Abstract
We theoretically investigate high-order harmonic generation (HHG) from a coherent superposition state of hydrogen atom in a circularly polarized (CP) laser field. The results show that, driven by the CP field, HHG from the coherent superposition state is enhanced by 4 to 5 orders of magnitude compared to that from the ground state. The enhanced intensity is comparable to that of the ground state in a linearly polarized laser field. Based on the classical and quantum analyses, we demonstrate that HHG in the CP laser field mainly arises from the recombination of electrons ionized at non-zero initial positions. The enhancement of HHG from the coherent superposition state is due to the higher ionization rate and also the larger probability density of electrons located far from the nucleus of the involved excited state. The obtained harmonic spectra support the generation of intense isolated attosecond pulses (IAPs) with the ellipticity as high as 0.93. Moreover, we show that the generation of IAPs with large ellipticity is robust against the variation of the carrier envelope phase (CEP) of the laser field. Our results provide a new route toward generating near-CP IAPs, which will be beneficial for ultrafast detection of chiral-sensitive light-matter interactions.
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Alon, O.E., Averbukh, V., Moiseyev, N.: Selection rules for the high harmonic generation spectra. Phys. Rev. Lett. 80, 3743 (1998)
Avetissian, H.K., Mkrtchian, G.F.: Multiphoton resonant excitation of atoms in strong laser fields and implementation of coherent superposition states. Phys. Rev. A 66, 033403 (2002)
Avetissian, H.K., Avchyan, B.R., Mkrtchian, G.F.: Two-color multiphoton resonant excitation of three-level atoms. Phys. Rev. A 74, 063413 (2006)
Baker, S., Robinson, J.S., Haworth, C.A., Teng, H., Smith, R.A., Chirilǎ, C.C., Lein, M., Tisch, J.W.G., Marangos, J.P.: Probing proton dynamics in molecules on an attosecond time scale. Science 312, 424–427 (2006)
Barreau, L., Veyrinas, K., Gruson, V., Weber, S.J., Auguste, T., Hergott, J., Lepetit, F., Carré, B., Houver, J., Dowek, D., Salières, P.: Evidence of depolarization and ellipticity of high harmonics driven by ultrashort bichromatic circularly polarized fields. Nat. Commun. 9, 4727 (2018)
Barth, I., Manz, J.: Electric ring currents in atomic orbitals and magnetic fields induced by short intense circularly polarized \(\pi\) pulses. Phys. Rev. A 75, 012510 (2007)
Bleda, E.A., Yavuz, I., Altun, Z., Topcu, T.: High-order-harmonic generation from Rydberg states at fixed Keldysh parameter. Phys. Rev. A 88, 043417 (2013)
Böwering, N., Lischke, T., Schmidtke, B., Müller, N., Khalil, T., Heinzmann, U.: Asymmetry in photoelectron emission from chiral molecules induced by circularly polarized light. Phys. Rev. Lett. 86, 1187 (2001)
Burnett, K., Reed, V.C., Cooper, J., Knight, P.L.: Calculation of the background emitted during high-harmonic generation. Phys. Rev. A 45, 3347 (1992)
Chen, J., Wang, R., Zhai, Z., Chen, J., Fu, P., Wang, B., Liu, W.: 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)
Chen, J., Wang, K., Long, H., Han, X., Hu, H., Liu, W., Wang, B., Lu, P.: Tungsten disulfide–gold nanohole hybrid metasurfaces for nonlinear metalenses in the visible region. Nano Lett. 18, 1344–1350 (2018)
Ciappina, M.F., Pérez-Hernández, J.A., Landsman, A.S., Okell, W., Zherebtsov, S., Förg, B., Schötz, J., Seiffert, J.L., Fennel, T., Shaaran, T., Zimmermann, T., Chacón, A., Guichard, R., Zaïr, A., Tisch, J.W.G., Marangos, J.P., Witting, T., Braun, A., Maier, S.A., Roso, L., Krüger, M., Hommelhoff, P., Kling, M.F., Krausz, F., Lewenstein, M.: Attosecond physics at the nanoscale. Rep. Prog. Phys. 80, 054401 (2017)
