Abstract

We theoretically investigate the high-order harmonic generation (HHG) from Rydberg atoms considering the spatial inhomogeneity of the driving field. It is found that in the inhomogeneous field, the effect of the cutoff extension in the harmonic spectrum from Rydberg atoms can be extended to multi-cycle regime, while in the homogeneous field case, the extension of the harmonic cutoff is limited to the few-cycle regime (less than two optical cycles). The underlying physics of the cutoff extension from Rydberg atoms in the inhomogeneous field is analyzed based on the classical and quantum-mechanical models. Furthermore, by optimizing the field inhomogeneity, the electron dynamics can be well controlled to generate a smooth supercontinuum in the extended spectral region. This can support the efficient generation of isolated attosecond pulses in Rydberg atoms from multi-cycle laser fields.

© 2014 Optical Society of America

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2014 (2)

Y. Li, X. Zhu, P. Lan, Q. Zhang, M. Qin, and P. Lu, “Molecular-orbital tomography beyond the plane-wave approximation,” Phys. Rev. A 89, 045401 (2014);;M. Qin, X. Zhu, Q. Zhang, and P. Lu, “Tomographic imaging of asymmetric molecular orbitals with a two-color multicycle laser field,” Opt. Lett. 37, 5208–5210 (2012).
[Crossref] [PubMed]

J. Luo, Y. Li, Z. Wang, L. He, Q. Zhang, P. Lan, and P. Lu, “Efficient supercontinuum generation by UV-assisted midinfrared plasmonic fields,” Phys. Rev. A 89, 023405 (2014).
[Crossref]

2013 (8)

L. He, Z. Wang, Y. Li, Q. Zhang, P. Lan, and P. Lu, “Wavelength dependence of high-order-harmonic yield in inhomogeneous fields,” Phys. Rev. A 88, 053404 (2013).
[Crossref]

Z. Wang, P. Lan, J. Luo, L. He, Q. Zhang, and P. Lu, “Control of electron dynamics with a multicycle two-color spatially inhomogeneous field for efficient single-attosecond-pulse generation,” Phys. Rev. A 88, 063838 (2013).
[Crossref]

A. S. Landsman, A. N. Pfeiffer, C. Hofmann, M. Smolarski, C. Cirelli, and U. Keller, “Rydberg state creation by tunnel ionization,” New J. Phys. 15, 013001 (2013).
[Crossref]

E. A. Bleda, I. Yavuz, Z. Altun, and T. Topcu, “High- order-harmonic generation from Rydberg states at fixed Keldysh parameter,” Phys. Rev. A 88, 043417 (2013).
[Crossref]

J. A. Pérez-Hernández, M. F. Ciappina, M. Lewenstein, L. Roso, and A. Zaïr, “Beyond Carbon K-Edge Harmonic Emission Using a Spatial and Temporal Synthesized Laser Field,” Phys. Rev. Lett. 110, 053001 (2013).
[Crossref] [PubMed]

J. Luo, Y. Li, Z. Wang, Q. Zhang, and P. Lu, “Ultra-short isolated attosecond emission in mid-infrared inhomogeneous fields without CEP stabilization,” J. Phys. B. 46, 145602 (2013).
[Crossref]

T. Shaaran, M. F. Ciappina, R. Guichard, J. A. Pérez-Hernández, L. Roso, M. Arnold, T. Siegel, A. Zaïr, and M. Lewenstein, “High-order-harmonic generation by enhanced plasmonic near-fields in metal nanoparticles,” Phys. Rev. A 87, 041402(R) (2013).
[Crossref]

Y.-Y. Yang, A. Scrinzi, A. Husakou, Q.-G. Li, S. L. Stebbings, F. Süßmann, H.-J. Yu, S. Kim, E. Rühl, J. Herrmann, X.-C. Lin, and M. F. Kling, “High-harmonic and single attosecond pulse generation using plasmonic field enhancement in ordered arrays of gold nanoparticles with chirped laser pulses,” Opt. Express 21, 2195–2205 (2013).
[Crossref] [PubMed]

2012 (8)

M. F. Ciappina, S. S. Aćimović, T. Shaaran, J. Biegert, R. Quidan, and M. Lewenstein, “Enhancement of high harmonic generation by confining electron motion in plasmonic nanostrutures,” Opt. Express 20, 26261–26274 (2012).
[Crossref] [PubMed]

