerstein, V. L. B. de Jesus, V. Sharma, C. Hofrichter, A. Rudenko, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Electron localization in molecular fragmentation of H2 by carrier-envelope phase stabilized laser pulses,” Phys. Rev. Lett.103, 213003 (2009).
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M. F. Kling, C. Siedschlag, A. J. Verhoef, J. I. Khan, M. Schultze, T. Uphues, Y. Ni, M. Uiberacker, M. Drescher, F. Krausz, and M. J. J. Vrakking, “Control of electron localization in molecular dissociation,” Science312, 246–248 (2006).
[CrossRef] [PubMed]

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M. F. Kling, C. Siedschlag, I. Znakovskaya, A. J. Verhoef, S. Zherebtsov, F. Krausz, M. Lezius, and M. J. J. Vrakking, “Strong-field control of electron localisation during molecular dissociation,” Mol. Phys.106, 455–465 (2008).
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M. F. Kling, C. Siedschlag, A. J. Verhoef, J. I. Khan, M. Schultze, T. Uphues, Y. Ni, M. Uiberacker, M. Drescher, F. Krausz, and M. J. J. Vrakking, “Control of electron localization in molecular dissociation,” Science312, 246–248 (2006).
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I. Znakovskaya, P. von den Hoff, G. Marcus, S. Zherebtsov, B. Bergues, X. Gu, Y. Deng, M. J. J. Vrakking, R. Kienberger, F. Krausz, R. de Vivie-Riedle, and M. F. Kling, “Subcycle controlled charge-directed reactivity with few-cycle midinfrared pulses,” Phys. Rev. Lett.108, 063002 (2012).
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F. Kelkensberg, G. Sansone, M. Y. Ivanov, and M. Vrakking, “A semi-classical model of attosecond electron localization in dissociative ionization of hydrogen,” Phys. Chem. Chem. Phys.13, 8647–8652 (2011).
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I. Znakovskaya, P. von den Hoff, G. Marcus, S. Zherebtsov, B. Bergues, X. Gu, Y. Deng, M. J. J. Vrakking, R. Kienberger, F. Krausz, R. de Vivie-Riedle, and M. F. Kling, “Subcycle controlled charge-directed reactivity with few-cycle midinfrared pulses,” Phys. Rev. Lett.108, 063002 (2012).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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M. F. Kling, C. Siedschlag, I. Znakovskaya, A. J. Verhoef, S. Zherebtsov, F. Krausz, M. Lezius, and M. J. J. Vrakking, “Strong-field control of electron localisation during molecular dissociation,” Mol. Phys.106, 455–465 (2008).
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M. F. Kling, C. Siedschlag, A. J. Verhoef, J. I. Khan, M. Schultze, T. Uphues, Y. Ni, M. Uiberacker, M. Drescher, F. Krausz, and M. J. J. Vrakking, “Control of electron localization in molecular dissociation,” Science312, 246–248 (2006).
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P. Q. Wang, A. M. Sayler, K. D. Carnes, J. F. Xia, M. A. Smith, B. D. Esry, and I. Ben-Itzhak, “Dissociation of H2+ in intense femtosecond laser fields studied by coincidence three-dimensional momentum imaging,” Phys. Rev. A74, 043411 (2006).
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P. Q. Wang, A. M. Sayler, K. D. Carnes, J. F. Xia, M. A. Smith, B. D. Esry, and I. Ben-Itzhak, “Dissociation of H2+ in intense femtosecond laser fields studied by coincidence three-dimensional momentum imaging,” Phys. Rev. A74, 043411 (2006).
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K. Liu, Q. Zhang, and P. Lu, “Enhancing electron localization in molecular dissociation by two-color mid- and near-infrared fields,” Phys. Rev. A86, 033410 (2012).
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I. Znakovskaya, P. von den Hoff, G. Marcus, S. Zherebtsov, B. Bergues, X. Gu, Y. Deng, M. J. J. Vrakking, R. Kienberger, F. Krausz, R. de Vivie-Riedle, and M. F. Kling, “Subcycle controlled charge-directed reactivity with few-cycle midinfrared pulses,” Phys. Rev. Lett.108, 063002 (2012).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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M. F. Kling, C. Siedschlag, I. Znakovskaya, A. J. Verhoef, S. Zherebtsov, F. Krausz, M. Lezius, and M. J. J. Vrakking, “Strong-field control of electron localisation during molecular dissociation,” Mol. Phys.106, 455–465 (2008).
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Zhou, Y.

Y. Zhou, C. Huang, Q. Liao, and P. Lu, “Classical simulations including electron correlations for sequential double ionization,” Phys. Rev. Lett.109, 053004 (2012).
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Znakovskaya, I.