Corkum, P.B.: Plasma perspective on strong field multiphoton ionization. Phys. Rev. Lett. 71, 1994 (1993)
Djotyan, G.P., Bakos, J.S., Sorlei, Zs, Szigeti, J.: Coherent control of atomic quantum states by single frequency-chirped laser pulses. Phys. Rev. A 70, 063406 (2004)
Dorney, K.M., Ellis, J.L., Hernández-García, C., Hickstein, D.D., Mancuso, C.A., Brooks, N., Fan, T., Fan, G., Zusin, D., Gentry, C., Grychtol, P., Kapteyn, H.C., Murnane, M.M.: Helicity-selective enhancement and polarization control of attosecond high harmonic waveforms driven by bichromatic circularly polarized laser fields. Phys. Rev. Lett. 119, 063201 (2017)
Ellis, J.L., Dorney, K.M., Hickstein, D.D., Brooks, N.J., Gentry, C., Hernández-García, C., Zusin, D., Shaw, J.M., Nguyen, Q.L., Mancuso, C.A., Jansen, G.S.M., Witte, S., Kapteyn, H.C., Murnane, M.M.: High harmonics with spatially varying ellipticity. Optica 5, 479–485 (2018)
Fan, T., Grychtol, P., Knut, R., Hernández-García, C., Hickstein, D.D., Zusin, D., Gentry, C., Dollar, F.J., Mancuso, C.A., Hogle, C.W., Kfir, O., Legut, D., Carva, K., Ellis, J.L., Dorney, K.M., Chen, C., Shpyrko, O.G., Fullerton, E.E., Cohen, O., Oppeneer, P.M., Milošević, D.B., Becker, A., Jaroń-Becker, A.A., Popmintchev, T., Murnane, M.M., Kapteyn, H.C.: Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism. Proc. Natl. Acad. Sci. USA 112, 14206–14211 (2015)
Feit, M.D., Fleck, J.A., Steiger, A.: Solution of the Schrödinger equation by a spectral method. J. Comput. Phys. 47, 412–433 (1982)
Feng, L.: Molecular harmonic extension and enhancement from H\(^+_2\) ions in the presence of spatially inhomogeneous fields. Phys. Rev. A 92, 053832 (2015)
Feng, L., Chu, T.: Generation of an isolated sub-40-as pulse using two-color laser pulses: Combined chirp effects. Phys. Rev. A 84, 053853 (2011)
Feng, L., Li, Y., Feng, Y.A.: Nano-plasmonic-pump-probe effect on the intensity enhancement of attosecond pulse from hydrogen molecular ion. Laser Phys. Lett. 15, 115301 (2018)
Ferré, A., Handschin, C., Dumergue, M., Burgy, F., Comby, A., Descamps, D., Fabre, B., Garcia, G.A., Géneaux, R., Merceron, L., Mével, E., Nahon, L., Petit, S., Pons, B., Staedter, D., Weber, S., Ruchon, T., Blanchet, V., Mairesse, Y.: A table-top ultrashort light source in the extreme ultraviolet for circular dichroism experiments. Nat. Photonics 9, 93–98 (2014)
Gaumnitz, T., Jain, A., Pertot, Y., Huppert, M., Jordan, I., Ardana-Lamas, F., Wörner, H.J.: Streaking of 43-attosecond soft-X-ray pulses generated by a passively CEP-stable mid-infrared driver. Opt. Express 25, 27506–27518 (2017)
Ghimire, S., DiChiara, A.D., Sistrunk, E., Agostini, P., DiMauro, L.F., Reis, D.A.: Observation of high-order harmonic generation in a bulk crystal. Nat. Phys. 7, 138–141 (2011)
Goulielmakis, E., Loh, Z.H., Wirth, A., Santra, R., Rohringer, N., Yakovlev, V.S., Zherebtsov, S., Pfeifer, T., Azzeer, A.M., Kling, M.F., Leone, S.R., Krausz, F.: Real-time observation of valence electron motion. Nature 466, 739–743 (2010)
Gui, D., Ji, L., Muhammad, A., Li, W., Cai, W., Li, Y., Li, X., Wu, X., Lu, P.: Jahn-Teller effect on framework flexibility of hybrid organic-inorganic perovskites. J. Phys. Chem. Lett. 9, 751–755 (2018)
He, M., Li, Y., Zhou, Y., Li, M., Cao, W., Lu, P.: Direct visualization of valence electron motion using strong-field photoelectron holography. Phys. Rev. Lett. 120(13), 133204 (2018a)
He, L., Zhang, Q., Lan, P., Cao, W., Zhu, X., Zhai, C., Wang, F., Shi, W., Li, M., Bian, X., Lu, P., Bandrauk, A.D.: Monitoring ultrafast vibrational dynamics of isotopic molecules with frequency modulation of high-order harmonics. Nat. Commun. 9, 1108 (2018b)
