Abstract

Carrier-envelope phase (CEP) dependence of high-order harmonic generation (HHG) from H2+ in a multi-cycle laser pulse is investigated by solving the non-Born-Oppenheimer time-dependent Schrödinger equation (TDSE). It is found that high harmonics in the plateau exhibit counterintuitive frequency modulation (FM) as the CEP of the multi-cycle laser varies. Based on the classical electron trajectories and time-frequency analysis, this multi-cycle CEP-dependent FM is demonstrated to result from the interference of half-cycle HHG radiations, which is modulated by laser-driven nuclear motion. The mechanism of the CEP-dependent FM is further confirmed by simulations based on a simple algorithm in the time domain, which satisfactorily reproduces the TDSE results. The CEP-dependent FM encodes rich information on the correlated electron and nuclear dynamics, which paves the way for probing nuclear motion with attosecond resolution.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (13)

L. He, P. Lan, A.-T. Le, B. Wang, B. Wang, X. Zhu, P. Lu, and C. D. Lin, “Real-time observation of molecular spinning with angular high-harmonic spectroscopy,” Phys. Rev. Lett. 121, 163201 (2018).
[Crossref] [PubMed]

X. Ma, Y. Zhou, N. Li, M. Li, and P. Lu, “Attosecond control of correlated electron dynamics in strong-field nonsequential double ionization by parallel two-color pulses,” Opt. Laser Technol. 108, 235–240 (2018).
[Crossref]

D. Wang, X. Zhu, L. Li, X. Zhang, X. Liu, P. Lan, and P. Lu, “Momentum gate for tunneling electrons with a circularly polarized control field,” Phys. Rev. A 98, 053410 (2018).
[Crossref]

B. Wang, L. He, F. Wang, H. Yuan, X. Zhu, P. Lan, and P. Lu, “Resonance-modulated wavelength scaling of high-order-harmonic generation from H2+,” Phys. Rev. A 97, 013417 (2018).
[Crossref]

L. He, Q. Zhang, P. Lan, W. Cao, X. Zhu, C. Zhai, F. Wang, W. Shi, M. Li, X. Bian, P. Lu, and A. D. Bandrauk, “Monitoring ultrafast vibrational dynamics of isotopic molecules with frequency modulation of high-order harmonics,” Nat. Commun. 9, 1108 (2018).
[Crossref] [PubMed]

J. Chen, K. Wang, H. Long, X. Han, H. Hu, W. Liu, B. Wang, and P. Lu, “Tungsten disulfide-gold nanohole hybrid metasurfaces for nonlinear metalenses in the visible region,” Nano Lett. 18, 1344–1350 (2018).
[Crossref] [PubMed]

S. Ke, D. Zhao, Q. Liu, and W. Liu, “Adiabatic transfer of surface plasmons in non-Hermitian graphene waveguides,” Opt. Quantum Electron. 50, 393 (2018).
[Crossref]

Q. Liu, S. Ke, and W. Liu, “Mode conversion and absorption in an optical waveguide under cascaded complex modulations,” Opt. Quantum Electron. 50, 356 (2018).
[Crossref]

C. Qin, L. Yuan, B. Wang, S. Fan, and P. Lu, “Effective electric-field force for a photon in a synthetic frequency lattice created in a waveguide modulator,” Phys. Rev. A 97, 063838 (2018).
[Crossref]

H. Yuan, L. He, F. Wang, B. Wang, X. Zhu, P. Lan, and P. Lu, “Tomography of asymmetric molecular orbitals with a one-color inhomogeneous field,” Opt. Lett. 43, 931–934 (2018).
[Crossref] [PubMed]

B. Major, E. Balogh, K. Kovács, S. Han, B. Schütte, P. Weber, M. J. J. Vrakking, V. Tosa, A. Rouzée, and K. Varjú, “Spectral shifts and asymmetries in mid-infrared assisted high-order harmonic generation,” J. Opt. Soc. Am. B 35, A32–A38 (2018).
[Crossref]

T. Gaumnitz, A. Jain, and H. J. Wörner, “Complete reconstruction of ultra-broadband isolated attosecond pulses including partial averaging over the angular distribution,” Opt. Express 26, 14719–14740 (2018).
[Crossref] [PubMed]

