Abstract

Enhancement of the conversion efficiency of high-order harmonics (HHG) generated from an atom in the superposition of two quantum states instead of the ground state is essential because of the recent application in the generation of ultrashort isolated attosecond pulses. In this study, we first confirm the enhancement for a more real system with full three-dimensional geometry and then investigate an interesting effect—the influence of the depletion on the HHG cutoff. For this purpose, we prepare a hydrogen atom initially in the coherent superposition of the ground and the first excited states and calculate the HHG by numerically solving the three-dimensional time-dependent Schrödinger equation (TDSE)—the TDSE method. We find that the plateau of HHG spectra with the coherent superposition state ends earlier than that of the ground state, which can be attributed to the depletion of the excited state. We justify this link by adopting the classical simulation and time-dependent ionization rate. Besides, we show that the conversion efficiency is sensitive to the existence of the excited state. Particularly, for some values of laser field intensity, the excited state population of about 1% increases HHG intensity by more than 5 orders. However, after a critical excited state population, the HHG intensity is stable with continuously increasing initial population of the excited state that is meaningful for experimental setups.

© 2020 Optical Society of America

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2019 (3)

S. Ghimire and D. A. Reis, “High-harmonic generation from solids,” Nat. Phys. 15, 10–16 (2019).
[Crossref]

X.-R. Xiao, M.-X. Wang, H. Liang, Q. Gong, and L.-Y. Peng, “Proposal for measuring electron displacement induced by a short laser pulse,” Phys. Rev. Lett. 122, 053201 (2019).
[Crossref]

D. A. Tumakov, D. A. Telnov, G. Plunien, and V. M. Shabaev, “Photoelectron spectra after multiphoton ionization of Li atoms in the one-photon Rabi-flopping regime,” Phys. Rev. A 100, 023407 (2019).
[Crossref]

2018 (3)

I. Hadas, L. Hareli, and A. Bahabad, “High-order harmonic generation with controllable temporal coherence generated from a coherently excited medium,” Phys. Rev. A 98, 053425 (2018).
[Crossref]

I. N. Ansari, M. S. Mrudul, M. F. Ciappina, M. Lewenstein, and G. Dixit, “Simultaneous control of harmonic yield and energy cutoff of high-order harmonic generation using seeded plasmonically enhanced fields,” Phys. Rev. A 98, 063406 (2018).
[Crossref]

D. Popmintchev, B. R. Galloway, M.-C. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

2017 (6)

J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, 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]

T. Gaumnitz, A. Jain, Y. Pertot, M. Huppert, I. Jordan, F. Ardana-Lamas, and H. J. Wörner, “Streaking of 43-attosecond soft-x-ray pulses generated by a passively CEP-stable mid-infrared driver,” Opt. Express 25, 27506–27518 (2017).
[Crossref]

H. Liu, K. Liu, and A. Feng, “Intensity enhancement in harmonic intensity by using He+ ions chain,” J. Nonlinear Opt. Phys. Mater. 26, 1750021 (2017).
[Crossref]

L. Feng, Y. Li, F. Meng, H. Liu, and R. Castle, “High-order harmonic and attosecond pulse generations from Rydberg state driven by the spatially inhomogeneous field,” Mod. Phys. Lett. B 31, 1750029 (2017).
[Crossref]

M. Yuan, P. Xin, T. Chu, and H. Liu, “Exploring tunneling time by instantaneous ionization rate in strong-field ionization,” Opt. Express 25, 23493–23501 (2017).
[Crossref]

V.-H. Hoang, V.-H. Le, C. D. Lin, and A.-T. Le, “Retrieval of target structure information from laser-induced photoelectrons by few-cycle bicircular laser fields,” Phys. Rev. A 95, 031402 (2017).
[Crossref]

2016 (3)

H. Liu, Z. Zhang, Y. Wu, S. Jiang, and C. Yu, “Isolated attosecond pulses generation from coherent superposition state of helium ion in static electric fields and spatial nonhomogeneous fields,” Int. J. Mod. Phys. B 30, 1650229 (2016).
[Crossref]

H. Z. Jooya, P.-C. Li, S.-L. Liao, and S.-I. Chu, “Generation of isolated ultra-short attosecond pulses by coherent control of the population of excited states,” Phys. Lett. A 380, 316–321 (2016).
[Crossref]

W. Y. Li, S. J. Yu, S. Wang, and Y. J. Chen, “Probing nuclear dynamics of oriented HeH+ with odd-even high-order harmonics,” Phys. Rev. A 94, 053407 (2016).
[Crossref]