I. Znakovskaya, P. von den Hoff, G. Marcus, S. Zherebtsov, B. Bergues, X. Gu, Y. Deng, M. J. J. Vrakking, R. Kienberger, F. Krausz, R. de Vivie-Riedle, and M. F. Kling, “Subcycle controlled charge-directed reactivity with few-cycle midinfrared pulses,” Phys. Rev. Lett.108, 063002 (2012).
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G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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D. Ray, F. He, S. De, W. Cao, H. Mashiko, P. Ranitovic, K. P. Singh, I. Znakovskaya, U. Thumm, G. G. Paulus, M. F. Kling, I. V. Litvinyuk, and C. L. Cocke, “Ion-energy dependence of asymmetric dissociation of D2 by a two-color laser field,” Phys. Rev. Lett.103, 223201 (2009).
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M. F. Kling, C. Siedschlag, I. Znakovskaya, A. J. Verhoef, S. Zherebtsov, F. Krausz, M. Lezius, and M. J. J. Vrakking, “Strong-field control of electron localisation during molecular dissociation,” Mol. Phys.106, 455–465 (2008).
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Int. J. Quant. Chem.

A. D. Bandrauk, S. Chelkowski, and H. S. Nguyen, “Attosecond Localization of Electrons in Molecules,” Int. J. Quant. Chem.100, 834–844 (2004).
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J. Phys. B

J. J. Hua and B. D. Esry, “The role of mass in the carrier-envelope phase effect for H2+ dissociation,” J. Phys. B42, 085601 (2009).
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Mol. Phys.

M. F. Kling, C. Siedschlag, I. Znakovskaya, A. J. Verhoef, S. Zherebtsov, F. Krausz, M. Lezius, and M. J. J. Vrakking, “Strong-field control of electron localisation during molecular dissociation,” Mol. Phys.106, 455–465 (2008).
[CrossRef]

Nature (London)

G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martín, and M. J. J. Vrakking, “Electron localization following attosecond molecular photoionization,” Nature (London)465, 763 (2010).
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Nature Comm.

F. Silva, D.R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, “Multi-octave supercontinuum generation from mid-infrared filamentation in a bulk crystal,” Nature Comm.3, 807 (2012).
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Nature Phys.

P. B. Corkum and F. Krausz, “Attosecond science,” Nature Phys.3, 381–387 (2007).
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New J. Phys.

E. Persson, J. Burgdörfer, and S. Gräfe, “Quantum control of electron localization in molecules driven by trains of half-cycle pulses,” New J. Phys.11, 105035 (2009).
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Opt. Express

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Phys. Chem. Chem. Phys.

F. Kelkensberg, G. Sansone, M. Y. Ivanov, and M. Vrakking, “A semi-classical model of attosecond electron localization in dissociative ionization of hydrogen,” Phys. Chem. Chem. Phys.13, 8647–8652 (2011).
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Phys. Rev. A

P. Q. Wang, A. M. Sayler, K. D. Carnes, J. F. Xia, M. A. Smith, B. D. Esry, and I. Ben-Itzhak, “Dissociation of H2+ in intense femtosecond laser fields studied by coincidence three-dimensional momentum imaging,” Phys. Rev. A74, 043411 (2006).
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P. Lan, E. J. Takahashi, and K. Midorikawa, “Efficient control of electron localization by subcycle waveform synthesis,” Phys. Rev. A86, 013418 (2012).
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M. Lein, “Attosecond probing of vibrational dynamics with high-harmonic generation” Phys. Rev. Lett94, 053004 (2005).
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Phys. Rev. Lett.

I. Znakovskaya, P. von den Hoff, G. Marcus, S. Zherebtsov, B. Bergues, X. Gu, Y. Deng, M. J. J. Vrakking, R. Kienberger, F. Krausz, R. de Vivie-Riedle, and M. F. Kling, “Subcycle controlled charge-directed reactivity with few-cycle midinfrared pulses,” Phys. Rev. Lett.108, 063002 (2012).
[CrossRef] [PubMed]