He, L., Lan, P., Le, A.-T., Wang, B., Wang, B., Zhu, X., Lu, P., Lin, C.D.: Real-time observation of molecular spinning with angular high-harmonic spectroscopy. Phys. Rev. Lett. 121, 163201 (2018c)
He, Y., He, L., Lan, P., Wang, B., Li, L., Zhu, X., Cao, W., Lu, P.: Molecular rotation movie filmed with high-harmonic generation. arXiv:1902.05662 [physics.optics] (2019)
Hernández-García, C., Durfee, C.G., Hickstein, D.D., Popmintchev, T., Meier, A., Murnane, M.M., Kapteyn, H.C., Sola, I.J., Jaron-Becker, A., Becker, A.: Schemes for generation of isolated attosecond pulses of pure circular polarization. Phys. Rev. A 93, 043855 (2016)
Hickstein, D.D., Dollar, F.J., Grychtol, P., Ellis, J.L., Knut, R., Hernández-García, C., Zusin, D., Gentry, C., Shaw, J.M., Fan, T., Dorney, K.M., Becker, A., Jaroń-Becker, A., Kapteyn, H.C., Murnane, M.M., Durfee, C.G.: Non-collinear generation of angularly isolated circularly polarized high harmonics. Nat. Photonics 9, 743–750 (2015)
Hu, S.X., Collins, L.A.: High-order harmonic generation from intense laser-driven inner electrons of Rydberg atoms. Phys. Rev. A 69, 033405 (2004)
Huang, P.C., Hernández-García, C., Huang, J., Huang, P., Lu, C., Rego, L., Hickstein, D.D., Ellis, J.L., Jaron-Becker, A., Becker, A., Yang, S., Durfee, C.G., Plaja, L., Kapteyn, H.C., Murnane, M.M., Kung, A.H., Chen, M.: Polarization control of isolated high-harmonic pulses. Nat. Photonics 12, 349–354 (2018)
Itatani, J., Levesque, J., Zeidler, D., Niikura, H., Pépin, H., Kieffer, J.C., Corkum, P.B., Villeneuve, D.M.: Tomographic imaging of molecular orbitals. Nature 432, 867–871 (2004)
Jiménez-Galán, Á., Zhavoronkov, N., Schloz, M., Morales, F., Ivanov, M.: Time-resolved high harmonic spectroscopy of dynamical symmetry breaking in bi-circular laser fields: the role of Rydberg states. Opt. Express 25, 22880–22896 (2017)
Kfir, O., Grychtol, P., Turgut, E., Knut, R., Zusin, D., Popmintchev, D., Popmintchev, T., Nembach, H., Shaw, J.M., Fleischer, A., Kapteyn, H., Murnane, M., Cohen, O.: Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics. Nat. Photonics 9, 99–105 (2015)
Kienberger, R., Goulielmakis, E., Uiberacker, M., Baltuska, A., Yakovlev, V., Bammer, F., Scrinzi, A., Westerwalbesloh, Th, Kleineberg, U., Heinzmann, U., Drescher, M., Krausz, F.: Atomic transient recorder. Nature 427, 817–821 (2004)
Kim, S., Jin, J., Kim, Y.J., Park, I.Y., Kim, Y., Kim, S.W.: High-harmonic generation by resonant plasmon field enhancement. Nature 453, 757–760 (2008)
Krausz, F., Ivanov, M.: Attosecond physics. Rev. Mod. Phys. 81, 163–234 (2009)
Krüger, M., Lemell, C., Wachter, G., Burgdörfer, J., Hommelhoff, P.: Attosecond physics phenomena at nanometric tips. J. Phys. B 51, 172001 (2018)
Lan, P., Ruhmann, M., He, L., Zhai, C., Wang, F., Zhu, X., Zhang, Q., Zhou, Y., Li, M., Lein, M., Lu, P.: Attosecond probing of nuclear dynamics with trajectory-resolved high-harmonic spectroscopy. Phys. Rev. Lett. 119, 033201 (2017)
Lewenstein, M., Balcou, P., Ivanov, M.Y., L’Huillier, A., Corkum, P.B.: Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A 49, 2117 (1994)
Li, J., Ren, X., Yin, Y., Zhao, K., Chew, A., Cheng, Y., Cunningham, E., Wang, Y., Hu, S., Wu, Y., Chini, M., Chang, Z.: 53-attosecond X-ray pulses reach the carbon K-edge. Nat. Commun. 8, 186 (2017a)
Li, L., Wang, Z., Li, F., Long, H.: Efficient generation of highly elliptically polarized attosecond pulses. Opt. Quant. Electon. 49(2), 73 (2017b)