2015 (5)

O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics,” Nat. Photonics 9, 99–105 (2015).
[Crossref]

T. Fan, P. Grychtol, R. Knut, C. Hernández-Garca, D. D. Hickstein, D. Zusin, C. Gentry, F. J. Dollar, C. A. Mancuso, C. W. Hogle, O. Kfir, D. Legut, K. Carva, J. L. Ellis, K. M. Dorney, C. Chen, O. G. Shpyrko, E. E. Fullerton, O. Cohen, P. M. Oppeneer, D. B. Milošević, A. Becker, A. A. Jaroń-Becker, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” Proc. Natl. Acad. Sci. USA 112, 14206 (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]

L. Feng, “Molecular harmonic extension and enhancement from H2+ ions in the presence of spatially inhomogeneous fields,” Phys. Rev. A 92, 053832 (2015).
[Crossref]

A. Chacón, M. F. Ciappina, and A. P. Conde, “High-order harmonic generation enhanced by coherent population return,” Eur. Phys. J. D 69, 133 (2015).
[Crossref]

2014 (3)

M. Mohebbi, “A strong single attosecond pulse generation from an atomic superposition state with chirped laser fields,” Optik 125, 3818–3821 (2014).
[Crossref]

F. Calegari, D. Ayuso, A. Trabattoni, L. Belshaw, S. De Camillis, S. Anumula, F. Frassetto, L. Poletto, A. Palacios, P. Decleva, J. B. Greenwood, F. Martn, and M. Nisoli, “Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses,” Science 346, 336–339 (2014).
[Crossref]

X.-Y. Miao and C.-P. Zhang, “Multichannel recombination in high-order-harmonic generation from asymmetric molecular ions,” Phys. Rev. A 89, 033410 (2014).
[Crossref]

2013 (3)

H. Du, Y. Wen, X. Wang, and B. Hu, “Intense supercontinuum generation exceeding 300  eV using a two-color field in combination with a 400-nm few-cycle control pulse,” Opt. Express 21, 21337–21348 (2013).
[Crossref]

M. Mohebbi and S. Batebi, “Two states hydrogenlike model for high-order harmonic generation and an isolated attosecond pulse generation in a He+ ion,” Opt. Commun. 296, 113–123 (2013).
[Crossref]

S. Chelkowski, T. Bredtmann, and A. D. Bandrauk, “High-harmonic generation from a coherent superposition of electronic states: controlling interference patterns via short and long quantum orbits,” Phys. Rev. A 88, 033423 (2013).
[Crossref]

2012 (3)

Y. Chen and B. Zhang, “Role of excited states in the emission times of harmonics from asymmetric molecules,” Phys. Rev. A 86, 023415 (2012).
[Crossref]

H. Du, L. Luo, X. Wang, and B. Hu, “Attosecond ionization control for broadband supercontinuum generation using a weak 400-nm few-cycle controlling pulse,” Opt. Express 20, 27226–27241 (2012).
[Crossref]

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-Garca, 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]

2011 (2)

T. Bredtmann, S. Chelkowski, and A. D. Bandrauk, “Monitoring attosecond dynamics of coherent electron-nuclear wave packets by molecular high-order-harmonic generation,” Phys. Rev. A 84, 021401 (2011).
[Crossref]

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]

2010 (2)

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, T. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, 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]

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]

2009 (2)

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]

A.-T. Le, R. R. Lucchese, S. Tonzani, T. Morishita, and C. D. Lin, “Quantitative rescattering theory for high-order harmonic generation from molecules,” Phys. Rev. A 80, 013401 (2009).
[Crossref]

2008 (1)

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]

2007 (2)

J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98, 013901 (2007).
[Crossref]

A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98, 113003 (2007).
[Crossref]

2006 (3)

A. P. Conde, L. Brandt, and T. Halfmann, “Trace isotope detection enhanced by coherent elimination of power broadening,” Phys. Rev. Lett. 97, 243004 (2006).
[Crossref]

D. B. Milosevic, “Theoretical analysis of high-order harmonic generation from a coherent superposition of states,” J. Opt. Soc. Am. B 23, 308–317 (2006).
[Crossref]

V. V. Strelkov, A. F. Sterjantov, N. Y. Shubin, and V. T. Platonenko, “XUV generation with several-cycle laser pulse in barrier-suppression regime,” J. Phys. B 39, 577–589 (2006).
[Crossref]

2005 (3)

