Abstract

An all-optical measurement of high-order fractional molecular echoes is demonstrated by using high-order harmonic generation (HHG). Excited by a pair of time-delayed short laser pulses, the signatures of full and high order fractional (1/2 and 1/3) alignment echoes are observed in the HHG signals measured from CO$_2$ molecules at various time delays of the probe pulse. By increasing the time delay of the pump pulses, much higher order fractional (1/4) alignment echo is also observed in N$_2$O molecules. With an analytic model based on the impulsive approximation, the spatiotemporal dynamics of the echo process are retrieved from the experiment. Compared to the typical molecular alignment revivals, high-order fractional molecular echoes are demonstrated to dephase more rapidly, which will open a new route towards the ultrashort-time measurement. The proposed HHG method paves an efficient way for accessing the high-order fractional echoes in molecules.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (16)

H. Zhang, B. Lavorel, F. Billard, J.-M. Hartmann, E. Hertz, O. Faucher, J. Ma, J. Wu, E. Gershnabel, Y. Prior, and I. S. Averbukh, “Rotational echoes as a tool for investigating ultrafast collisional dynamics of molecules,” Phys. Rev. Lett. 122(19), 193401 (2019).
[Crossref]

S. Luo, M. Li, W. Xie, K. Liu, Y. Feng, B. Du, Y. Zhou, and P. Lu, “Exit momentum and instantaneous ionization rate of nonadiabatic tunneling ionization in elliptically polarized laser fields,” Phys. Rev. A 99(5), 053422 (2019).
[Crossref]

Y. Zhao, Y. Zhou, J. Liang, Z. Zeng, Q. Ke, Y. Liu, M. Li, and P. Lu, “Frustrated tunneling ionization in the elliptically polarized strong laser fields,” Opt. Express 27(15), 21689 (2019).
[Crossref]

J. Tan, Y. Zhou, M. He, Q. Ke, J. Liang, Y. Li, M. Li, and P. Lu, “Time-resolving tunneling ionization via strong-field photoelectron holography,” Phys. Rev. A 99(3), 033402 (2019).
[Crossref]

C. Zhai, Y. Zhang, and Q. Zhang, “Characterizing the ellipticity of an isolated attosecond pulse,” Opt. Commun. 437(3), 104–109 (2019).

A. Tong, Q. Li, X. Ma, Y. Zhou, and P. Lu, “Internal collision induced strong-field nonsequential double ionization in molecules,” Opt. Express 27(5), 6415 (2019).
[Crossref]

J. Li, Q. Zhang, L. Li, X. Zhu, T. Huang, P. Lan, and P. Lu, “Orientation dependence of high-order harmonic generation in nanowire,” Phys. Rev. A 99(3), 033421 (2019).
[Crossref]

L. Li, P. Lan, X. Zhu, T. Huang, Q. Zhang, M. Lein, and P. Lu, “Reciprocal-space-trajectory perspective on high-harmonic generation in solids,” Phys. Rev. Lett. 122(19), 193901 (2019).
[Crossref]

X. Li, W. Liu, Y. Song, C. Zhang, H. Long, K. Wang, B. Wang, and P. Lu, “Enhancement of the second harmonic generation from WS$_2$2 monolayers by cooperating with dielectric microspheres,” Adv. Opt. Mater. 7(3), 1801270 (2019).
[Crossref]

D. M. Kinyua, H. Long, X. Xing, S. Njoroge, K. Wang, B. Wang, and P. Lu, “Gigahertz acoustic vibrations of Ga-doped ZnO nanoparticle array,” Nanotechnology 30(30), 305201 (2019).
[Crossref]

W. Wei, X. Jiang, L. Dong, W. Liu, X. Han, Y. Qin, K. Li, W. Li, Z. Lin, X. Bu, and P. Lu, “IRegulating second-Harmonic generation by van der Waals interactions in two-dimensional lead halide perovskite nanosheets,” J. Am. Chem. Soc. 141, 9134–9139 (2019).

