Strong-field control and spectroscopy of attosecond electron-hole dynamics in molecules Olga Smirnovaa,b, Serguei Patchkovskiia, Yann Mairessea,c, Nirit Dudovicha,d, and Misha Yu Ivanova,e,1 aNational Research Council of Canada, 100 Sussex Drive, Ottawa, ON, Canada K1A 0R6; bMax Born Institute, Max Born Strasse 2a, D-12489 Berlin, Germany; cCentre Lasers Intenses et Applications, Universite´Bordeaux I, Unite´Mixte de Recherche 5107 (Centre National de la Recherche Scientifique, Bordeaux 1, CEA), 351 Cours de la Libe´ration, 33405 Talence Cedex, France; dDepartment of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel; and eDepartment of Physics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom Communicated by Stephen E. Harris, Stanford University, Stanford, CA, July 19, 2009 (received for review August 8, 2008) Molecular structures, dynamics and chemical properties are deter- electron from either ⌸ vs. ⌺ or bonding vs. nonbonding orbital. mined by shared electrons in valence shells. We show how one can Increasing laser wavelength ␭ suppresses runaway nonadiabatic selectively remove a valence electron from either ⌸ vs. ⌺ or excitations (19) while keeping ionization channels intact. Con- bonding vs. nonbonding orbital by applying an intense infrared trol over the initial electronic excitation is a gateway to control- laser field to an ensemble of aligned molecules. In molecules, such ling molecular fragmentation that follows. ionization often induces multielectron dynamics on the attosecond Because tunnel ionization can create electronic excitations, time scale. Ionizing laser field also allows one to record and the hole left in a molecule will move on attosecond time-scale reconstruct these dynamics with attosecond temporal and sub- determined by inverse energy spacing between excited electronic Ångstrom spatial resolution. Reconstruction relies on monitoring states, ␶ Ϸប/⌬E. How can one image such motion? Using and controlling high-frequency emission produced when the lib- attosecond probe pulses is problematic: necessarily high carrier erated electron recombines with the valence shell hole created by frequency of such pulses interacts with core rather than valence ionization. electrons. The electron current also does not record hole dy- namics, see below. However, when ionization occurs in a laser high harmonic generation ͉ multielectron dynamics ͉ field, the liberated electron does not immediately leave the strong-field ionization vicinity of the parent ion: Oscillations in the laser electric field can bring the electron back (21). We show how the hole dynamics lectrons in valence molecular shells hold keys to molecular is recorded in the spectrum of the radiation emitted when the Estructures and properties. This article focuses on finding liberated electron recombines with the hole left in the molecule. ways to control and record their dynamics with attosecond (1 asec ϭ 10Ϫ18 sec) temporal resolution. Imaging structures and Results dynamics at different temporal and spatial scales is a major We first consider control of optical tunneling. Consider an direction of modern science that encompasses physics, chemistry example of a CO2 molecule interacting with intense infrared and biology (1). Electrons in atoms, molecules and solids move laser field. The critical factors in strong-field tunnel ionization on attosecond timescale; resolving and controlling their dynam- are the ionization potential Ip and the geometry of the ionizing ics are goals of attosecond and strong-field science (2–6). orbital (22, 23). Removal of an electron, which leaves the ion in A natural route in manipulating valence electrons is to apply an electronic state j, is visualized using the Dyson orbital ⌿D,j ϭ ͌ ͗⌿(NϪ1)⌿(N)͘ ⌿(N) laser pulses with electric fields comparable with the electrostatic N NT . Here, NT is the N-electron wave function of j ⌿(NϪ1) forces binding these electrons in molecules. Combination of the neutral molecule and j describes the ion in the state j. 2 pulse-shaping techniques and adaptive (learning) algorithms Dyson orbitals for the ground state X˜ ⌸g (j ϭ X˜) and the first ˜ 2⌸ ϭ ˜ ˜2⌺ϩ ϭ ˜ (7–16) turn intense ultrashort laser pulses into ‘‘photonic re- two excited states A u (j A) and B u (j B) of the CO2 agents’’ (8), allowing one to steer molecular dynamics toward a molecule are shown in Fig. 1 A and C. Because tunnel ionization desired outcome by tailoring oscillations of the laser electric is exponentially sensitive to Ip, one would expect that only field. Strong-field techniques find applications in controlling ground state of the ion is excited after ionization, i.e., X˜ is the unimolecular reactions (9, 14), nonadiabatic coupling of elec- only participating ionization channel. tronic and nuclear motion (15), suppression of decoherence (16, However, the nodal structure of ⌿D,X˜ (Fig. 1A) suppresses 17), etc. From the fundamental standpoint, one of intriguing ionization for