B. Wang, T. Cheng, X. Li, P. Fu, S. Chen, and J. Liu, “Pulse-duration dependence of high-order harmonic generation with coherent superposition state,” Phys. Rev. A 72, 063412 (2005).
[Crossref]

Z. Kis, N. V. Vitanov, A. Karpati, C. Barthel, and K. Bergmann, “Creation of arbitrary coherent superposition states by stimulated Raman adiabatic passage,” Phys. Rev. A 72, 033403 (2005).
[Crossref]

A. P. Conde, L. P. Yatsenko, J. Klein, M. Oberst, and T. Halfmann, “Experimental demonstration of population inversion driven by retroreflection-induced bichromatic adiabatic passage,” Phys. Rev. A 72, 053808 (2005).
[Crossref]

2004 (1)

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, S. Backus, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-order harmonic generation up to 250  eV from highly ionized argon,” Phys. Rev. Lett. 92, 033001 (2004).
[Crossref]

2003 (3)

M. Lein, P. P. Corso, J. P. Marangos, and P. L. Knight, “Orientation dependence of high-order harmonic generation in molecules,” Phys. Rev. A 67, 023819 (2003).
[Crossref]

L. P. Yatsenko, B. W. Shore, N. V. Vitanov, and K. Bergmann, “Retroreflection-induced bichromatic adiabatic passage,” Phys. Rev. A 68, 043405 (2003).
[Crossref]

F. Vewinger, M. Heinz, R. Garcia Fernandez, N. V. Vitanov, and K. Bergmann, “Creation and measurement of a coherent superposition of quantum states,” Phys. Rev. Lett. 91, 213001 (2003).
[Crossref]

2001 (1)

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 (2001).
[Crossref]

1999 (1)

N. V. Vitanov, K.-A. Suominen, and B. W. Shore, “Creation of coherent atomic superpositions by fractional stimulated Raman adiabatic passage,” J. Phys. B 32, 4535–4546 (1999).
[Crossref]

1998 (1)

J. P. Marangos, “Electromagnetically induced transparency,” J. Mod. Opt. 45, 471–503 (1998).
[Crossref]

1997 (1)

X.-M. Tong and S.-I. Chu, “Theoretical study of multiple high-order harmonic generation by intense ultrashort pulsed laser fields: a new generalized pseudospectral time-dependent method,” Chem. Phys. 217, 119–130 (1997).
[Crossref]

1996 (2)

J. B. Watson, A. Sanpera, X. Chen, and K. Burnett, “Harmonic generation from a coherent superposition of states,” Phys. Rev. A 53, R1962 (1996).
[Crossref]

A. Sanpera, J. B. Watson, M. Lewenstein, and K. Burnett, “Harmonic-generation control,” Phys. Rev. A 54, 4320–4326 (1996).
[Crossref]

1995 (2)

F. I. Gauthey, C. H. Keitel, P. L. Knight, and A. Maquet, “Role of initial coherence in the generation of harmonics and sidebands from a strongly driven two-level atom,” Phys. Rev. A 52, 525–540 (1995).
[Crossref]

C.-G. Wahlström, S. Borgström, J. Larsson, and S.-G. Pettersson, “High-order harmonic generation in laser-produced ions using a near-infrared laser,” Phys. Rev. A 51, 585–591 (1995).
[Crossref]

1994 (2)

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]

G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization: a classical model,” J. Phys. B 27, L703 (1994).
[Crossref]

1993 (1)

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

1991 (1)

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[Crossref]

1988 (2)

M. R. Hermann and J. A. Fleck, “Split-operator spectral method for solving the time-dependent Schrödinger equation in spherical coordinates,” Phys. Rev. A 38, 6000–6012 (1988).
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M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B 21, L31 (1988).
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1985 (1)

J. C. Light, I. P. Hamilton, and J. V. Lill, “Generalized discrete variable approximation in quantum mechanics,” J. Chem. Phys. 82, 1400–1409 (1985).
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1982 (1)

M. Feit, J. Fleck, and A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982).
[Crossref]

Adams, C. S.

A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98, 113003 (2007).
[Crossref]

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).
[Crossref]

J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98, 013901 (2007).
[Crossref]

Ališauskas, S.

D. Popmintchev, B. R. Galloway, M.-C. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

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-Garca, 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]

Andriukaitis, G.

D. Popmintchev, B. R. Galloway, M.-C. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

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-Garca, 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]

Ansari, I. N.