D. Kinyua, L. Niu, H. Long, K. Wang, and B. Wang, “Tuning the photoinduced charge transfer from CdTe quantum dots to ZnO nanofilms through Ga doping,” Opt. Mater. 96, 109311 (2019).
[Crossref]

G. Hu, X. Hong, K. Wang, J. Wu, H. Xu, W. Zhao, W. Liu, S. Zhang, F. Garcia-Vidal, B. Wang, P. Lu, and C. Qiu, “Coherent steering of nonlinear chiral valley photons with a synthetic Au-WS$_2$2 metasurface,” Nat. Photonics 13(7), 467–472 (2019).
[Crossref]

D. Zhao, S. Ke, Y. Hu, B. Wang, and P. Lu, “Optical bistability of graphene embedded in parity-time-symmetric photonic lattices,” J. Opt. Soc. Am. B 36(7), 1731 (2019).
[Crossref]

Y. He, L. He, P. Lan, B. Wang, L. Li, X. Zhu, W. Cao, and P. Lu, “Direct imaging of molecular rotation with high-order-harmonic generation,” Phys. Rev. A 99(5), 053419 (2019).
[Crossref]

Z. Hong, F. Hu, X. Fu, W. Cao, Q. Zhang, and P. Lu, “Few-cycle 1.9-$\mu$μm pulse generation via collinear spectrum synthesis in multiple-crystal OPA,” Opt. Lett. 44(14), 3438 (2019).
[Crossref]

2018 (5)

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(16), 163201 (2018).
[Crossref]

L. He, Q. Zhang, P. Lan, W. Cao, X. Zhu, C. Zhai, F. Wang, W. Shi, M. Li, X.-B. Bian, and P. Lu, “Monitoring ultrafast vibrational dynamics of isotopic molecules with frequency modulation of high-order harmonics,” Nat. Commun. 9(1), 1108 (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(4), 931 (2018).
[Crossref]

J. Tan, Y. Zhou, M. He, Y. Chen, Q. Ke, J. Liang, X. Zhu, M. Li, and P. Lu, “Determination of the ionization time using attosecond photoelectron interferometry,” Phys. Rev. Lett. 121(18), 253203 (2018).

D. Rosenberg, R. Damari, and S. Fleischer, “Echo spectroscopy in multilevel quantum-mechanical rotors,” Phys. Rev. Lett. 121(23), 234101 (2018).
[Crossref]

2017 (5)

D. Rosenberg, R. Damari, and S. Fleischer, “Rotational echoes: rephasing of centrifugal distortion in laser-induced molecular alignment,” J. Phys. Chem. Lett. 8(20), 5128–5135 (2017).
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Y. Pertot, C. Schmidt, M. Matthews, A. Chauvet, M. Huppert, V. Svoboda, A. V. Conta, A. Tehlar, D. Baykusheva, J.-P. Wolf, and H. J. Wöner, “Time-resolved x-ray absorption spectroscopy with a water window high-harmonic source,” Science 355(6322), 264–267 (2017).
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A. Shalit, S. Ahmed, J. Savolainen, and P. Hamm, “Terahertz echoes reveal the inhomogeneity of aqueous salt solutions,” Nat. Chem. 9(3), 273–278 (2017).
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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(3), 033201 (2017).
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2016 (3)

J. Lu, Y. Zhang, H. Y. Hwang, B. K. Ofori-Okai, S. Fleischer, and K. A. Nelson, “Nonlinear two-dimensional terahertz photon echo and rotational spectroscopy in the gas phase,” Proc. Natl. Acad. Sci. U. S. A. 113(42), 11800–11805 (2016).
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G. Karras, E. Hertz, F. Billard, B. Lavorel, G. Siour, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y. Prior, and I. Sh. Averbukh, “Experimental observation of fractional echoes,” Phys. Rev. A 94(3), 033404 (2016).
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K. Lin, P. Lu, J. Ma, X. Gong, Q. Song, Q. Ji, W. Zhang, H. Zeng, J. Wu, G. Karras, G. Siour, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y. Prior, and I. S. Averbukh, “Echoes in space and time,” Phys. Rev. X 6(4), 041056 (2016).
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2015 (3)

