氢分子离子的超快动力学研究
|
摘要
分子中的超快动力学一直是人们研究的热点,利用高次谐波和阿秒激光脉冲光电离电子谱我们可以研究相关的动力学过程。本文以氢分子离子为例,用分裂算符法求解含时薛定谔方程,对不同条件下的动力学过程进行模拟探测。
当体系处于最低两个电子本征态时,电子将会以固定频率在两个核之间“跳跃”,此时用一束红外激光与分子相互作用产生高次谐波,但由于电离时刻电子局域性影响,高次谐波也不尽相同。通过改变初始相位差控制高次谐波辐射强度,我们利用不同复合通道的干涉效应探测了谐波啁啾参数,这是一种新的测量方案。由于实验上难以通过改变两个本征态的初始相位差从而改变电离时刻电子的局域性,因此我们试图通过改变激光场包络相位(CEP)从而改变电离时刻来观察电子的局域性对高次谐波产生的影响。计算表明,采用一束半宽为一个周期的飞秒激光,不同CEP下分子产生的高次谐波不同。在CEP变化不大的情况下,结果和改变两本征态初始相位差得到的结果基本相同,也就是说我们可以通过改变激光场CEP来控制电离时刻以揭示电子的局域性对高次谐波产生的影响,探测电子的超快动力学行为。
我们进一步探索利用阿秒脉冲实时探测分子中的电子动力学过程的可能性。针对的自由演化,研究了电子占据最低两个本征态时,阿秒脉冲作用所得光电子谱随时间的变化。利用动量角分布谱信息,分析电子瞬时局域化的影响,提取了电子干涉、各态占据数以及两态相位差等信息。在此基础上研究了在激光场驱动下的演化。由于阿秒脉冲电离的光电子受激光场强烈影响,电子动量角分布谱信息不直接反映阿秒脉冲作用时刻系统的状态。通过定义对比度,在不作任何信息还原的情况下,可以很好地测得电子的局域度变化情况。如果将测量的角分布谱进行信息还原,甚至可以得到激光场驱动下的电子基态占据数的变化。
最后,对于的光致解离过程,我们应用三维程序,计算了核的波函数概率密度分布随时间的变化,得到了解离过程中核的运动行为。通过利用阿秒脉冲探测电离时电子干涉图样,提取了只由激发态贡献的电子动量谱,从而获取光致解离过程中核间距的变化信息。
The ultrafast dynamics in molecules are popular researched by people. We may monitor these dynamics via analyzing high-order harmonic generation and photon electron spectrum ionized by attosecond pulses. In our article, the object is hydrogen molecular ion. By using the split-operator technique to solve time-dependent Schrodinger equation, the dynamics of H2+ in varied conditions are studied.
The electron‘hops’from one nuclear to another in fixed frequency when it occupies the lowest two eigenstates. While an infrared laser pulse interacting on , the harmonic spectra are different due to the varied electron localization at the time of ionization. By changing initial phase difference of the lowest two eigenstates we can control the harmonic intensity, and we get the harmonic chirp by interference effect of two harmonic channels, this is a new way to measure the harmonic chirp. In experiment, it is difficult to control the initial phase difference of the two eigenstates to change the electron localization when it ionized. So we try to investigate the influence on harmonic spectra relied on different localization by changing the carried envelop phase of the laser pulse in order to change the ionization time. The calculation results show: when the pulse duration is a single cycle, the harmonic spectra are different in different CEP, and if we change CEP in a narrow range, the results are almost the same as results by changing the initial phase difference. That is to say we can change the CEP to reveal the influence of electron localization to harmonic spectra by controlling the ionization time, and to probe the ultrafast dynamics of the electron.
We study more on the probability of probing the electron dynamics in molecules by attosecond pulses in time. For the free evolution of H+2 , we use attosecond pulses as probe pulses and obtain the time-varying photoelectron spectrum, when the electron occupies the lowest two eigenstates. By analyzing the momentum angular distributional spectrum and the effect of electron localization, we get much useful information about the interference of electron, the population and the phase difference of these two eigenstates. Based these, we study the evolution of H+2 driven by laser pulses. Because the photon electrons are also driven by the laser pulse, the momentum distributional spectrum cannot show the right state in the ionization time directly. By defining contrast parameter, without reduction of data, we can probe the variety of electron localization finely. And we can even probe the ground state population of H+2 in time with the reduction of the electron momentum angular distributional spectrum.