L. Li, P. Lan, X. Liu, L. He, X. Zhu, O. D. Mücke, and P. Lu, “Method for direct observation of Bloch oscillations in semiconductors,” Opt. Express 26, 23844–23853 (2018).
[Crossref] [PubMed]

2017 (4)

B. Wang, L. He, F. Wang, H. Yuan, X. Zhu, P. Lan, and P. Lu, “Resonance enhanced high-order harmonic generation in H2+ by two sequential laser pulses,” Opt. Express 25, 17777–17787 (2017).
[Crossref] [PubMed]

P. Lan, M. Ruhmann, L. He, C. Zhai, F. Wang, X. Zhu, Q. Zhang, Y. Zhou, M. Li, M. Lein, and P. Lu, “Attosecond probing of nuclear dynamics with trajectory-resolved high-harmonic spectroscopy,” Phys. Rev. Lett. 119, 033201 (2017).
[Crossref] [PubMed]

M. Li, G. Jia, and X.-B. Bian, “Alignment dependent ultrafast electron-nuclear dynamics in molecular high-order harmonic generation,” J. Chem. Phys. 146, 084305 (2017).
[Crossref] [PubMed]

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Chang, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref] [PubMed]

2016 (3)

R. E. F. Silva, P. Rivière, F. Morales, O. Smirnova, M. Ivanov, and F. Martín, “Even harmonic generation in isotropic media of dissociating homonuclear molecules,” Sci. Rep. 6, 32653 (2016).
[Crossref] [PubMed]

M. Lara-Astiaso, R. E. F. Silva, A. Gubaydullin, P. Rivière, C. Meier, and F. Martín, “Enhancing high-order harmonic generation in light molecules by using chirped pulses,” Phys. Rev. Lett. 117, 093003 (2016).
[Crossref] [PubMed]

D. Baykusheva, M. S. Ahsan, N. Lin, and H. J. Wörner, “Bicircular high-harmonic spectroscopy reveals dynamical symmetries of atoms and molecules,” Phys. Rev. Lett. 116, 123001 (2016).
[Crossref] [PubMed]

2015 (3)

M. F. Ciappina, J. A. Pérez-Hernández, A. S. Landsman, T. Zimmermann, M. Lewenstein, L. Roso, and F. Krausz, “Carrier-wave Rabi-flopping signatures in high-order harmonic generation for alkali atoms,” Phys. Rev. Lett. 114, 143902 (2015).
[Crossref] [PubMed]

L. Medišauskas, J. Wragg, H. V. D. Hart, and M. Y. Ivanov, “Generating isolated elliptically polarized attosecond pulses using bichromatic counterrotating circularly polarized laser fields,” Phys. Rev. Lett. 115, 153001 (2015).
[Crossref]

P. M. Kraus, B. Mignolet, D. Baykusheva, A. Rupenyan, L. Horný, E. F. Penka, G. Grassi, O. I. Tolstikhin, J. Schneider, F. Jensen, L. B. Madsen, A. D. Bandrauk, F. Remacle, and H. J. Wörner, “Measurement and laser control of attosecond charge migration in ionized iodoacetylene,” Science 350, 790–795 (2015).
[Crossref] [PubMed]

2014 (6)

X.-B. Bian and A. D. Bandrauk, “Probing nuclear motion by frequency modulation of molecular high-order harmonic generation,” Phys. Rev. Lett. 113, 193901 (2014).
[Crossref] [PubMed]

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillation,” Nat. Photon. 8, 119–123 (2014).
[Crossref]

A. Fleischer, O. Kfir, T. Diskin, P. Sidorenko, and O. Cohen, “Spin angular momentum and tunable polarization in high-harmonic generation,” Nat. Photonics 8, 543–549 (2014).
[Crossref]

F. Morales, P. Rivière, M. Richter, A. Gubaydullin, M. Y. Ivanov, O. Smirnova, and F. Martín, “High harmonic spectroscopy of electron localization in the hydrogen molecular ion,” J. Phys. B: At. Mol. Opt. Phys. 47, 204015 (2014).
[Crossref]

N. Ishii, K. Kaneshima, K. Kitano, T. Kanai, S. Watanabe, and J. Itatani, “Carrier-envelope phase-dependent high harmonic generation in the water window using few-cycle infrared pulses,” Nat. Commun. 5, 3331 (2014).
[Crossref] [PubMed]