G. Karras, E. Hertz, F. Billard, B. Lavorel, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y. Prior, and I. S. Averbukh, “Orientation and alignment echoes,” Phys. Rev. Lett. 114(15), 153601 (2015).
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M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
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2013 (3)

S. J. Weber, M. Oppermann, and J. P. Marangos, “Role of rotational wave packets in strong field experiments,” Phys. Rev. Lett. 111(26), 263601 (2013).
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M. C. H. Wong, A.-T. Le, A. F. Alharbi, A. E. Boguslavskiy, R. R. Lucchese, J.-P. Brichta, C. D. Lin, and V. R. Bhardwaj, “High harmonic spectroscopy of the cooper minimum in molecules,” Phys. Rev. Lett. 110(3), 033006 (2013).
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J.-M. Hartmann, C. Boulet, T. Vieillard, F. Chaussard, F. Billard, O. Faucher, and B. Lavorel, “Dissipation of alignment in CO$_2$2 gas: A comparison between ab initio predictions and experiments,” J. Chem. Phys. 139(2), 024306 (2013).
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2012 (5)

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(6086), 1287–1291 (2012).
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J. B. Bertrand, H. J. Wörner, P. Hockett, D. M. Villeneuve, and P. B. Corkum, “Revealing the cooper minimum of N$_2$2 by molecular frame high-harmonic spectroscopy,” Phys. Rev. Lett. 109(14), 143001 (2012).
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Z. Zhao, D. Wang, J. Chen, Z. Chen, H. Deng, J. Ding, C. Feng, Q. Gu, M. Huang, T. Lan, Y. Leng, D. Li, G. Lin, B. Liu, E. Prat, X. Wang, Z. Wang, K. Ye, L. Yu, H. Zhang, J. Zhang, M. Zhang, M. Zhang, T. Zhang, S. Zhong, and Q. Zhou, “First lasing of an echo-enabled harmonic generation free-electron laser,” Nat. Photonics 6(6), 360–363 (2012).
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2011 (2)

K. Yoshii, G. Miyaji, and K. Miyazaki, “Retrieving angular distributions of high-order harmonic generation from a single molecule,” Phys. Rev. Lett. 106(1), 013904 (2011).
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S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
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2010 (3)

C. D. Lin, A. T. Le, Z. Chen, T. Morishita, and R. Lucchese, “Strong-field rescattering physics–self-imaging of a molecule by its own electrons,” J. Phys. B 43(12), 122001 (2010).
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H. J. Wörner, J. B. Bertrand, P. Hockett, P. B. Corkum, and D. M. Villeneuve, “Controlling the interference of multiple molecular orbitals in high-harmonic generation,” Phys. Rev. Lett. 104(23), 233904 (2010).
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D. Xiang, E. Colby, M. Dunning, S. Gilevich, C. Hast, K. Jobe, D. McCormick, J. Nelson, T. O. Raubenheimer, K. Soong, G. Stupakov, Z. Szalata, D. Walz, S. Weathersby, and M. Woodley, “Demonstration of the echo-enabled harmonic generation technique for short-wavelength seeded free electron lasers,” Phys. Rev. Lett. 105(11), 114801 (2010).
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2009 (6)

G. Stupakov, “Using the beam-echo effect for generation of short-wavelength radiation,” Phys. Rev. Lett. 102(7), 074801 (2009).
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O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, and M. Ivanov, “High harmonic interferometry of multi-electron dynamics in molecules,” Nature 460(7258), 972–977 (2009).
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2008 (1)

W. Li, X. Zhou, R. Lock, S. Patchkovskii, A. Stolow, H. C. Kapteyn, and M. M. Murnan, “Time-resolved dynamics in $\textrm{N}_2 \textrm{O}_4$N2O4 probed using high harmonic generation,” Science 322(5905), 1207–1211 (2008).
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2007 (3)