At last, we calculate three-dimension program to study laser-induced dissociation of H+2, and the probability density distribution of nuclear wave function in this way. Based on the interference effect in single-photon ionization by attosecond pulse, and by getting the momentum spectra only excitated by the electrons in excited states, we can acquire the information of varied nuclear distance in the way of laser-induced dissociation.
当体系处于最低两个电子本征态时,电子将会以固定频率在两个核之间“跳跃”,此时用一束红外激光与分子相互作用产生高次谐波,但由于电离时刻电子局域性影响,高次谐波也不尽相同。通过改变初始相位差控制高次谐波辐射强度,我们利用不同复合通道的干涉效应探测了谐波啁啾参数,这是一种新的测量方案。由于实验上难以通过改变两个本征态的初始相位差从而改变电离时刻电子的局域性,因此我们试图通过改变激光场包络相位(CEP)从而改变电离时刻来观察电子的局域性对高次谐波产生的影响。计算表明,采用一束半宽为一个周期的飞秒激光,不同CEP下分子产生的高次谐波不同。在CEP变化不大的情况下,结果和改变两本征态初始相位差得到的结果基本相同,也就是说我们可以通过改变激光场CEP来控制电离时刻以揭示电子的局域性对高次谐波产生的影响,探测电子的超快动力学行为。
我们进一步探索利用阿秒脉冲实时探测分子中的电子动力学过程的可能性。针对的自由演化,研究了电子占据最低两个本征态时,阿秒脉冲作用所得光电子谱随时间的变化。利用动量角分布谱信息,分析电子瞬时局域化的影响,提取了电子干涉、各态占据数以及两态相位差等信息。在此基础上研究了在激光场驱动下的演化。由于阿秒脉冲电离的光电子受激光场强烈影响,电子动量角分布谱信息不直接反映阿秒脉冲作用时刻系统的状态。通过定义对比度,在不作任何信息还原的情况下,可以很好地测得电子的局域度变化情况。如果将测量的角分布谱进行信息还原,甚至可以得到激光场驱动下的电子基态占据数的变化。
最后,对于的光致解离过程,我们应用三维程序,计算了核的波函数概率密度分布随时间的变化,得到了解离过程中核的运动行为。通过利用阿秒脉冲探测电离时电子干涉图样,提取了只由激发态贡献的电子动量谱,从而获取光致解离过程中核间距的变化信息。
The ultrafast dynamics in molecules are popular researched by people. We may monitor these dynamics via analyzing high-order harmonic generation and photon electron spectrum ionized by attosecond pulses. In our article, the object is hydrogen molecular ion. By using the split-operator technique to solve time-dependent Schrodinger equation, the dynamics of H2+ in varied conditions are studied.
The electron‘hops’from one nuclear to another in fixed frequency when it occupies the lowest two eigenstates. While an infrared laser pulse interacting on , the harmonic spectra are different due to the varied electron localization at the time of ionization. By changing initial phase difference of the lowest two eigenstates we can control the harmonic intensity, and we get the harmonic chirp by interference effect of two harmonic channels, this is a new way to measure the harmonic chirp. In experiment, it is difficult to control the initial phase difference of the two eigenstates to change the electron localization when it ionized. So we try to investigate the influence on harmonic spectra relied on different localization by changing the carried envelop phase of the laser pulse in order to change the ionization time. The calculation results show: when the pulse duration is a single cycle, the harmonic spectra are different in different CEP, and if we change CEP in a narrow range, the results are almost the same as results by changing the initial phase difference. That is to say we can change the CEP to reveal the influence of electron localization to harmonic spectra by controlling the ionization time, and to probe the ultrafast dynamics of the electron.
We study more on the probability of probing the electron dynamics in molecules by attosecond pulses in time. For the free evolution of H+2 , we use attosecond pulses as probe pulses and obtain the time-varying photoelectron spectrum, when the electron occupies the lowest two eigenstates. By analyzing the momentum angular distributional spectrum and the effect of electron localization, we get much useful information about the interference of electron, the population and the phase difference of these two eigenstates. Based these, we study the evolution of H+2 driven by laser pulses. Because the photon electrons are also driven by the laser pulse, the momentum distributional spectrum cannot show the right state in the ionization time directly. By defining contrast parameter, without reduction of data, we can probe the variety of electron localization finely. And we can even probe the ground state population of H+2 in time with the reduction of the electron momentum angular distributional spectrum.