M. F. Ciappina, J. Biegert, R. Quidant, and M. Lewenstein, “High-order-harmonic generation from inhomogeneous fields,” Phys. Rev. A 85, 033828 (2012).
[Crossref]

T. Shaaran, M. F. Ciappina, and M. Lewenstein, “Quantum-orbit analysis of high-order-harmonic generation by resonant plasmon field enhancement,” Phys. Rev. A 86, 023408 (2012).
[Crossref]

J. Chen, R. Wang, Z. Zhai, J. Chen, P. Fu, B. Wang, and W. M. Liu, “Frequency-selected enhancement of high-order-harmonic generation by interference of degenerate Rydberg states in a few-cycle laser pulse,” Phys. Rev. A 86, 033417 (2012).
[Crossref]

I. Yavuz, E. A. Bleda, Z. Altun, and T. Topcu, “Generation of a broadband xuv continuum in high-order-harmonic generation by spatially inhomogeneous fields,” Phys. Rev. A 85, 013416 (2012).
[Crossref]

Q. Liao, Y. Zhou, C. Huang, and P. Lu, “Multiphoton Rabi oscillations of correlated electrons in strong-field nonsequential double ionization,” New J. Phys. 14, 013001 (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]

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 Regime from Mid-Infrared Femtosecond Lasers,” Science 336, 1287–1291 (2012).
[Crossref] [PubMed]

S. Neppl, R. Ernstorfer, E. M. Bothschafter, A. L. Cavalieri, D. Menzel, J. V. Barth, F. Krausz, R. Kienberger, and P. Feulner, “Attosecond Time-Resolved Photoemission from Core and Valence States of Magnesium,” Phys. Rev. Lett. 109, 087401 (2012).
[Crossref] [PubMed]

2011 (7)

K. Klünder, J. M. Dahlström, M. Gisselbrecht, T. Fordell, T. Fordell, D. Guénot, P. Johnsson, J. Caillat, J. Mauritsson, A. Maquet, R. Taïeb, and A. L’Huillier, “Probing Single-Photon Ionization on the Attosecond Time Scale,” Phys. Rev. Lett. 106, 143002 (2011).
[Crossref] [PubMed]

Z. Zhai, Q. Zhu, J. Chen, Z. C. Yan, P. Fu, and B. Wang, “High-order harmonic generation with Rydberg atoms by using an intense few-cycle pulse,” Phys. Rev. A 83, 043409 (2011).
[Crossref]

I.-Y. Park, S. Kim, J. Choi, D.-H. Lee, Y.-J. Kim, M. F. Kling, M. I. Stockman, and S.-W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Photon. 5, 677–681 (2011).
[Crossref]

Y. Li, W. Hong, Q. Zhang, S. Wang, and P. Lu, “Mid-infrared laser-driven broadband water-window supercontinuum generation from pre-excited medium,” Opt. Express 19, 24376–24386 (2011).
[Crossref] [PubMed]

A. Husakou, F. Kelkensberg, J. Herrmann, and M. J. J. Vrakking, “Polarization gating and circularly-polarized high harmonic generation using plasmonic enhancement in metal nanostructures,” Opt. Express 19, 25346–25354 (2011).
[Crossref]

S. L. Stebbings, F. Süßmann, Y.-Y. Yang, A. Scrinzi, M. Durach, A. Rusina, M. I. Stockman, and M. F. Kling, “Generation of isolated attosecond extreme ultraviolet pulses employing nanoplasmonic field enhancement: optimization of coupled ellipsoids,” New J. Phys. 13, 073010 (2011).
[Crossref]

A. Husakou, S.-J. Im, and J. Herrmann, “Theory of plasmon-enhanced high-harmonic generation in the vicinity of metal nanostructures in noble gases,” Phys. Rev. A 83, 043839 (2011).
[Crossref]

2010 (3)

P. Lan, E. J. Takahashi, and K. Midorikawa, “Wavelength scaling of efficient high-order harmonic generation by two-color infrared laser fields,” Phys. Rev. A 81, 061802(R) (2010).
[Crossref]