I. N. Ansari, M. S. Mrudul, M. F. Ciappina, M. Lewenstein, and G. Dixit, “Simultaneous control of harmonic yield and energy cutoff of high-order harmonic generation using seeded plasmonically enhanced fields,” Phys. Rev. A 98, 063406 (2018).
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Anumula, S.

F. Calegari, D. Ayuso, A. Trabattoni, L. Belshaw, S. De Camillis, S. Anumula, F. Frassetto, L. Poletto, A. Palacios, P. Decleva, J. B. Greenwood, F. Martn, and M. Nisoli, “Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses,” Science 346, 336–339 (2014).
[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]

Ardana-Lamas, F.

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-Garca, 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]

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]

Auguste, T.

J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98, 013901 (2007).
[Crossref]

Ayuso, D.

F. Calegari, D. Ayuso, A. Trabattoni, L. Belshaw, S. De Camillis, S. Anumula, F. Frassetto, L. Poletto, A. Palacios, P. Decleva, J. B. Greenwood, F. Martn, and M. Nisoli, “Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses,” Science 346, 336–339 (2014).
[Crossref]

Azzeer, A. M.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, T. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, 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]

Backus, S.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, S. Backus, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-order harmonic generation up to 250  eV from highly ionized argon,” Phys. Rev. Lett. 92, 033001 (2004).
[Crossref]

Bahabad, A.

I. Hadas, L. Hareli, and A. Bahabad, “High-order harmonic generation with controllable temporal coherence generated from a coherently excited medium,” Phys. Rev. A 98, 053425 (2018).
[Crossref]

Balciunas, T.

D. Popmintchev, B. R. Galloway, M.-C. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

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-Garca, 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]

Balcou, P.

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]

Baltuška, A.

D. Popmintchev, B. R. Galloway, M.-C. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge x-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

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-Garca, 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]

Bandrauk, A. D.

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]

S. Chelkowski, T. Bredtmann, and A. D. Bandrauk, “High-harmonic generation from a coherent superposition of electronic states: controlling interference patterns via short and long quantum orbits,” Phys. Rev. A 88, 033423 (2013).
[Crossref]

T. Bredtmann, S. Chelkowski, and A. D. Bandrauk, “Monitoring attosecond dynamics of coherent electron-nuclear wave packets by molecular high-order-harmonic generation,” Phys. Rev. A 84, 021401 (2011).
[Crossref]

Barthel, C.

Z. Kis, N. V. Vitanov, A. Karpati, C. Barthel, and K. Bergmann, “Creation of arbitrary coherent superposition states by stimulated Raman adiabatic passage,” Phys. Rev. A 72, 033403 (2005).
[Crossref]

Batebi, S.

M. Mohebbi and S. Batebi, “Two states hydrogenlike model for high-order harmonic generation and an isolated attosecond pulse generation in a He+ ion,” Opt. Commun. 296, 113–123 (2013).
[Crossref]

Baykusheva, D.

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]

Becker, A.

T. Fan, P. Grychtol, R. Knut, C. Hernández-Garca, D. D. Hickstein, D. Zusin, C. Gentry, F. J. Dollar, C. A. Mancuso, C. W. Hogle, O. Kfir, D. Legut, K. Carva, J. L. Ellis, K. M. Dorney, C. Chen, O. G. Shpyrko, E. E. Fullerton, O. Cohen, P. M. Oppeneer, D. B. Milošević, A. Becker, A. A. Jaroń-Becker, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” Proc. Natl. Acad. Sci. USA 112, 14206 (2015).
[Crossref]

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-Garca, 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]

Becker, W.

G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization: a classical model,” J. Phys. B 27, L703 (1994).
[Crossref]

Belshaw, L.

F. Calegari, D. Ayuso, A. Trabattoni, L. Belshaw, S. De Camillis, S. Anumula, F. Frassetto, L. Poletto, A. Palacios, P. Decleva, J. B. Greenwood, F. Martn, and M. Nisoli, “Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses,” Science 346, 336–339 (2014).
[Crossref]

Bergmann, K.

Z. Kis, N. V. Vitanov, A. Karpati, C. Barthel, and K. Bergmann, “Creation of arbitrary coherent superposition states by stimulated Raman adiabatic passage,” Phys. Rev. A 72, 033403 (2005).
[Crossref]

L. P. Yatsenko, B. W. Shore, N. V. Vitanov, and K. Bergmann, “Retroreflection-induced bichromatic adiabatic passage,” Phys. Rev. A 68, 043405 (2003).
[Crossref]

F. Vewinger, M. Heinz, R. Garcia Fernandez, N. V. Vitanov, and K. Bergmann, “Creation and measurement of a coherent superposition of quantum states,” Phys. Rev. Lett. 91, 213001 (2003).
[Crossref]

Boller, K.-J.