At last, we calculate three-dimension program to study laser-induced dissociation of H+2, and the probability density distribution of nuclear wave function in this way. Based on the interference effect in single-photon ionization by attosecond pulse, and by getting the momentum spectra only excitated by the electrons in excited states, we can acquire the information of varied nuclear distance in the way of laser-induced dissociation.
引文
[1] T. Brabec and F. Krausz. Intense few-cycle laser fields: Frontiers of nonlinear optics. Reviews of Modern Physics. 2000, 72: 2.
[2] M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. B. Corkum, U. Heinzamann, M. Drescher and F. Krausz. Attosecond metrology. Nature. 2001, 414: 509.
[3] M. Protopapas, C. H. Keitel and P. L. Knight. Atomic physics with super high intensity laser. Rep. Prog. Phys. 1997, 60: 389.
[4] D. Strickland and G. Mourou. Compression of amplified chirped optical pulses. Opt. Commun. 1985, 56: 219.
[5] P. B. Corkum, N. H. Burnett and M. Y. Ivanov. Subfemtosecond pulses. Opt. Lett. 1994, 19: 1870.
[6] P. M. Paul, P. Breger, P. Agostini, E. S. Toma, H. G. Muller, G. Mullot, F. Auge and P. Balcou. Observation of a Train of Attosecond Pulses from High Harmonic Generation. Science. 2001, 292: 1689.
[7] M. Uesaka. Femtosecond Beam Science. Imperial College Press. 2005.
[8] P. Agostini, F. Fabre, G. Mainfray, G. Petite and N. K. Rahman. Free-free transitions following six-photon ionization of xenon atoms. Phys. Rev. Lett. 1979, 42: 1127.
[9] L. A. Lompre, G. Mainfray, C. Manus and J. Thebault. Multiphoton ionization of rare gases by a tunable-wavelength 30-psec laser pulse at 1.06μm. Phys. Rev. A. 1977, 15: 1604.
[10] F. Fabre, G. Petite, P. Agostini and M. Clement. Multiphoton above-threshold ionization of xenon at 0.53 and 1.06μm. J. Phys. B. 1982, 15: 1353.
[11] F. Yergeau, G. Petite and P. Agostini. Above-threshold ionization without space charge. J. Phys. B. 1986, 19: L663.
[12] L. V. K. Zh. Ionization in the fields of a strong electromagnetic wave Sov. Phys. 1965, JETP20: 1307-1314.
[13] B. W. Shore and P. L. Knight. Enhancement of high optical harmonics by excess-photon ionization. J. Phys. B. 1987, 20: 413-423.
[14] A. Mcpherson, G. Gibson, H. Jara, U. Johann and T. S. Luk. Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases. J. Opt. Soc. Am. B. 1987, 4: 595-601.
[15] M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray and C. Manus. Multiple-harmonic conversion of 1064nm radiation in rare gases. J. Phys. B. 1988, 21: L31.
[16] Z. Chang, A. Rundquist, H. Wang, M. M. Murnane and H. C. Kapteyn.Generation of coherent soft x rays at 2.7 nm using high harmonics. Phys. Rev. Lett. 1997, 79: 2967.
[17] J. L. Krause, K. J. Schafer and K. C. Kulander. High-order harmonic generation from atoms and ions in the high intensity regime. Phys. Rev. Lett. 1992, 68: 3535.
[18] P. B. Corkum. Plasma perspective on strong-field multiphoton ionization. Phys. Rev. Lett. 1993, 71: 1994.
[19] J. H. Posthumus. The dynamics of small molecules in intense laser fields. Rep. Prog. Phys. 2004, 67: 623-665.
[20] Z. X. Zhao, X. M. Tong and C. D. Lin. Alignment-dependent ionization probability of molecules in a double-pulse laser field. Phys. Rev. A. 2005, 76: 043404.
[21] X. M. Tong, Z. X. Zhao and C. D. Lin. Theory of molecular tunneling ionization. Phys. Rev. A. 2002, 66: 033402.
[22] M. Lein, P. P. Corso, J. P. Marangos and P. L. Knight. Orientation dependence of high-order harmonic generation in molecules. Phys. Rev. A. 2003, 67: 023819.
[23] T. Kanai, S. Minemoto and H. Sakai. Quantum interference during high-order harmonic generation from aligned molecules. Nature. 2005, 435: 470.
[24] J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum and D. M. Villeneuve. Tomographic imaging of molecular orbitals. Nature. 2004, 432: 867.