S. Ramakrishna and T. Seideman, “Information content of high harmonics generated from aligned molecules,” Phys. Rev. Lett. 99(11), 113901 (2007).
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F. H. M. Faisal, A. Abdurrouf, K. Miyazaki, and G. Miyaji, “Origin of anomalous spectra of dynamic alignments observed in N$_2$2 and O$_2$2,” Phys. Rev. Lett. 98(14), 143001 (2007).
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S. Park, K. Kwak, and M. D. Fayer, “Ultrafast 2D-IR vibrational echo spectroscopy: a probe of molecular dynamics,” Laser Phys. Lett. 4(10), 704–718 (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(5772), 424–427 (2006).
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2005 (1)

T. Meunier, S. Gleyzes, P. Maioli, A. Auffeves, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Rabi oscillations revival induced by time reversal: a test of mesoscopic quantum coherence,” Phys. Rev. Lett. 94(1), 010401 (2005).
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2004 (1)

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 432(7019), 867–871 (2004).
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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(5584), 1144–1148 (2002).
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X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A 66(3), 033402 (2002).
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2001 (1)

K. A. Merchant, D. E. Thompson, and M. D. Fayer, “Two-dimensional time-frequency ultrafast infrared vibrational echo spectroscopy,” Phys. Rev. Lett. 86(17), 3899–3902 (2001).
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1998 (2)

J. D. Hybl, A. W. Albrecht, S. M. G. Faeder, and D. M. Jonas, “Two-dimensional electronic spectroscopy,” Chem. Phys. Lett. 297(3-4), 307–313 (1998).
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1996 (1)

L. K. Spentzouris, J.-F. Ostiguy, and P. L. Colestock, “Direct measurement of diffusion rates in high energy synchrotrons using longitudinal beam echoes,” Phys. Rev. Lett. 76(4), 620–623 (1996).
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1994 (1)

M. Lewenstein, P. Balcou, M. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
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1993 (2)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
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1982 (1)

R. R. Lucchese, G. Raseev, and V. McKoy, “Studies of differential and total photoionization cross sections of molecular nitrogen,” Phys. Rev. A 25(5), 2572–2587 (1982).
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1971 (1)

R. Damadian, “Tumor detection by nuclear magnetic resonance,” Science 171(3976), 1151–1153 (1971).
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1967 (1)

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1965 (2)

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1964 (1)

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1950 (1)

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Abdurrouf, A.

F. H. M. Faisal, A. Abdurrouf, K. Miyazaki, and G. Miyaji, “Origin of anomalous spectra of dynamic alignments observed in N$_2$2 and O$_2$2,” Phys. Rev. Lett. 98(14), 143001 (2007).
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N. A. Kurnit, I. D. Abella, and S. R. Hartmann, “Observation of a photon echo,” Phys. Rev. Lett. 13(19), 567–568 (1964).
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Ahmed, S.

A. Shalit, S. Ahmed, J. Savolainen, and P. Hamm, “Terahertz echoes reveal the inhomogeneity of aqueous salt solutions,” Nat. Chem. 9(3), 273–278 (2017).
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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(6086), 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(6086), 1287–1291 (2012).
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M. Herrera, T. M. Antonsen, E. Ott, and S. Fishman, “Echoes and revival echoes in systems of anharmonically confined atoms,” Phys. Rev. A 86(2), 023613 (2012).
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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 from mid-infrared femtosecond lasers,” Science 336(6086), 1287–1291 (2012).
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T. Meunier, S. Gleyzes, P. Maioli, A. Auffeves, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Rabi oscillations revival induced by time reversal: a test of mesoscopic quantum coherence,” Phys. Rev. Lett. 94(1), 010401 (2005).
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Averbukh, I. S.