K.-J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[Crossref]

Borgström, S.

C.-G. Wahlström, S. Borgström, J. Larsson, and S.-G. Pettersson, “High-order harmonic generation in laser-produced ions using a near-infrared laser,” Phys. Rev. A 51, 585–591 (1995).
[Crossref]

Brandt, L.

A. P. Conde, L. Brandt, and T. Halfmann, “Trace isotope detection enhanced by coherent elimination of power broadening,” Phys. Rev. Lett. 97, 243004 (2006).
[Crossref]

Bredtmann, T.

S. Chelkowski, T. Bredtmann, and A. D. Bandrauk, “High-harmonic generation from a coherent superposition of electronic states: controlling interference patterns via short and long quantum orbits,” Phys. Rev. A 88, 033423 (2013).
[Crossref]

T. Bredtmann, S. Chelkowski, and A. D. Bandrauk, “Monitoring attosecond dynamics of coherent electron-nuclear wave packets by molecular high-order-harmonic generation,” Phys. Rev. A 84, 021401 (2011).
[Crossref]

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-Garca, 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]

Burgdörfer, J.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, T. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, 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]

Burnett, K.

J. B. Watson, A. Sanpera, X. Chen, and K. Burnett, “Harmonic generation from a coherent superposition of states,” Phys. Rev. A 53, R1962 (1996).
[Crossref]

A. Sanpera, J. B. Watson, M. Lewenstein, and K. Burnett, “Harmonic-generation control,” Phys. Rev. A 54, 4320–4326 (1996).
[Crossref]

Calegari, F.

F. Calegari, D. Ayuso, A. Trabattoni, L. Belshaw, S. De Camillis, S. Anumula, F. Frassetto, L. Poletto, A. Palacios, P. Decleva, J. B. Greenwood, F. Martn, and M. Nisoli, “Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses,” Science 346, 336–339 (2014).
[Crossref]

Carva, K.

T. Fan, P. Grychtol, R. Knut, C. Hernández-Garca, D. D. Hickstein, D. Zusin, C. Gentry, F. J. Dollar, C. A. Mancuso, C. W. Hogle, O. Kfir, D. Legut, K. Carva, J. L. Ellis, K. M. Dorney, C. Chen, O. G. Shpyrko, E. E. Fullerton, O. Cohen, P. M. Oppeneer, D. B. Milošević, A. Becker, A. A. Jaroń-Becker, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” Proc. Natl. Acad. Sci. USA 112, 14206 (2015).
[Crossref]

Castle, R.

L. Feng, Y. Li, F. Meng, H. Liu, and R. Castle, “High-order harmonic and attosecond pulse generations from Rydberg state driven by the spatially inhomogeneous field,” Mod. Phys. Lett. B 31, 1750029 (2017).
[Crossref]

Cavalieri, A. L.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, T. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, 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]

Chacón, A.

A. Chacón, M. F. Ciappina, and A. P. Conde, “High-order harmonic generation enhanced by coherent population return,” Eur. Phys. J. D 69, 133 (2015).
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Figures (5)