Z. Zhai, J. Chen, Z. C. Yan, P. Fu, and B. Wang, “Direct probing of electronic density distribution of a Rydberg state by high-order harmonic generation in a few-cycle laser pulse,” Phys. Rev. A 82, 043422 (2010).
[Crossref]

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdrfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
[Crossref] [PubMed]

2009 (5)

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

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

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Yu. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature (London) 460, 972–977 (2009).
[Crossref]

G. Doumy, J. Wheeler, C. Roedig, R. Chirla, P. Agostini, and L. F. DiMauro, “Attosecond Synchronization of High-Order Harmonics from Midinfrared Drivers,” Phys. Rev. Lett. 102, 093002 (2009).
[Crossref] [PubMed]

W. Hong, P. Lu, Q. Li, and Q. Zhang, “Broadband water window supercontinuum generation with a tailored mid-IR pulse in neutral media,” Opt. Lett. 34, 2102–2104 (2009);;W. Hong, Q. Zhang, Z. Yang, and P. Lu, “Electron dynamic control for the quantum path in the midinfrared regime using a weak near-infrared pulse,” Phys. Rev. A 80, 053407 (2009);;W. Hong, P. Wei, Q. Zhang, S. Wang, and P. Lu, “Mid-infrared modulated polarization gating for ultra-broadband supercontinuum generation,” Opt. Express 18, 11308–11315 (2010).
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2008 (5)

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (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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B. K. McFarland, J. P. Farrell, P. H. Bucksbaum, and M. Guhr, “High Harmonic Generation from Multiple Orbitals in N2,” Science 322, 1232–1235 (2008).
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T. Nubbemeyer, K. Gorling, A. Saenz, U. Eichmann, and W. Sandner, “Strong-Field Tunneling without Ionization,” Phys. Rev. Lett. 101, 233001 (2008).
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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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2007 (5)

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(R) (2007);;P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A 76, 051801(R) (2007).
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M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunnelling in atoms,” Nature (London) 446, 627–632 (2007).
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A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltuska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
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2006 (1)

H. K. Avetissian, G. F. Mkrtchian, and M. G. Poghosyan, “Creation of coherent superposition states in hydrogenlike ions via multiphoton resonant excitation,” Phys. Rev. A 73, 063413 (2006).
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2004 (3)

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 (London) 432, 867–871 (2004).
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R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
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S. X. Hu and L. A. Collins, “High-order harmonic generation from intense laser-driven inner electrons of Rydberg atoms,” Phys. Rev. A 69, 033405 (2004).
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2003 (1)

K. Ishikawa, “Photoemission and Ionization of He+ under Simultaneous Irradiation of Fundamental Laser and High-Order Harmonic Pulses,” Phys. Rev. Lett. 91, 043002 (2003).
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2002 (1)

H. K. Avetissian and G. F. Mkrtchian, “Multiphoton resonant excitation of atoms in strong laser fields and implementation of coherent superposition states,” Phys. Rev. A 66, 033403 (2002).
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2001 (2)

G. L. Yudin and M. Y. Ivanov, “Physics of correlated double ionization of atoms in intense laser fields: Quasistatic tunneling limit,” Phys. Rev. A 63, 033404 (2001).
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B. Shan and Z. Chang, “Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field,” Phys. Rev. A 65, 011804(R) (2001).
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2000 (1)

T. Brabec and F. Krausz, “Intense few-cycle laser elds: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000).
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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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1992 (1)

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45, 3347–3349 (1992).
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1987 (1)

Acimovic, S. S.

Agostini, P.

G. Doumy, J. Wheeler, C. Roedig, R. Chirla, P. Agostini, and L. F. DiMauro, “Attosecond Synchronization of High-Order Harmonics from Midinfrared Drivers,” Phys. Rev. Lett. 102, 093002 (2009).
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J. Tate, T. Auguste, H. Muller, P. Salières, P. Agostini, and L. DiMauro, “Scaling of Wave-Packet Dynamics in an Intense Midinfrared Field,” Phys. Rev. Lett. 98, 013901 (2007).
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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 Regime from Mid-Infrared Femtosecond Lasers,” Science 336, 1287–1291 (2012).
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Altun, Z.