Li, L., Lan, P., He, L., Zhu, X., Chen, J., Lu, P.: Scaling law of high harmonic generation in the framework of photon channels. Phys. Rev. Lett. 120(22), 223203 (2018)
Li, L., Lan, P., Zhu, X., Huang, T., Zhang, Q., Lein, M., Lu, P.: Reciprocal-space-trajectory perspective on high harmonic generation in solids. Phys. Rev. Lett. 122(19), 193901 (2019a)
Li, M., Xie, H., Cao, W., Luo, S., Tan, J., Feng, Y., Du, B., Zhang, W., Li, Y., Zhang, Q., Lan, P., Zhou, Y., Lu, P.: Photoelectron holographic interferometry to probe the longitudinal momentum offset at the tunnel exit. Phys. Rev. Lett. 122(18), 183202 (2019b)
Li, J., Zhang, Q., Li, L., Zhu, X., Huang, T., Lan, P., Lu, P.: Orientation dependence of high-order harmonic generation in nanowire. Phys. Rev. A 99(3), 033421 (2019c)
Liu, W., Li, X., Song, Y., Zhang, C., Han, X., Long, H., Wang, B., Wang, K., Lu, P.: Cooperative enhancement of two-photon-absorption-induced photoluminescence from a 2D perovskite-microsphere hybrid dielectric structure. Adv. Funct. Mater. 28, 1707550 (2018)
Liu, K., Luo, S., Li, M., Li, Y., Feng, Y., Du, B., Zhou, Y., Lu, P., Barth, I.: Detecting and characterizing the nonadiabaticity of laser-induced quantum tunneling. Phys. Rev. Lett. 122(5), 053202 (2019a)
Liu, Y., Tan, J., He, M., Xie, H., Qin, Y., Zhao, Y., Li, M., Zhou, Y., Lu, P.: Photoelectron holographic interferences from multiple returning in strong-field tunneling ionization. Opt. Quant. Electron. 51(5), 145 (2019b)
López-Flores, V., Arabski, J., Stamm, C., Halté, V., Pontius, N., Beaurepaire, E., Boeglin, C.: Time-resolved x-ray magnetic circular dichroism study of ultrafast demagnetization in a CoPd ferromagnetic film excited by circularly polarized laser pulse. Phys. Rev. B 86, 014424 (2012)
Luo, S., Li, M., Xie, W., Liu, K., Feng, Y., Du, B., Zhou, Y., Lu, P.: Exit momentum and instantaneous ionization rate of nonadiabatic tunneling ionization in elliptically polarized laser fields. arXiv:1905.06162 [physics.atom-ph] (2019)
Ma, X., Zhou, Y., Chen, Y., Li, M., Li, Y., Zhang, Q., Lu, P.: Timing the release of the correlated electrons in strong-field nonsequential double ionization by circularly polarized two-color laser fields. Opt. Express 27(3), 1825–1837 (2019)
Mauger, F., Bandrauk, A.D., Kamor, A., Uzer, T., Chandre, C.: Quantum-classical correspondence in circularly polarized high harmonic generation. J. Phys. B 47(4), 041001 (2014)
Medišauskas, L., Wragg, J., van der Hart, H., Ivanov, M.Y.: Generating isolated elliptically polarized attosecond pulses using bichromatic counterrotating circularly polarized laser fields. Phys. Rev. Lett. 115, 153001 (2015)
Milošević, D.B.: Generation of elliptically polarized attosecond pulse trains. Opt. Lett. 40, 2381–2384 (2015)
Pfeifer, T., Gallmann, L., Abel, M.J., Nagel, P.M., Neumark, D.M., Leone, S.R.: Heterodyne mixing of laser fields for temporal gating of high-order harmonic generation. Phys. Rev. Lett. 97, 163901 (2006)
Popmintchev, T., Chen, M.C., Popmintchev, D., Arpin, P., Brown, S., Ališauskas, S., Andriukaitis, G., Balčiunas, T., Mücke, O.D., Pugzlys, A., Baltuška, A., Shim, B., Schrauth, S.E., Gaeta, A., Hernández-Garcĺa, C., Plaja, L., Becker, A., Jaron-Becker, A., Murnane, M.M., Kapteyn, H.C.: Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers. Science 336, 1287–1291 (2012)
Qin, Y.N., Li, M., Li, Y., He, M., Luo, S., Liu, Y., Zhou, Y., Lu, P.: Asymmetry of the photoelectron momentum distribution from molecular ionization in elliptically polarized laser pulses. Phys. Rev. A 99(1), 013431 (2019)
Sansone, G., Benedetti, E., Calegari, F., Vozzi, C., Avaldi, L., Flammini, R., Poletto, L., Villoresi, P., Altucci, C., Velotta, R., Stagira, S., Silvestri, S.D., Nisoli, M.: Isolated single-cycle attosecond pulses. Science 314, 443–446 (2006)