P. M. Kraus, D. Baykusheva, and H. J. Wörner, “Two-pulse field-free orientation reveals anisotropy of molecular shape resonance,” Phys. Rev. Lett. 113, 023001 (2014).
[Crossref] [PubMed]

2013 (2)

C. Ott, M. Schönwald, P. Raith, A. Kaldun, G. Sansone, M. Krüger, P. Hommelhoff, Y. Patil, Y. Zhang, K. Meyer, M. Laux, and T. Peifer, “Strong-field spectral interferometry using the carrier-envelope phase,” New J. Phys. 15, 073031 (2013).
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A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-filed-induced current in dielectrics,” Nature (London) 493, 70–74 (2013).
[Crossref]

2012 (2)

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Yu. Ivanov, O. Smirnova, and N. Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature (London) 485, 343–346 (2012).
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2011 (1)

2010 (2)

H. J. Wörner, J. B. Bertrand, D. V. Kartashov, P. B. Corkum, and D. M. Villeneuve, “Following a chemical reaction using high-harmonic interferometry,” Nature (London) 466, 604–607 (2010).
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M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft x-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105, 173901 (2010).
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2009 (3)

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Légaré, M. Giguère, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103, 073902 (2009).
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E. Mansten, J. M. Dahlström, J. Mauritsson, T. Ruchon, A. L’Huillier, J. Tate, M. B. Gaarde, P. Eckle, A. Guandalini, M. Holler, F. Schapper, L. Gallmann, and U. Keller, “Spectral signature of short attosecond pulse trains,” Phys. Rev. Lett. 102, 083002 (2009).
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O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Y. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature (London) 460, 972–977 (2009).
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2008 (2)

E.J. Takahashi, T. Kanai, K. L. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent water window x-ray by phase-matched high-order harmonic generation in neutral media,” Phys. Rev. Lett. 101, 253901 (2008).
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E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
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2007 (3)

M. Uiberacker, T. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. Kabachnik, H. Schroeder, M. Lezius, K. L. Kompa, and H.-G. Muller, “Attosecond real-time observation of electron tunneling in atoms,” Nature (London) 446, 627–632 (2007).
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C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Knight, J. P. Marangos, and J. W. G. Tisch, “Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval,” Nat. Phys. 3, 52–57 (2007).
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J. Levespue, D. Zeidler, J. P. Marangos, P. B. Corkum, and D. M. Villenuve, “High harmonic generation and the role of atomic orbital wave functions,” Phys. Rev. Lett. 98, 183903 (2007).
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2006 (1)

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science 312, 424–427 (2006).
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2005 (4)

M. Lein, “Attosecond probing of vibrational dynamics with high harmonic generation,” Phys. Rev. Lett. 94, 053004 (2005).
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F. Giammanco, A. Pirri, F. Brandi, M. Barkauskas, and W. Ubachs, “Measurements of chirp-induced frequency shift in high-order harmonic generation in xenon,” Laser Phys. 15, 328–333 (2005).

T. Kanai, S. Minemoto, and H. Sakai, “Quantum interference during high-order harmonic generation from aligned molecules,” Nature (London) 435, 470–474 (2005).
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K. Varjú, Y. Mairesse, B. Carré, M. B. Gaarde, P. Johnsson, S. Kazamias, R. López-Martens, J. Mauritsson, K. J. Schafer, P. Balcou, A. L’huillier, and P. Salières, “Frequency chirp of harmonic and attosecond pulses,” J. Mod. Opt. 52, 379–394 (2005).
[Crossref]

2004 (2)

A. D. Bandrauk, S. Chelkowski, and H. S. Nguyen, “Attosecond localization of electrons in molecules,” Int. J. Quantum Chem. 100, 834–844 (2004).
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J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432, 867–871 (2004).
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2003 (2)

A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic process by intense light fields,” Nature (London) 421, 611–615 (2003).
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M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, and G. Tondello, “Effects of carrier-envelope phase differences of few-optical-cylce light pulses in single-shot high-order-harmonic spectra,” Phys. Rev. Lett. 91, 213905 (2003).
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2002 (2)