E. A. Bleda, I. Yavuz, Z. Altun, and T. Topcu, “High- order-harmonic generation from Rydberg states at fixed Keldysh parameter,” Phys. Rev. A 88, 043417 (2013).
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I. Yavuz, E. A. Bleda, Z. Altun, and T. Topcu, “Generation of a broadband xuv continuum in high-order-harmonic generation by spatially inhomogeneous fields,” Phys. Rev. A 85, 013416 (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 Regime from Mid-Infrared Femtosecond Lasers,” Science 336, 1287–1291 (2012).
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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).
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Arnold, M.

T. Shaaran, M. F. Ciappina, R. Guichard, J. A. Pérez-Hernández, L. Roso, M. Arnold, T. Siegel, A. Zaïr, and M. Lewenstein, “High-order-harmonic generation by enhanced plasmonic near-fields in metal nanoparticles,” Phys. Rev. A 87, 041402(R) (2013).
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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 Regime from Mid-Infrared Femtosecond Lasers,” Science 336, 1287–1291 (2012).
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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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Auguste, T.

J. Tate, T. Auguste, H. Muller, P. Salières, P. Agostini, and L. DiMauro, “Scaling of Wave-Packet Dynamics in an Intense Midinfrared Field,” Phys. Rev. Lett. 98, 013901 (2007).
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Avetissian, H. K.

H. K. Avetissian, G. F. Mkrtchian, and M. G. Poghosyan, “Creation of coherent superposition states in hydrogenlike ions via multiphoton resonant excitation,” Phys. Rev. A 73, 063413 (2006).
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H. K. Avetissian and G. F. Mkrtchian, “Multiphoton resonant excitation of atoms in strong laser fields and implementation of coherent superposition states,” Phys. Rev. A 66, 033403 (2002).
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Azzeer, A. M.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdrfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
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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 Regime from Mid-Infrared Femtosecond Lasers,” Science 336, 1287–1291 (2012).
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A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltuska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
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R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
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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 Regime from Mid-Infrared Femtosecond Lasers,” Science 336, 1287–1291 (2012).
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Bammer, F.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
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Barth, J. V.

S. Neppl, R. Ernstorfer, E. M. Bothschafter, A. L. Cavalieri, D. Menzel, J. V. Barth, F. Krausz, R. Kienberger, and P. Feulner, “Attosecond Time-Resolved Photoemission from Core and Valence States of Magnesium,” Phys. Rev. Lett. 109, 087401 (2012).
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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 Regime from Mid-Infrared Femtosecond Lasers,” Science 336, 1287–1291 (2012).
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Biegert, J.

Bleda, E. A.

E. A. Bleda, I. Yavuz, Z. Altun, and T. Topcu, “High- order-harmonic generation from Rydberg states at fixed Keldysh parameter,” Phys. Rev. A 88, 043417 (2013).
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I. Yavuz, E. A. Bleda, Z. Altun, and T. Topcu, “Generation of a broadband xuv continuum in high-order-harmonic generation by spatially inhomogeneous fields,” Phys. Rev. A 85, 013416 (2012).
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Blümel, L.

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltuska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
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Bothschafter, E. M.

S. Neppl, R. Ernstorfer, E. M. Bothschafter, A. L. Cavalieri, D. Menzel, J. V. Barth, F. Krausz, R. Kienberger, and P. Feulner, “Attosecond Time-Resolved Photoemission from Core and Valence States of Magnesium,” Phys. Rev. Lett. 109, 087401 (2012).
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Boyer, K.

Brabec, T.

T. Brabec and F. Krausz, “Intense few-cycle laser elds: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000).
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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 Regime from Mid-Infrared Femtosecond Lasers,” Science 336, 1287–1291 (2012).
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Bucksbaum, P. H.

B. K. McFarland, J. P. Farrell, P. H. Bucksbaum, and M. Guhr, “High Harmonic Generation from Multiple Orbitals in N2,” Science 322, 1232–1235 (2008).
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Burgdrfer, J.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdrfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
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Burnett, K.

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45, 3347–3349 (1992).
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Caillat, J.

K. Klünder, J. M. Dahlström, M. Gisselbrecht, T. Fordell, T. Fordell, D. Guénot, P. Johnsson, J. Caillat, J. Mauritsson, A. Maquet, R. Taïeb, and A. L’Huillier, “Probing Single-Photon Ionization on the Attosecond Time Scale,” Phys. Rev. Lett. 106, 143002 (2011).
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Cao, W.