Schultze, M., Ramasesha, K., Pemmaraju, C., Sato, S., Whitmore, D., Gandman, A., Prell, J.S., Borja, L., Prendergast, D., Yabana, K., Neumark, D.M., Leone, S.R.: Attosecond band-gap dynamics in silicon. Science 346, 1348–1352 (2014)
Tan, J., Zhou, Y., He, M., Chen, Y., Ke, Q., Liang, J., Zhu, X., Li, M., Lu, P.: Determination of the ionization time using attosecond photoelectron interferometry. Phys. Rev. Lett. 121(25), 253203 (2018)
Tan, J., Zhou, Y., He, M., Ke, Q., Liang, J., Li, Y., Li, M., Lu, P.: Time-resolving tunneling ionization via strong-field photoelectron holography. Phys. Rev. A 99(3), 033402 (2019)
Teichmann, S.M., Silva, F., Cousin, S.L., Hemmer, M., Biegert, J.: 0.5-keV soft x-ray attosecond continua. Nat. Commun. 7, 11493 (2016)
Vampa, G., Hammond, T.J., Thiré, N., Schmidt, B.E., Légaré, F., McDonald, C.R., Brabec, T., Corkum, P.B.: Linking high harmonics from gases and solids. Nature (London) 522, 462–464 (2015)
Wang, Z., He, L., Luo, J., Lan, P., Lu, P.: High-order harmonic generation from Rydberg atoms in inhomogeneous fields. Opt. Express 22, 25909–25922 (2014)
Wang, B., He, L., Yuan, H., Zhang, Q., Lan, P., Lu, P.: Carrier-envelope phase-dependent molecular high-order harmonic generation from H\(^+_2\) in a multi-cycle regime. Opt. Express 26(25), 33440–33452 (2018)
Wang, R., Zhang, Q., Li, D., Xu, S., Cao, P., Zhou, Y., Cao, W., Lu, P.: Identification of tunneling and multiphoton ionization in intermediate Keldysh parameter regime. Opt. Express 27(5), 6471–6482 (2019)
Xie, X., Scrinzi, A., Wickenhauser, M., Baltuška, A., Barth, I., Kitzler, M.: Internal momentum state mapping using high harmonic radiation. Phys. Rev. Lett. 101, 033901 (2008)
Yuan, K.J., Bandrauk, A.D.: Single circularly polarized attosecond pulse generation by intense few cycle elliptically polarized laser pulses and terahertz fields from molecular media. Phys. Rev. Lett. 110, 023003 (2013)
Yuan, H., He, L., Wang, F., Wang, B., Zhu, X., Lan, P., Lu, P.: Tomography of asymmetric molecular orbitals with a one-color inhomogeneous field. Opt. Lett. 43, 931–934 (2018)
Zhai, Z., Chen, J., Yan, Z.C., Fu, P., Wang, B.: 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)
Zhai, Z., Zhu, Q., Chen, J., Yan, Z.C., Fu, P., Wang, B.: High-order harmonic generation with Rydberg atoms by using an intense few-cycle pulse. Phys. Rev. A 83, 043409 (2011)
Zhang, X., Zhu, X., Wang, D., Li, L., Liu, X., Liao, Q., Lan, P., Lu, P.: Ultrafast oscillating-magnetic-field generation based on electronic-current dynamics. Phys. Rev. A 99(1), 013414 (2019)
Zhou, Y., Huang, C., Liao, Q., Lu, P.: Classical simulations including electron correlations for sequential double ionization. Phys. Rev. Lett. 109(5), 053004 (2012)
Acknowledgements
This work was supported by the National Natural Science Foundation of China under Grants No. 11627809, No. 11874165, No. 11704137 and No. 11774109; Fundamental Research Funds for the Central Universities (2017KFXKJC002); Program for HUST Academic Frontier Youth Team. Numerical simulations presented in this paper were carried out using the High Performance Computing experimental testbed in SCTS/CGCL.
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Yuan, H., Wang, F., Zhang, Y. et al. Near-circularly polarized isolated attosecond pulse generation from coherent superposition state by a circularly polarized laser field. Opt Quant Electron 51, 177 (2019). https://doi.org/10.1007/s11082-019-1888-7
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DOI: https://doi.org/10.1007/s11082-019-1888-7