[25] S. Patchkovskii, Z. X. Zhao, T. Brabec and D. M. Villeneuve. High Harmonic Generation and Molecular Orbital Tomography in Multielectron Systems:Beyond the Single Active Electron Approximation. Phys, Rev. Lett. 2006, 97: 123003.
[26] B. Shan, X. M. Tong, Z. X. Zhao, Z. H. Chang and C. D. Lin. High-order harmonic cutoff extension of the O2 molecule due to ionization suppression. Phys. Rev. A. 2002, 66: R061401.
[27] C. Lynga, A. L’Huiller and C. G. Wahlstrom. High-Order Harmonic Generaion in Molecular Gases. J. Phys. B. 1996, 29: 3293.
[28] M. Lein, N. Hay, R. Velotta, J. P. Marangos and P. L. Knight. Interference effects in high-order harmonic generation with molecules. Phys. Rev. A. 2002, 66: 023805.
[29] 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. Science. 2006, 312: 246.
[30] S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirila, M. Lein, J. W. G. Tisch and J. P. Marangos. Probing Proton Dynamics in Molecules on an Attosecond Time Scale. Science. 2006, 312: 424.
[31] A. Staudte. Attosecond Strobing of Two-Surface Population Dynamics inDissociating H2+. Phys. Rev. Lett. 2007, 98: 073003.
[32] A. H. Zewail. Femtochemistry: Atomic-scale dynamics of the chemical bond. J. Phys. Chem. A. 2000, 104: 5560.
[33] H. Niikura, F. L. e. e?, R. Hasbani, M. Y. Ivanov, D. M. Villeneuve and P. B. Corkum. Probing molecular dynamics with attosecond resolution using correlated wave packet pairs. Nature. 2003, 421: 826.
[34] S. Baker. Probing proton dynamics in molecules on an attosecond time scale. Science. 2006, 312: 424.
[35] M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann and F. Krausz. Time-resolved atomic inner-shell spectroscopy. Nature. 2002, 419: 803.
[36] R. Kienberger, M. Hentschel, M. Uiberacker, C. Spielmann, M. Kitzler, A. Scrinzi, M. Wieland, T. W.-. erwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher and F. Krausz. Steering attosecond electron wave packets with light. Science. 2002, 297: 1144.
[37] A. L. Cavalieri. Attosecond spectroscopy in condensed matter. Nature. 2007, 449: 1029.
[38]徐克尊.高等原子分子物理学.科学出版社. 2006.
[39]钟立晨,丁海曙.分子光谱及激光.电子工业出版社. 1987.
[40] M. D. Feit, J. A. Fleck, Jr. and A. Steiger. Solution of the Schrodinger equation by a spectral method. J. Comput. Phys. 1982, 47: 412.
[41] Q. Su and J. H. Eberly. Model atom for multiphoton physics. Phys. Rev. A. 1991, 44: 5997.
[42] S. Kazamias and Ph. Balcou. Intrinsic chirp of attosecond pulses: Single-atom model versus experiment. Phys. Rev. A. 2004, 69: 063416
[43] Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovacev, R. Taieb. B. Carre, H. G. Muller, P. Agostini, P. Salieres. Attosecond Synchronization of High-Harmonic Soft X-rays. Science. 2003, 302: 1540
[44] G. L. Yudin, S. Chelkowski, J. Itatani, A. D. Bandrauk and P. B. Corkum. Attosecond photoionization of coherently coupled electronic states. Phys. Rev. A. 2005, 72: 051401(R).
[45] S. Chelkowski, G. L. Yudin and A. D. Bandrauk. Observing electron motion in molecules. J. Phys. B. 2006, 39: S409.
[46] P. Agostini and L. F. DiMauro. The physics of attosecond light pulses. Rep. Prog. Phys. 2004, 67: 813.
[47] C. Dimopoulou. Dissociative ionization of H2 by fast protons: three-body break-up and molecule-frame electron emission. J. Phys. B. 2005, 38: 593.
[48] H. Niikura. Sub-laser-cycle electron pulses for probing molecular dynamics. Nature. 2002, 417: 917.
[49] T. Weber. Complete photo-fragmentation of the deuterium molecular. Nature. 2004, 431: 437.
[50] T. Zuo, S. Chelkowski and A. D. Bandrauk. Harmonic generation by the H2+ molecular ion in intense laser fields. Phys, Rev. A. 1993, 48: 3837.