R. Kienberger, M. Hentschel, M. Uiberacker, C. Spielmann, M. Kitzler, A. Scrinzi, M. Wieland, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Steering attosecond electron wave packet with light,” Science 297, 1144–1148 (2002).
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M. Lein, N. Hay, R. Velotta, J. P. Marangos, and P. L. Knight, “Role of the intramolecular phase in high-harmonic generation,” Phys. Rev. Lett. 88, 183903 (2002).
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1996 (2)

P. Dietrich, M. Y. Ivanov, F. A. Ilkov, and P. B. Corkum, “Two-electron dissociative ionization of H2 and D2 in infrared laser fields,” Phys. Rev. Lett. 77, 4150–4153 (1996).
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K. C. Kulander, F. H. Mies, and K. J. Schafer, “Model for studies of laser-induced nonlinear processes in molecules,” Phys. Rev. A 53, 2562–2570 (1996).
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1995 (2)

T. Zuo and A. D. Bandrauk, “Charge-resonance-enhanced ionization of diatomic molecular ions by intense lasers,” Phys. Rev. A 52, R2511–R2514 (1995).
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T. Seideman, M. Y. Ivanov, and P. B. Corkum, “Role of electron localization in intense-field molecular ionization,” Phys. Rev. Lett. 75, 2819–2822 (1995).
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1994 (1)

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
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1993 (1)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
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Ahsan, M. S.

D. Baykusheva, M. S. Ahsan, N. Lin, and H. J. Wörner, “Bicircular high-harmonic spectroscopy reveals dynamical symmetries of atoms and molecules,” Phys. Rev. Lett. 116, 123001 (2016).
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Ališauskas, S.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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Andriukaitis, G.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
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Apalkov, V.

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-filed-induced current in dielectrics,” Nature (London) 493, 70–74 (2013).
[Crossref]

Aquila, A. L.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Arpin, P.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref] [PubMed]

M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft x-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105, 173901 (2010).
[Crossref]

Attwood, D. T.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref] [PubMed]

Baker, S.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science 312, 424–427 (2006).
[Crossref] [PubMed]

Balciunas, T.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref] [PubMed]

Balcou, P.

K. Varjú, Y. Mairesse, B. Carré, M. B. Gaarde, P. Johnsson, S. Kazamias, R. López-Martens, J. Mauritsson, K. J. Schafer, P. Balcou, A. L’huillier, and P. Salières, “Frequency chirp of harmonic and attosecond pulses,” J. Mod. Opt. 52, 379–394 (2005).
[Crossref]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref] [PubMed]

Balogh, E.

Baltuška, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref] [PubMed]

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

Bandrauk, A. D.

L. He, Q. Zhang, P. Lan, W. Cao, X. Zhu, C. Zhai, F. Wang, W. Shi, M. Li, X. Bian, P. Lu, and A. D. Bandrauk, “Monitoring ultrafast vibrational dynamics of isotopic molecules with frequency modulation of high-order harmonics,” Nat. Commun. 9, 1108 (2018).
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P. M. Kraus, B. Mignolet, D. Baykusheva, A. Rupenyan, L. Horný, E. F. Penka, G. Grassi, O. I. Tolstikhin, J. Schneider, F. Jensen, L. B. Madsen, A. D. Bandrauk, F. Remacle, and H. J. Wörner, “Measurement and laser control of attosecond charge migration in ionized iodoacetylene,” Science 350, 790–795 (2015).
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X.-B. Bian and A. D. Bandrauk, “Probing nuclear motion by frequency modulation of molecular high-order harmonic generation,” Phys. Rev. Lett. 113, 193901 (2014).
[Crossref] [PubMed]

A. D. Bandrauk, S. Chelkowski, and H. S. Nguyen, “Attosecond localization of electrons in molecules,” Int. J. Quantum Chem. 100, 834–844 (2004).
[Crossref]

T. Zuo and A. D. Bandrauk, “Charge-resonance-enhanced ionization of diatomic molecular ions by intense lasers,” Phys. Rev. A 52, R2511–R2514 (1995).
[Crossref] [PubMed]

Bandulet, H.-C.

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Légaré, M. Giguère, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103, 073902 (2009).
[Crossref] [PubMed]

Barkauskas, M.

F. Giammanco, A. Pirri, F. Brandi, M. Barkauskas, and W. Ubachs, “Measurements of chirp-induced frequency shift in high-order harmonic generation in xenon,” Laser Phys. 15, 328–333 (2005).