molecules aligned parallel or perpendicular to the challenges lies in understanding and taming the complexity of laser polarization. Indeed, opposite phases of the adjacent lobes strong-field dynamics, where multiple routes to various final in ⌿D,X˜ lead to the destructive interference of the ionization states are open simultaneously and multiple control mechanisms currents for molecular alignment angles around ⌰ϭ0° and ⌰ϭ operate at the same time. 90°, as observed in the experiment (24). Due to the interference Although nuclei in molecules move on the femtosecond time suppression of ionization in the X˜-channel, ionization channels scale, attosecond component of the electronic response often with higher Ip, (e.g., A˜, B˜) become important. For the ion left in plays crucial role (see, e.g., ref. 18). For example, in polyatomic 2 the first excited state A˜ ⌸u (Fig. 1B), the same argument shows molecules electronic excitations in intense infrared laser fields that ionization is suppressed near ⌰ϭ0° but enhanced near ⌰ϭ are created via laser-induced nonadiabatic multielectron (NME) 90°, perpendicular to the molecular axis. In the latter case, there transitions (14, 19, 20). These transitions occur on the sublaser is no destructive interference between the adjacent lobes with cycle time scale and determine femtosecond dynamics that the opposite phases, because only the lobe near the ‘‘down- follows. Although laser-induced NME transitions open multiple excitation channels (14) and lead to molecular breakup into a multitude of fragments (15, 19, 20), in practice, they can be hard Author contributions: O.S. and M.Y.I. designed research; O.S. and S.P. performed research; to control. We show that tunnel ionization in low-frequency laser Y.M. and N.D. analyzed data; and O.S. and M.Y.I. wrote the paper. fields is an alternative way of creating a set of electronic The authors declare no conflict of interest. excitations in the ion, which can be controlled by changing 1To whom correspondence should be addressed. E-mail: [email protected]. molecular alignment relative to laser polarization. The control This article contains supporting information online at www.pnas.org/cgi/content/full/ mechanism uses symmetries of molecular orbitals to remove an 0907434106/DCSupplemental. 16556–16561 ͉ PNAS ͉ September 29, 2009 ͉ vol. 106 ͉ no. 39 www.pnas.org͞cgi͞doi͞10.1073͞pnas.0907434106 Downloaded by guest on September 26, 2021 AB C D Fig. 1. Dyson orbitals corresponding to different ionization channels of CO2.(A) X˜ .(B) A˜ .(C) B˜ . Red and orange correspond to positive and negative lobes. The orbitals are shown at the level of 90% of the electron density. (D) Shown is the degree of control over strong-field ionization amplitudes, as a function of molecular alignment angle ⌰: green and blue curves show control over electron detachment from ⌸ vs. ⌺ orbital, the red curve shows control over electron detachment from bonding (channel A˜ ) vs. nonbonding (channel-X˜ ) orbital. The plotted value is the ionization amplitude (square root of probability) at the peak of the electric field, which is the relevant quantity for the process of harmonic generation discussed later. The laser wavelength is ␭ ϭ 1,140 nm, and the intensity I ϭ 2.2 ϫ 1014 W/cm2. bending’’ part of the ion potential will contribute into ionization. (see Methods). Continuum wave packets ⌽C,X˜(t) and ⌽C,A˜(t) are ˜2⌺ϩ For the ion left in the second excited state B u , the Dyson normalized to unity. Due to the entanglement between the ion orbital (Fig. 1C) shows that ionization is favored along the and the electron (the hole and the electron), the dynamics of the PHYSICS molecular axis. Our calculations (see Methods) confirm these ionic subsystem is undetermined until the measurement of this expectations. Fig. 1D shows the degree of control for the removal dynamics is specified (25, 26). of bonding (channel A˜) vs. nonbonding (channel X˜) electron or Consider first an example of the measurement, which ‘‘pre- for the ionization from ⌸ vs. ⌺ states (A˜ or B˜ channels). The pares’’ the electron wave packet in the ion. One way of obtaining control parameter is the molecular alignment angle ⌰. Although such wave packet is to project the continuum wave packets X˜ channel dominates ionization for all angles, the control is very ⌽C,X˜(t) and ⌽C,A˜(t) on the same continuum state, e.g., the state ⌿(NϪ1) ϭ͗ ˆ⌿(N) ͘ϭ substantial, with the ratio of amplitudes (square roots of ion- having a momentum p at the detector: I (t) p A eI (t) ͗ ⌽ ͘⌿(NϪ1) ϩ ͗ ⌽ ͘⌿(NϪ1) ization probabilities) for various ionization channels changing by aX˜(t) p C,X˜(t) X˜ aA˜(t) p C,A˜(t) A˜ . Here, we have over an order of magnitude. postulated that there is no exchange between the continuum Ionization leaves a hole in the valence shell of the molecule. electron at the detector and the electrons remaining in the ⌿(NϪ1) If several electronic states of the cation are excited, will the hole ion.