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(R) (2007);;P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A 76, 051801(R) (2007).
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Cavalieri, A. L.

S. Neppl, R. Ernstorfer, E. M. Bothschafter, A. L. Cavalieri, D. Menzel, J. V. Barth, F. Krausz, R. Kienberger, and P. Feulner, “Attosecond Time-Resolved Photoemission from Core and Valence States of Magnesium,” Phys. Rev. Lett. 109, 087401 (2012).
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M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdrfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
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A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltuska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature (London) 449, 1029–1032 (2007).
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Chang, Z.

B. Shan and Z. Chang, “Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field,” Phys. Rev. A 65, 011804(R) (2001).
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Chen, J.

J. Chen, R. Wang, Z. Zhai, J. Chen, P. Fu, B. Wang, and W. M. Liu, “Frequency-selected enhancement of high-order-harmonic generation by interference of degenerate Rydberg states in a few-cycle laser pulse,” Phys. Rev. A 86, 033417 (2012).
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J. Chen, R. Wang, Z. Zhai, J. Chen, P. Fu, B. Wang, and W. M. Liu, “Frequency-selected enhancement of high-order-harmonic generation by interference of degenerate Rydberg states in a few-cycle laser pulse,” Phys. Rev. A 86, 033417 (2012).
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Z. Zhai, Q. Zhu, J. Chen, Z. C. Yan, P. Fu, and B. Wang, “High-order harmonic generation with Rydberg atoms by using an intense few-cycle pulse,” Phys. Rev. A 83, 043409 (2011).
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Z. Zhai, J. Chen, Z. C. Yan, P. Fu, and B. Wang, “Direct probing of electronic density distribution of a Rydberg state by high-order harmonic generation in a few-cycle laser pulse,” Phys. Rev. A 82, 043422 (2010).
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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 Regime from Mid-Infrared Femtosecond Lasers,” Science 336, 1287–1291 (2012).
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Chirla, R.

G. Doumy, J. Wheeler, C. Roedig, R. Chirla, P. Agostini, and L. F. DiMauro, “Attosecond Synchronization of High-Order Harmonics from Midinfrared Drivers,” Phys. Rev. Lett. 102, 093002 (2009).
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Choi, J.

I.-Y. Park, S. Kim, J. Choi, D.-H. Lee, Y.-J. Kim, M. F. Kling, M. I. Stockman, and S.-W. Kim, “Plasmonic generation of ultrashort extreme-ultraviolet light pulses,” Nat. Photon. 5, 677–681 (2011).
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Ciappina, M. F.

T. Shaaran, M. F. Ciappina, R. Guichard, J. A. Pérez-Hernández, L. Roso, M. Arnold, T. Siegel, A. Zaïr, and M. Lewenstein, “High-order-harmonic generation by enhanced plasmonic near-fields in metal nanoparticles,” Phys. Rev. A 87, 041402(R) (2013).
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J. A. Pérez-Hernández, M. F. Ciappina, M. Lewenstein, L. Roso, and A. Zaïr, “Beyond Carbon K-Edge Harmonic Emission Using a Spatial and Temporal Synthesized Laser Field,” Phys. Rev. Lett. 110, 053001 (2013).
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M. F. Ciappina, J. Biegert, R. Quidant, and M. Lewenstein, “High-order-harmonic generation from inhomogeneous fields,” Phys. Rev. A 85, 033828 (2012).
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M. F. Ciappina, S. S. Aćimović, T. Shaaran, J. Biegert, R. Quidan, and M. Lewenstein, “Enhancement of high harmonic generation by confining electron motion in plasmonic nanostrutures,” Opt. Express 20, 26261–26274 (2012).
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T. Shaaran, M. F. Ciappina, and M. Lewenstein, “Quantum-orbit analysis of high-order-harmonic generation by resonant plasmon field enhancement,” Phys. Rev. A 86, 023408 (2012).
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A. S. Landsman, A. N. Pfeiffer, C. Hofmann, M. Smolarski, C. Cirelli, and U. Keller, “Rydberg state creation by tunnel ionization,” New J. Phys. 15, 013001 (2013).
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Collins, L. A.