Barth, J. V.

A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korbman, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-filed-induced current in dielectrics,” Nature (London) 493, 70–74 (2013).
[Crossref]

Baykusheva, D.

D. Baykusheva, M. S. Ahsan, N. Lin, and H. J. Wörner, “Bicircular high-harmonic spectroscopy reveals dynamical symmetries of atoms and molecules,” Phys. Rev. Lett. 116, 123001 (2016).
[Crossref] [PubMed]

P. M. Kraus, B. Mignolet, D. Baykusheva, A. Rupenyan, L. Horný, E. F. Penka, G. Grassi, O. I. Tolstikhin, J. Schneider, F. Jensen, L. B. Madsen, A. D. Bandrauk, F. Remacle, and H. J. Wörner, “Measurement and laser control of attosecond charge migration in ionized iodoacetylene,” Science 350, 790–795 (2015).
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P. M. Kraus, D. Baykusheva, and H. J. Wörner, “Two-pulse field-free orientation reveals anisotropy of molecular shape resonance,” Phys. Rev. Lett. 113, 023001 (2014).
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Becker, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref] [PubMed]

Bertrand, J. B.

H. J. Wörner, J. B. Bertrand, D. V. Kartashov, P. B. Corkum, and D. M. Villeneuve, “Following a chemical reaction using high-harmonic interferometry,” Nature (London) 466, 604–607 (2010).
[Crossref]

Bian, X.

L. He, Q. Zhang, P. Lan, W. Cao, X. Zhu, C. Zhai, F. Wang, W. Shi, M. Li, X. Bian, P. Lu, and A. D. Bandrauk, “Monitoring ultrafast vibrational dynamics of isotopic molecules with frequency modulation of high-order harmonics,” Nat. Commun. 9, 1108 (2018).
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Bian, X.-B.

M. Li, G. Jia, and X.-B. Bian, “Alignment dependent ultrafast electron-nuclear dynamics in molecular high-order harmonic generation,” J. Chem. Phys. 146, 084305 (2017).
[Crossref] [PubMed]

X.-B. Bian and A. D. Bandrauk, “Probing nuclear motion by frequency modulation of molecular high-order harmonic generation,” Phys. Rev. Lett. 113, 193901 (2014).
[Crossref] [PubMed]

Brandi, F.

F. Giammanco, A. Pirri, F. Brandi, M. Barkauskas, and W. Ubachs, “Measurements of chirp-induced frequency shift in high-order harmonic generation in xenon,” Laser Phys. 15, 328–333 (2005).

Brown, S.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref] [PubMed]

Bruner, B. D.

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M. Yu. Ivanov, O. Smirnova, and N. Dudovich, “Resolving the time when an electron exits a tunnelling barrier,” Nature (London) 485, 343–346 (2012).
[Crossref]

Cao, W.

L. He, Q. Zhang, P. Lan, W. Cao, X. Zhu, C. Zhai, F. Wang, W. Shi, M. Li, X. Bian, P. Lu, and A. D. Bandrauk, “Monitoring ultrafast vibrational dynamics of isotopic molecules with frequency modulation of high-order harmonics,” Nat. Commun. 9, 1108 (2018).
[Crossref] [PubMed]

Carré, B.

K. Varjú, Y. Mairesse, B. Carré, M. B. Gaarde, P. Johnsson, S. Kazamias, R. López-Martens, J. Mauritsson, K. J. Schafer, P. Balcou, A. L’huillier, and P. Salières, “Frequency chirp of harmonic and attosecond pulses,” J. Mod. Opt. 52, 379–394 (2005).
[Crossref]

Chang, Y.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Chang, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
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Chang, Z.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Chang, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref] [PubMed]

Chelkowski, S.

A. D. Bandrauk, S. Chelkowski, and H. S. Nguyen, “Attosecond localization of electrons in molecules,” Int. J. Quantum Chem. 100, 834–844 (2004).
[Crossref]

Chen, J.

J. Chen, K. Wang, H. Long, X. Han, H. Hu, W. Liu, B. Wang, and P. Lu, “Tungsten disulfide-gold nanohole hybrid metasurfaces for nonlinear metalenses in the visible region,” Nano Lett. 18, 1344–1350 (2018).
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Chen, M.-C.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernández-García, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[Crossref] [PubMed]

M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft x-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105, 173901 (2010).
[Crossref]

Chew, A.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Chang, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
[Crossref] [PubMed]

Chini, M.