H. Zhang, B. Lavorel, F. Billard, J.-M. Hartmann, E. Hertz, O. Faucher, J. Ma, J. Wu, E. Gershnabel, Y. Prior, and I. S. Averbukh, “Rotational echoes as a tool for investigating ultrafast collisional dynamics of molecules,” Phys. Rev. Lett. 122(19), 193401 (2019).
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G. Karras, E. Hertz, F. Billard, B. Lavorel, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y. Prior, and I. S. Averbukh, “Orientation and alignment echoes,” Phys. Rev. Lett. 114(15), 153601 (2015).
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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(5772), 424–427 (2006).
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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 from mid-infrared femtosecond lasers,” Science 336(6086), 1287–1291 (2012).
[Crossref]

Balcou, P.

M. Lewenstein, P. Balcou, M. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
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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 from mid-infrared femtosecond lasers,” Science 336(6086), 1287–1291 (2012).
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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(6262), 790–795 (2015).
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Baykusheva, D.

Y. Pertot, C. Schmidt, M. Matthews, A. Chauvet, M. Huppert, V. Svoboda, A. V. Conta, A. Tehlar, D. Baykusheva, J.-P. Wolf, and H. J. Wöner, “Time-resolved x-ray absorption spectroscopy with a water window high-harmonic source,” Science 355(6322), 264–267 (2017).
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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(6262), 790–795 (2015).
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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(6086), 1287–1291 (2012).
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Bertrand, J. B.

J. B. Bertrand, H. J. Wörner, P. Hockett, D. M. Villeneuve, and P. B. Corkum, “Revealing the cooper minimum of N$_2$2 by molecular frame high-harmonic spectroscopy,” Phys. Rev. Lett. 109(14), 143001 (2012).
[Crossref]

H. J. Wörner, J. B. Bertrand, P. Hockett, P. B. Corkum, and D. M. Villeneuve, “Controlling the interference of multiple molecular orbitals in high-harmonic generation,” Phys. Rev. Lett. 104(23), 233904 (2010).
[Crossref]

Bhardwaj, V. R.

M. C. H. Wong, A.-T. Le, A. F. Alharbi, A. E. Boguslavskiy, R. R. Lucchese, J.-P. Brichta, C. D. Lin, and V. R. Bhardwaj, “High harmonic spectroscopy of the cooper minimum in molecules,” Phys. Rev. Lett. 110(3), 033006 (2013).
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L. He, Q. Zhang, P. Lan, W. Cao, X. Zhu, C. Zhai, F. Wang, W. Shi, M. Li, X.-B. Bian, and P. Lu, “Monitoring ultrafast vibrational dynamics of isotopic molecules with frequency modulation of high-order harmonics,” Nat. Commun. 9(1), 1108 (2018).
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H. Zhang, B. Lavorel, F. Billard, J.-M. Hartmann, E. Hertz, O. Faucher, J. Ma, J. Wu, E. Gershnabel, Y. Prior, and I. S. Averbukh, “Rotational echoes as a tool for investigating ultrafast collisional dynamics of molecules,” Phys. Rev. Lett. 122(19), 193401 (2019).
[Crossref]

G. Karras, E. Hertz, F. Billard, B. Lavorel, G. Siour, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y. Prior, and I. Sh. Averbukh, “Experimental observation of fractional echoes,” Phys. Rev. A 94(3), 033404 (2016).
[Crossref]

G. Karras, E. Hertz, F. Billard, B. Lavorel, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y. Prior, and I. S. Averbukh, “Orientation and alignment echoes,” Phys. Rev. Lett. 114(15), 153601 (2015).
[Crossref]

J.-M. Hartmann, C. Boulet, T. Vieillard, F. Chaussard, F. Billard, O. Faucher, and B. Lavorel, “Dissipation of alignment in CO$_2$2 gas: A comparison between ab initio predictions and experiments,” J. Chem. Phys. 139(2), 024306 (2013).
[Crossref]

Boguslavskiy, A. E.

M. C. H. Wong, A.-T. Le, A. F. Alharbi, A. E. Boguslavskiy, R. R. Lucchese, J.-P. Brichta, C. D. Lin, and V. R. Bhardwaj, “High harmonic spectroscopy of the cooper minimum in molecules,” Phys. Rev. Lett. 110(3), 033006 (2013).
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Boulet, C.

