High-Order Harmonic Transient Grating Spectroscopy in a Molecular Jet Y. Mairesse, 1,2 D. Zeidler, 1,3 N. Dudovich, 1,4 M. Spanner, 5 J. Levesque, 1 D. M. Villeneuve, 1 and P. B. Corkum 1 1 National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada 2 Centre Lasers Intenses et Applications, Universite ´ Bordeaux I, UMR 5107 (CNRS, Bordeaux 1, CEA), 351 Cours de la Libe ´ration, 33405 Talence Cedex, France 3 Carl Zeiss SMT AG, D-73447 Oberkochen, Germany 4 Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel 5 Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, M5S 3H6 Canada (Received 11 May 2007; revised manuscript received 2 October 2007; published 11 April 2008) We study high-order harmonic generation in excited media using a four-wave-mixing-like configura- tion. We analyze the spatial profile of high harmonics emitted by a grating of rotationally excited molecules as a function of the pump-probe delay. We demonstrate a dramatic improvement in the contrast of the diffracted signal relative to the total high harmonic signal. This allows us to observe subtle effects in the rotational wave packet excitation such as the pump-intensity dependence of the wave packet dynamics. High harmonic transient grating spectroscopy can be extended to all forms of molecular excitation and to weak resonant excitation. DOI: 10.1103/PhysRevLett.100.143903 PACS numbers: 42.65.Ky, 33.15.Mt, 33.80.Rv Transient grating spectroscopy (TGS) is the method of choice for measuring femtosecond dynamics in solids, liquids, or gases whenever background suppression is im- portant [1,2]. In TGS, temporal information about the low- order nonlinear light-matter interaction is mapped into the spatial domain where it can be observed against a zero background. Thus, TGS allows measurements where only a small fraction of the molecules are excited, as the dif- fracted signal only arises from exactly this fraction. If we could extend TGS from perturbative nonlinear optics to nonperturbative nonlinear optics, then it could be applied in high harmonic generation (HHG) experi- ments. This would be important since the harmonic signal encodes structural information on the orbital which can be used to perform a full reconstruction of an orbital [3]. It would benefit any measurement where a modification of the orbital, resulting from a rotational [4 – 6], vibrational [7– 9], electronic [10,11], or photochemical excitation, is measured. We show that TGS can be applied where the probe pulse is intense enough to create high harmonics or attosecond pulses. We use two beams to create a grating of molecular excitation and a third beam to generate high-order har- monic radiation. The pump and probe beams do not tem- porally overlap, and the excitation and harmonic generation processes are thus decoupled. We study the case of rotational wave packets in N 2 molecules because their behavior is so well understood that we are able to critically examine the applicability of strong field TGS. We compare the total harmonic signal with the transient grat- ing signal measured from the far-field spatial profile. We obtain a contrast enhancement from the transient grating signal with respect to the total signal that reaches 300:1. Our sensitivity allows us to observe that the second order diffraction peak revives at a different time than the first order peak and that the full and half revivals are not exactly time reversed. These are two subtle effects of strongly excited rotational wave packets. Transient grating spectroscopy is a special case of non- linear space-time coupling. It will be clear from our results that space-time coupling can be used in strong field and attosecond science, in much the same way that it is used in perturbative nonlinear optics. Rotational wave packets can be created in molecules by focusing an intense laser pulse in a gas jet [12,13]. A superposition of rotational states is then excited, leading to the appearance of a periodic structure in the dynamics of the molecular alignment distribution. The periodicity of these revivals is equal to the rotational period of the considered molecule. Many studies of the rotational wave packet dynamics have been carried out, showing that molecules are aligned parallel to the pump laser polariza- tion slightly after the revival time and antialigned (i.e., contained in a plane perpendicular to the pump polariza- tion) slightly before [14]. Around the half-revival time, a similar (but reversed) evolution exists: molecules are first aligned, then antialigned. In addition to this transient align- ment evolution, a permanent ‘‘incoherent alignment’’ is created by the pump pulse: the alignment distribution is slightly peaked along the laser polarization even off the revivals [14]. Since HHG results from the interference of an electron wave packet driven by the laser field and the molecular orbital [15,16], it is sensitive to the alignment of the molecule with respect to the laser polarization. Several experimental studies of the harmonic emission in rotation- ally excited molecules have revealed different behaviors for different molecular species [4,5]. We focus on N 2 , for PRL 100, 143903 (2008) PHYSICAL REVIEW LETTERS week ending 11 APRIL 2008 0031-9007= 08=100(14)=143903(4) 143903-1  2008 The American Physical Society