[51] S. Saugout, C. Cornaggia, A. S. Weiner and E. Charron, Ultrafast Electronuclear Dynamics of H2 Double Ionization, Phys. Rev. Lett. 2007, 98: 253003
[2] M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. B. Corkum, U. Heinzamann, M. Drescher and F. Krausz. Attosecond metrology. Nature. 2001, 414: 509.
[3] M. Protopapas, C. H. Keitel and P. L. Knight. Atomic physics with super high intensity laser. Rep. Prog. Phys. 1997, 60: 389.
[4] D. Strickland and G. Mourou. Compression of amplified chirped optical pulses. Opt. Commun. 1985, 56: 219.
[5] P. B. Corkum, N. H. Burnett and M. Y. Ivanov. Subfemtosecond pulses. Opt. Lett. 1994, 19: 1870.
[6] P. M. Paul, P. Breger, P. Agostini, E. S. Toma, H. G. Muller, G. Mullot, F. Auge and P. Balcou. Observation of a Train of Attosecond Pulses from High Harmonic Generation. Science. 2001, 292: 1689.
[7] M. Uesaka. Femtosecond Beam Science. Imperial College Press. 2005.
[8] P. Agostini, F. Fabre, G. Mainfray, G. Petite and N. K. Rahman. Free-free transitions following six-photon ionization of xenon atoms. Phys. Rev. Lett. 1979, 42: 1127.
[9] L. A. Lompre, G. Mainfray, C. Manus and J. Thebault. Multiphoton ionization of rare gases by a tunable-wavelength 30-psec laser pulse at 1.06μm. Phys. Rev. A. 1977, 15: 1604.
[10] F. Fabre, G. Petite, P. Agostini and M. Clement. Multiphoton above-threshold ionization of xenon at 0.53 and 1.06μm. J. Phys. B. 1982, 15: 1353.
[11] F. Yergeau, G. Petite and P. Agostini. Above-threshold ionization without space charge. J. Phys. B. 1986, 19: L663.
[12] L. V. K. Zh. Ionization in the fields of a strong electromagnetic wave Sov. Phys. 1965, JETP20: 1307-1314.
[13] B. W. Shore and P. L. Knight. Enhancement of high optical harmonics by excess-photon ionization. J. Phys. B. 1987, 20: 413-423.
[14] A. Mcpherson, G. Gibson, H. Jara, U. Johann and T. S. Luk. Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases. J. Opt. Soc. Am. B. 1987, 4: 595-601.
[15] M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray and C. Manus. Multiple-harmonic conversion of 1064nm radiation in rare gases. J. Phys. B. 1988, 21: L31.
[16] Z. Chang, A. Rundquist, H. Wang, M. M. Murnane and H. C. Kapteyn.Generation of coherent soft x rays at 2.7 nm using high harmonics. Phys. Rev. Lett. 1997, 79: 2967.
[17] J. L. Krause, K. J. Schafer and K. C. Kulander. High-order harmonic generation from atoms and ions in the high intensity regime. Phys. Rev. Lett. 1992, 68: 3535.
[18] P. B. Corkum. Plasma perspective on strong-field multiphoton ionization. Phys. Rev. Lett. 1993, 71: 1994.
[19] J. H. Posthumus. The dynamics of small molecules in intense laser fields. Rep. Prog. Phys. 2004, 67: 623-665.
[20] Z. X. Zhao, X. M. Tong and C. D. Lin. Alignment-dependent ionization probability of molecules in a double-pulse laser field. Phys. Rev. A. 2005, 76: 043404.
[21] X. M. Tong, Z. X. Zhao and C. D. Lin. Theory of molecular tunneling ionization. Phys. Rev. A. 2002, 66: 033402.
[22] M. Lein, P. P. Corso, J. P. Marangos and P. L. Knight. Orientation dependence of high-order harmonic generation in molecules. Phys. Rev. A. 2003, 67: 023819.
[23] T. Kanai, S. Minemoto and H. Sakai. Quantum interference during high-order harmonic generation from aligned molecules. Nature. 2005, 435: 470.
[24] J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum and D. M. Villeneuve. Tomographic imaging of molecular orbitals. Nature. 2004, 432: 867.
[25] S. Patchkovskii, Z. X. Zhao, T. Brabec and D. M. Villeneuve. High Harmonic Generation and Molecular Orbital Tomography in Multielectron Systems:Beyond the Single Active Electron Approximation. Phys, Rev. Lett. 2006, 97: 123003.