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Chang, E. Cunningham, Y. Wang, S. Hu, Y. Wu, M. Chini, and Z. Chang, “53-attosecond X-ray pulses reach the carbon K-edge,” Nat. Commun. 8, 186 (2017).
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Chipperfield, L. E.

C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Knight, J. P. Marangos, and J. W. G. Tisch, “Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval,” Nat. Phys. 3, 52–57 (2007).
[Crossref]

Chirila, C. C.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science 312, 424–427 (2006).
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Ciappina, M. F.

M. F. Ciappina, J. A. Pérez-Hernández, A. S. Landsman, T. Zimmermann, M. Lewenstein, L. Roso, and F. Krausz, “Carrier-wave Rabi-flopping signatures in high-order harmonic generation for alkali atoms,” Phys. Rev. Lett. 114, 143902 (2015).
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Cohen, O.

A. Fleischer, O. Kfir, T. Diskin, P. Sidorenko, and O. Cohen, “Spin angular momentum and tunable polarization in high-harmonic generation,” Nat. Photonics 8, 543–549 (2014).
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Figures (8)

Fig. 1
Fig. 1 (a) Harmonic spectra of moving H 2 + with the CEP of 0 (solid line), 0.4π (dashed line), 0.8π (dash-doted line). (b) Same as (a), but for the results of H29–H33. For clarity, the intensities of these three harmonics are plotted in linear scale and shifted vertically.
Fig. 2
Fig. 2 (a) The CEP-dependent spectra of H29–H33 for moving H 2 +. (b) Same as (a), but for static H 2 +.
Fig. 3
Fig. 3 (a) Temporal profile of H31 from moving H 2 + as a function of the CEP. The inset illustrates CEP-dependent spectra of H31. (b) Temporal profile of H31 from moving H 2 + with the CEP of 0 (solid line), 0.2π (dashed line), 0.8π (dash-doted line). For clarity, the profiles of these cases have been shifted vertically. (c) and (d) Same as (a) and (b), but for static H 2 +.
Fig. 4
Fig. 4 (a) Mechanism of HHG from moving H 2 +. For static H 2 +, the ionization occurs at the equilibrium distance (Process 1). For moving H 2 +, the nuclear wave packet is forced to larger internuclear distance (Process 2) and then the ionization occurs with a lower ionization threshold (Process 3). (b) Time-dependent internuclear distance 〈R(t)〉 calculated for different CEPs.
Fig. 5
Fig. 5 The classical electron kinetic energy as a function of the emission time for ϕ0 = (a) 0, (b) 0.4π, (c) 0.8π. The energy corresponding to H31 is indicated as the horizontal lines and the time delays Δt between two consecutive emissions for H31 are also illustrated.
Fig. 6
Fig. 6 Time delays between two consecutive emissions near 14T0 (red solid line) and 10T0 (blue dashed line) as a function of the laser CEP.
Fig. 7
Fig. 7 (a) The spectra of H31 from moving H 2 + reproduced by Eq. (4). (b) Same as (a), but for the static H 2 +.
Fig. 8
Fig. 8 Left panels: CEP-dependent FM in HHG from H 2 + with the laser intensity of 1.5 × 1014W/cm2, 2.5 × 1014W/cm2, 3.5 × 1014W/cm2, 4.5 × 1014W/cm2, respectively. Right panels: CEP-dependent temporal profiles of the harmonics presented in the left panels.

Equations (6)

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i t ψ ( R , z ; t ) = [ H 0 + V ( t ) ] ψ ( R , z ; t ) ,
H 0 = T + V 0 = 1 2 μ 2 R 2 1 2 μ e 2 z 2 1 ( z R / 2 ) 2 + α 1 ( z + R / 2 ) 2 + α + 1 R 2 + β .
S ( ω ; ϕ 0 ) = | Σ A n ( ω ) e i ( ω t n + ϕ n ) | 2 .
Δ ω = α q I ( t ) t | t d ,
Δ ω ω = Γ ( R r , I ) Γ ( R f , I ) 2 Γ ( R e , I ) .
Δ ω ω R e R f 2 R e .