Fig. 1.
Fig. 1. HHG spectra of a hydrogen atom exposed to laser with wavelength of 1600 nm, pulse duration of 27 fs, and intensities of (a) $ 0.15{I_0} $, (b) $ 0.5{I_0} $, and (c) $ 2{I_0} $. The initial states are either the superposition states $ (|1s\rangle + |2s\rangle )/\sqrt 2 $ (black solid curve) or the pure ground state $ |1s\rangle $ (red dotted curve). Arrows indicate the positions of cutoff. The cutoff of HHG spectra with coherent superposition states differently respond to lasers with various intensity.
Fig. 2.
Fig. 2. Time-dependent survival probability of the ground (red dotted curve) and excited states (blue solid curve) for a hydrogen atom in the coherent superposition state. Lasers with a wavelength of 1600 nm, pulse duration of 27 fs, and intensities of (a) $ 0.15{I_0} $, (b) $ 0.5{I_0} $, and (c) $ 2{I_0} $, where $ {{\rm I}_0}= {10^{14}}\,\,{{\rm W/cm}^2} $ is used. The violet and green vertical lines indicate the ionization time $ {t_2} $ and $ {t_1} $ that electrons accumulate maximum kinetic energy of $ 3.17{U_p} $ and $ 2.68{U_p} $, respectively.
Fig. 3.
Fig. 3. (a) Electric field of the five-cycle laser pulse and (b) the classical simulation of kinetic energy acquired by the returning electron when it meets the parent ion. The kinetic energy of the returning electron is a function of the ionization time. The electron ionized at time $ {t_1} = 1.53{T_0} $ and $ {t_2} = 2.04{T_0} $ can return to the parent ion with the maximum kinetic energy $ 2.68{U_p} $ and $ 3.17{U_p} $, respectively.
Fig. 4.
Fig. 4. Time-dependent ionization rates of the ground (dotted curve) and excited states (solid curve) when the initial state of the hydrogen atom is a coherent superposition state. The laser pulses with the same parameters in Fig. 2 are used.
Fig. 5.
Fig. 5. Dependence of the HHG intensity on the population of the excited state (solid curve). A laser with a wavelength of 1600 nm, pulse duration of 27 fs, and intensity of $ 0.2 {I_0} $ is used. Here, the 35th-harmonic order is selected. The HHG intensity of the hydrogen atom with the coherent superposition state significantly enhances with only a small population of the excited state.

Tables (1)

Tables Icon

Table 1. Harmonics Corresponding to the Classical Cutoff Laws I p 1 + 3.17 U p and I p 1 + 2.68 U p , and the Cutoff by TDSE Calculation for Five-Cycle Laser with Wavelength of 1600 nm and Various Intensities

Equations (23)

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i t | Ψ ( r , t ) = [ H ^ 0 + H ^ i ( r , t ) ] | Ψ ( r , t ) ,
H ^ 0 = 2 2 1 r
H ^ i ( r , t ) = r cos θ E ( t ) .
E ( t ) = E 0 sin 2 ( π t τ ) cos ( ω 0 t + π ) ,
| Ψ ( r , t + Δ t ) e i H ^ 0 Δ t / 2 e i H ^ i ( r , t + Δ t / 2 ) Δ t × e i H ^ 0 Δ t / 2 | Ψ ( r , t ) .
Ψ ( r , t ) = nl c nl ( t ) R nl ( r ) Y lm ( r ^ ) .
c nl ( t + Δ t ) n l [ e i H ^ 0 Δ t / 2 e i H ^ i ( r , t + Δ t / 2 ) Δ t × e i H ^ 0 Δ t / 2 ] n l , n l c n l ( t ) ,
| Ψ ( r , t = 0 ) = c 10 ( t = 0 ) | 1 s + c 20 ( t = 0 ) | 2 s ,
P nl s ( t ) = | c nl ( t ) | 2 .
a ( t ) = Ψ ( r , t ) | O ^ | Ψ ( r , t ) ,
O ^ = V ( r , t ) z ,
S ( ω ) | 0 τ a ( t ) e i ω t d t | 2 .
| Ψ ( r , t ) = | Ψ 1 ( r , t ) + | Ψ 2 ( r , t ) .
Ψ 1 ( r , t ) = C 1 [ α ( t ) e i I p 1 t | 1 + γ k ( t ) e i ω k ( 1 ) t | k d k ] ,
Ψ 2 ( r , t ) = C 2 [ β ( t ) e i I p 2 t | 2 + δ k ( t ) e i ω k ( 2 ) t | k d k ] .
a ( t ) = a 11 ( t ) + a 22 ( t ) + a 12 ( t ) + a 21 ( t ) ,
a 11 ( t ) = C 1 2 α ( t ) γ k ( t ) e i ( ω k ( 1 ) I p 1 ) t 1 | O ^ | k d k + c . c . ,
a 22 ( t ) = C 2 2 β ( t ) δ k ( t ) e i ( ω k ( 2 ) I p 2 ) t 2 | O ^ | k d k + c . c . ,
a 12 ( t ) = C 1 C 2 α ( t ) δ k ( t ) e i ( ω k ( 2 ) I p 1 ) t 1 | O ^ | k d k + c . c . ,
a 21 ( t ) = C 1 C 2 β ( t ) γ k ( t ) e i ( ω k ( 1 ) I p 2 ) t 2 | O ^ | k d k + c . c .
N c u t o f f ω 0 = I p 1 + 3.17 U p ,
N c u t o f f ω 0 = I p 1 + 2.68 U p .
Γ nl ( t ) = d d t | c nl ( t ) | 2 .

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