[26] B. Shan, X. M. Tong, Z. X. Zhao, Z. H. Chang and C. D. Lin. High-order harmonic cutoff extension of the O2 molecule due to ionization suppression. Phys. Rev. A. 2002, 66: R061401.
[27] C. Lynga, A. L’Huiller and C. G. Wahlstrom. High-Order Harmonic Generaion in Molecular Gases. J. Phys. B. 1996, 29: 3293.
[28] M. Lein, N. Hay, R. Velotta, J. P. Marangos and P. L. Knight. Interference effects in high-order harmonic generation with molecules. Phys. Rev. A. 2002, 66: 023805.
[29] 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. Science. 2006, 312: 246.
[30] S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirila, M. Lein, J. W. G. Tisch and J. P. Marangos. Probing Proton Dynamics in Molecules on an Attosecond Time Scale. Science. 2006, 312: 424.
[31] A. Staudte. Attosecond Strobing of Two-Surface Population Dynamics inDissociating H2+. Phys. Rev. Lett. 2007, 98: 073003.
[32] A. H. Zewail. Femtochemistry: Atomic-scale dynamics of the chemical bond. J. Phys. Chem. A. 2000, 104: 5560.
[33] H. Niikura, F. L. e. e?, R. Hasbani, M. Y. Ivanov, D. M. Villeneuve and P. B. Corkum. Probing molecular dynamics with attosecond resolution using correlated wave packet pairs. Nature. 2003, 421: 826.
[34] S. Baker. Probing proton dynamics in molecules on an attosecond time scale. Science. 2006, 312: 424.
[35] M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann and F. Krausz. Time-resolved atomic inner-shell spectroscopy. Nature. 2002, 419: 803.
[36] R. Kienberger, M. Hentschel, M. Uiberacker, C. Spielmann, M. Kitzler, A. Scrinzi, M. Wieland, T. W.-. erwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher and F. Krausz. Steering attosecond electron wave packets with light. Science. 2002, 297: 1144.
[37] A. L. Cavalieri. Attosecond spectroscopy in condensed matter. Nature. 2007, 449: 1029.
[38]徐克尊.高等原子分子物理学.科学出版社. 2006.
[39]钟立晨,丁海曙.分子光谱及激光.电子工业出版社. 1987.
[40] M. D. Feit, J. A. Fleck, Jr. and A. Steiger. Solution of the Schrodinger equation by a spectral method. J. Comput. Phys. 1982, 47: 412.
[41] Q. Su and J. H. Eberly. Model atom for multiphoton physics. Phys. Rev. A. 1991, 44: 5997.
[42] S. Kazamias and Ph. Balcou. Intrinsic chirp of attosecond pulses: Single-atom model versus experiment. Phys. Rev. A. 2004, 69: 063416
[43] Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovacev, R. Taieb. B. Carre, H. G. Muller, P. Agostini, P. Salieres. Attosecond Synchronization of High-Harmonic Soft X-rays. Science. 2003, 302: 1540
[44] G. L. Yudin, S. Chelkowski, J. Itatani, A. D. Bandrauk and P. B. Corkum. Attosecond photoionization of coherently coupled electronic states. Phys. Rev. A. 2005, 72: 051401(R).
[45] S. Chelkowski, G. L. Yudin and A. D. Bandrauk. Observing electron motion in molecules. J. Phys. B. 2006, 39: S409.
[46] P. Agostini and L. F. DiMauro. The physics of attosecond light pulses. Rep. Prog. Phys. 2004, 67: 813.
[47] C. Dimopoulou. Dissociative ionization of H2 by fast protons: three-body break-up and molecule-frame electron emission. J. Phys. B. 2005, 38: 593.
[48] H. Niikura. Sub-laser-cycle electron pulses for probing molecular dynamics. Nature. 2002, 417: 917.
[49] T. Weber. Complete photo-fragmentation of the deuterium molecular. Nature. 2004, 431: 437.
[50] T. Zuo, S. Chelkowski and A. D. Bandrauk. Harmonic generation by the H2+ molecular ion in intense laser fields. Phys, Rev. A. 1993, 48: 3837.
[51] S. Saugout, C. Cornaggia, A. S. Weiner and E. Charron, Ultrafast Electronuclear Dynamics of H2 Double Ionization, Phys. Rev. Lett. 2007, 98: 253003