J.-M. Hartmann, C. Boulet, T. Vieillard, F. Chaussard, F. Billard, O. Faucher, and B. Lavorel, “Dissipation of alignment in CO$_2$2 gas: A comparison between ab initio predictions and experiments,” J. Chem. Phys. 139(2), 024306 (2013).
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Brichta, J.-P.

M. C. H. Wong, A.-T. Le, A. F. Alharbi, A. E. Boguslavskiy, R. R. Lucchese, J.-P. Brichta, C. D. Lin, and V. R. Bhardwaj, “High harmonic spectroscopy of the cooper minimum in molecules,” Phys. Rev. Lett. 110(3), 033006 (2013).
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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 from mid-infrared femtosecond lasers,” Science 336(6086), 1287–1291 (2012).
[Crossref]

Brune, M.

T. Meunier, S. Gleyzes, P. Maioli, A. Auffeves, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Rabi oscillations revival induced by time reversal: a test of mesoscopic quantum coherence,” Phys. Rev. Lett. 94(1), 010401 (2005).
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Figures (4)

Fig. 1.
Fig. 1. Experiment setup of harmonic generation from molecular ensemble excited by a pair of time-delayed laser pulses.
Fig. 2.
Fig. 2. Measured time-dependent harmonic signals from the CO$_2$ molecules excited by pump P$_1$ and P$_2$ (blue squares with dashed line). For comparison, the results from the molecules excited by P$_1$ alone are also presented (red circles with dotted line). The dashed rectangles show the locations of the full, 1/2, and 1/3 echoes. Shaded areas represent the standard deviation of five independent measurements. Blue solid and black dashed lines are the simulated results with the optimized laser intensities of P$_1$ and P$_2$.
Fig. 3.
Fig. 3. (a) The time-dependent angular distribution of molecular rotational wavepacket of CO$_2$ molecule simulated with the optimal intensities of P$_1$ and P$_2$ (I$_1$=4$\times 10^{13}$W/cm$^2$ and I$_2$=1.5$\times 10^{13}$W/cm$^2$). (b)–(c) Polar plots of the angular distributions of full echo at t=8.7 ps (in the left column) and t=9.2 ps (in the right column). (d)–(e) Same as (b)–(c), but for 1/2 echo at t=7.3 ps and t=7.6 ps. (f)–(g) Same as (b)–(c), but for 1/3 echo at t=6.6 ps and t=6.8 ps.
Fig. 4.
Fig. 4. (a) Measured time-dependent harmonic signals (H25) from the N$_2$O molecules excited by pump P$_1$ and P$_2$ (blue squares with dashed line). For comparison, the results from the molecules excited by P$_1$ alone are also presented (red circles with dotted line). The dashed rectangles show the locations of the 1/3 and 1/4 echoes. Shaded areas represent the standard deviation of five independent measurements. Blue solid and black dashed lines are the simulated results with the optimized laser intensities of P$_1$ and P$_2$. (b) Same as (a), but for the results measured at the half quantum revival.

Equations (6)

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S ( α , t ) = | ϕ = 0 2 π θ = 0 π D q ( θ ) ρ ( θ , ϕ , t ) s i n θ d θ d ϕ | 2 .
Ψ J M = e i P 1 c o s 2 θ Ψ J M 0 .
Ψ J M ( θ , ϕ , t ) = Σ J C J M , J M e i E J t Y J M ( θ , ϕ ) .
Ψ J M = e i P 2 c o s 2 θ Ψ J M ( θ , ϕ , Δ t ) .
Ψ J M ( θ , ϕ , t ) = Σ J M C J M , J M e i E J ( t Δ t ) Y J M ( θ , ϕ ) .
ρ ( θ , ϕ , t ) = Σ J M Γ J M | Ψ J M ( θ , ϕ , t ) | 2 .

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