The study of chemical reactions on the molecular (femtosecond) timescale typically uses pump laser pulses to excite molecules and subsequent probe pulses to interrogate them. The ultrashort pump pulse can excite only a small fraction of molecules, and the probe wavelength must be carefully chosen to discriminate between excited and unexcited molecules. The past decade has seen the emergence of new methods that are also aimed at imaging chemical reactions as they occur, based on X-ray diffraction1, electron diffraction2 or laser-induced recollision3, 4—with spectral selection not available for any of these new methods. Here we show that in the case of high-harmonic spectroscopy based on recollision, this apparent limitation becomes a major advantage owing to the coherent nature of the attosecond high-harmonic pulse generation. The coherence allows the unexcited molecules to act as local oscillators against which the dynamics are observed, so a transient grating technique5, 6 can be used to reconstruct the amplitude and phase of emission from the excited molecules. We then extract structural information from the amplitude, which encodes the internuclear separation, by quantum interference at short times and by scattering of the recollision electron at longer times. The phase records the attosecond dynamics of the electrons, giving access to the evolving ionization potentials and the electronic structure of the transient molecule. In our experiment, we are able to document a temporal shift of the high-harmonic field of less than an attosecond (1 as = 10−18 s) between the stretched and compressed geometry of weakly vibrationally excited Br2 in the electronic ground state. The ability to probe structural and electronic features, combined with high time resolution, make high-harmonic spectroscopy ideally suited to measuring coupled electronic and nuclear dynamics occurring in photochemical reactions and to characterizing the electronic structure of transition states.
Figures at a glance
Figure 1: High-harmonic interferometry of dissociating Br2. 
a, Potential energy curves of the ground and excited (C 1Π1u) state of Br2 (black and blue lines, respectively) and the lowest electronic states of Br2+ (red lines) as a function of the internuclear separation, R. Also shown (thicker lines) are the ground-state nuclear wavefunction (black) and the calculated excited-state wave packet (blue) at selected delays Δt following a 40-fs excitation pulse centred at 400 nm. b, Starting from the electronic ground state of Br2, a small fraction of the sample is excited and undergoes dissociation. An intense 30-fs 800-nm pulse (red) probes the dissociation dynamics at variable delays after excitation. The two electronic states, represented by their most weakly bound orbital, emit high harmonics (turquoise) that differ in amplitude and in phase (Δϕ).
Figure 2: High-harmonic transient grating spectroscopy. 
a, Two synchronized excitation pulses (400 nm) set up a transient grating of excitation in the molecular beam. A delayed 800-nm pulse generates high harmonics from the excited sample. The periodic modulation of the high-harmonic amplitude and phase in the near field (in the laser focus) results, in the far field (at the detector), in additional first-order diffraction (m = 1) signal. b, c, Evolution of the normalized intensities of harmonics 13 to 21 for parallel pump and probe polarizations in the zeroth order (b) and the first-order diffraction side band (c) with pump–probe delay. All signals have been normalized to the signal in the zeroth order at negative time delays, corresponding to molecules in the ground electronic state only.
Figure 3: Reconstruction of high-harmonic phases and amplitudes. 
a, b, Reconstructed amplitudes (middle) and phases (right) of the excited state relative to the ground state for parallel (a) and perpendicular (b) polarizations of the 400-nm excitation pulse relative to the 800-nm generating pulse. As the C ← X transition in Br2 is perpendicular, the tunnel-ionized electron wave packet will follow a recolliding trajectory mostly perpendicular to the disk of excited molecules in a and parallel to it in b, as shown in the left column. In the insets of a and b (middle), the curves have been shifted vertically to show that the minimum occurs at different delays for different harmonic orders. c, Measured internuclear separation (R) as determined by the two-centre interference condition (illustrated on the left) of the dissociating molecule for each harmonic order q (error bars, s.d.). λq represents the de Broglie wavelength of the electron.
Figure 4: Vibration-induced modulation of the high-harmonic phase. 
Reconstructed relative phases of harmonics 13 to 21 in an experiment similar to that shown in Fig. 3a but at higher intensity of the 400-nm excitation pulses. The fast transient in the first 200 fs measures the dissociation of the excited state. The subsequent modulation with a period of 100 fs measures the variation of the phase of the vibrating ground-state molecules relative to that of the atoms generated in the photo-dissociation process.
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