D. Ray, F. He, S. De, W. Cao, H. Mashiko, P. Ranitovic, K. P. Singh, I. Znakovskaya, U. Thumm, G. G. Paulus, M. F. Kling, I. V. Litvinyuk, and C. L. Cocke, “Ion-energy dependence of asymmetric dissociation of D2 by a two-color laser field,” Phys. Rev. Lett.103, 223201 (2009).
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B. Fischer, M. Kremer, T. Pfeifer, B. Feuerstein, V. Sharma, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Steering the electron in H2+ by nuclear wave packet dynamics,” Phys. Rev. Lett.105, 223001 (2010).
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V. Roudnev, B. D. Esry, and I. Ben-Itzhak, “Controlling HD+ and H2+ dissociation with the carrier-envelope phase difference of an intense ultrashort laser pulse,” Phys. Rev. Lett.93, 163601 (2004).
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Y. Zhou, C. Huang, Q. Liao, and P. Lu, “Classical simulations including electron correlations for sequential double ionization,” Phys. Rev. Lett.109, 053004 (2012).
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M. Kremer, B. Fischer, B. Feuerstein, V. L. B. de Jesus, V. Sharma, C. Hofrichter, A. Rudenko, U. Thumm, C. D. Schröter, R. Moshammer, and J. Ullrich, “Electron localization in molecular fragmentation of H2 by carrier-envelope phase stabilized laser pulses,” Phys. Rev. Lett.103, 213003 (2009).
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S. Gräfe and M. Y. Ivanov, “Effective fields in laser-driven electron recollision and charge localization,” Phys. Rev. Lett.99, 163603 (2007).
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F. He, C. Ruiz, and A. Becker, “Control of electron excitation and localization in the dissociation of H2+ and its isotopes using two sequential ultrashort laser pulses,” Phys. Rev. Lett.99, 083002 (2007).
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K. P. Singh, F. He, P. Ranitovic, W. Cao, S. De, D. Ray, S. Chen, U. Thumm, A. Becker, M. M. Murnane, H. C. Kapteyn, I. V. Litvinyuk, and C. L. Cocke, “Control of electron localization in deuterium molecular ions using an attosecond pulse train and a many-cycle infrared pulse,” Phys. Rev. Lett.104, 023001 (2010).
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M. F. Kling, C. Siedschlag, A. J. Verhoef, J. I. Khan, M. Schultze, T. Uphues, Y. Ni, M. Uiberacker, M. Drescher, F. Krausz, and M. J. J. Vrakking, “Control of electron localization in molecular dissociation,” Science312, 246–248 (2006).
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S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smit, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science312, 424–427 (2006).
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Figures (5)

Fig. 1
Fig. 1

The CEP dependence of the electron localization asymmetry of H2+ and its isotopes, D2+ and T2+, for the pulse wavelengths of 3000 (first row) and 800 nm (second row). The third row shows the results (for the 3000-nm pulse) calculated by the molecular model of one-dimensional nuclear motion and one-dimensional electronic motion. The results have been averaged over all the initial vibrational states weighted by FC factors.

Fig. 2
Fig. 2

The asymmetry parameter A(Ek, ϕ) as a function of the CEP and the kinetic energy for (a) H2+, (b) D2+, and (c) T2+ in the 3000-nm pulse. The other laser parameters are the same as in Figs. 1(a)–1(c).

Fig. 3
Fig. 3

The time evolution of the physical quantities of the electron localization process in the 800- and 3000-nm fields for H2+ (thick curve) and D2+ (thin curve). (a)–(b) The electric field. (c)–(d) The quasi-state eigenvalues. (e)–(f) The internuclear distance. (g)–(h) The transition probability. (i)–(j) The localization asymmetry. The shadows indicate the regions where the electron localization is established.

Fig. 4
Fig. 4

(a) Illustration of the dissociation model for H2+ in the 3000-nm field. The vertical lines with arrows reveal the coupling channels that are noted by the text-arrows. The thin gray curves indicate the BO potentials dressed by net absorbed numbers of photons. The blue dashed arrow shows one of the possible dissociation pathways. (b) The absolute value of a cut of the asymmetry A(Ek, ϕ) normalized to the maximum asymmetry at the given CEP of ϕ = 0.5π, as marked by the vertical dashed lines in Fig. 2. (c) The KER spectra normalized to the maximum value for the H2+ dissociation under the 3000-nm pulse with the CEP of 0.5π and 1.0π.

Fig. 5
Fig. 5

The CEP dependence of the electron localization asymmetry (upper row) and the CEP-dependent KER spectra of the asymmetry (lower row) for the dissociation of H2+ and its isotopes in the 3000-nm pulse with two different intensities, 7.11 × 1012 (left part) and 5 × 1013 W/cm2 (right part). The other laser parameters are the same as in Figs. 1(a)–1(c).

Equations (3)

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i t ( χ g χ u ) = ( 2 2 μ + V g V g u V g u * 2 2 μ + V u ) × ( χ g χ u ) ,
V 1 , 2 = V g + V u 2 ( V u V g ) 2 4 + V g u 2 .
P t s ( t ) = exp { π [ V u ( R ¯ ) V g ( R ¯ ) ] 2 4 ω D g u ( R ¯ ) E 0 ( t ) } ,

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