S. X. Hu and L. A. Collins, “High-order harmonic generation from intense laser-driven inner electrons of Rydberg atoms,” Phys. Rev. A 69, 033405 (2004).
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Cooper, J.

K. Burnett, V. C. Reed, J. Cooper, and P. L. Knight, “Calculation of the background emitted during high-harmonic generation,” Phys. Rev. A 45, 3347–3349 (1992).
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Corkum, P.

O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Yu. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature (London) 460, 972–977 (2009).
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Corkum, P. B.

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 (London) 432, 867–871 (2004).
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K. Klünder, J. M. Dahlström, M. Gisselbrecht, T. Fordell, T. Fordell, D. Guénot, P. Johnsson, J. Caillat, J. Mauritsson, A. Maquet, R. Taïeb, and A. L’Huillier, “Probing Single-Photon Ionization on the Attosecond Time Scale,” Phys. Rev. Lett. 106, 143002 (2011).
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DiMauro, L.

J. Tate, T. Auguste, H. Muller, P. Salières, P. Agostini, and L. DiMauro, “Scaling of Wave-Packet Dynamics in an Intense Midinfrared Field,” Phys. Rev. Lett. 98, 013901 (2007).
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Science (4)

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]

B. K. McFarland, J. P. Farrell, P. H. Bucksbaum, and M. Guhr, “High Harmonic Generation from Multiple Orbitals in N2,” Science 322, 1232–1235 (2008).
[Crossref] [PubMed]

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdrfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
[Crossref] [PubMed]

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[Crossref] [PubMed]

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Figures (9)

Fig. 1
Fig. 1 The harmonic spectra in the homogeneous field with different pulse durations.
Fig. 2
Fig. 2 The harmonic spectra in the inhomogeneous field with different pulse durations. The carrier-envelope phase φ is 1.0π.
Fig. 3
Fig. 3 Dependence of maximum harmonic order on the spatial inhomogeneity ε for the ground state Ψ1s (in blue) and for the Rydberg state Ψ6p (in red). The carrier-envelope phase φ is 1.0π.
Fig. 4
Fig. 4 Dependence of harmonic order on the recombination time of the electron for the ground state Ψ1s and for the Rydberg state Ψ6p in the inhomogeneous field. The carrier-envelope phase φ is 1.0π.
Fig. 5
Fig. 5 Dependence of the recombination time on the initial position of the 6p Rydberg atom in the inhomogeneous field for different values of ε. The pulse duration is 4 fs. The carrier-envelope phase φ is 1.0π.
Fig. 6
Fig. 6 (a) Classical trajectories of the Rydberg electrons with different initial positions in the inhomogeneous field. (b) The harmonic energy with the Rydberg atom as a function of the initial position Z0. ω is the frequency of the 800 nm pulse. (c) The time-frequency distribution of the harmonics from the superposition state Ψ1s+6p. (d) Radial density distribution of the 6p state. The pulse duration is 4 fs. The spatial nonhomogeneity ε=0.004. The carrier-envelope phase φ is 1.0π.
Fig. 7
Fig. 7 (a) variation of the maximum harmonic order as a function of CEP. The pulse duration is 4 fs and the spatial nonhomogeneity ε=0.004. (b) Classical trajectories with different initial positions in the inhomogeneous field. (c) and (d) are the time-frequency distribution and harmonic spectrum using the superposition state Ψ1s+6p. The CEP used in (b)–(d) is 0.
Fig. 8
Fig. 8 The time-frequency distribution (background), and the superimposed classical trajectories for the ground state Ψ1s and the Rydberg state Ψ9d in the multi-cycle inhomogeneous field.
Fig. 9
Fig. 9 The harmonic spectra (a, c, e and g) and temporal profiles of the obtained attosecond pulses (b, d, f and h) from the superposition state Ψ1s+9d with the 10 fs inhomogeneous field.

Equations (3)

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i Ψ ( r , t ) t = [ 1 2 2 1 r + V laser ( r , t ) ] Ψ ( r , t ) ,
V laser ( r , t ) = E ( r , t ) r .
E ( r , t ) = E 0 ( 1 + ε z ) f ( t ) sin ( ω t + φ ) z ^ .

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