^{1}, C. Handschin

^{1}, A. Ferré

^{1}, N. Thiré

^{2}, J. B. Bertrand

^{3}, L. Bonnet

^{4}, R. Cireasa

^{2}, E. Constant

^{1}, P. B. Corkum

^{3}, D. Descamps

^{1}, B. Fabre

^{1}, P. Larregaray

^{4}, E. Mével

^{1}, S. Petit

^{1}, B. Pons

^{1}, D. Staedter

^{2}, H. J. Wörner

^{3}, D. M. Villeneuve

^{3}, Y. Mairesse

^{1,a)}, P. Halvick

^{4,a)}and V. Blanchet

^{2}

### Abstract

We study theoretically and experimentally the electronic relaxation of NO_{2} molecules excited by absorption of one ∼400 nm pump photon. Semiclassical simulations based on trajectory surface hopping calculations are performed. They predict fast oscillations of the electronic character around the intersection of the ground and first excited diabatic states. An experiment based on high-order harmonic transient grating spectroscopy reveals dynamics occurring on the same time scale. A systematic study of the detected transient is conducted to investigate the possible influence of the pump intensity, pump wavelength, and rotational temperature of the molecules. The quantitative agreement between measured and predicted dynamics shows that, in NO_{2}, high harmonic transient grating spectroscopy encodes vibrational dynamics underlying the electronic relaxation.

We acknowledge R. Schinke for providing the PESs used in the TSH calculations. We thank R. Bouillaud and C. Medina for their technical assistance. We acknowledge financial support by the ANR (ANR-08-JCJC-0029 HarMoDyn), the Conseil Regional Aquitaine (20091304003 ATTOMOL and 2.1.3-09010502 COLA2 projects), and the European Union through the MOLCOTUV and ITN-ICONIC contracts.

I. INTRODUCTION

II. SIMULATIONS

A. Background

B. Trajectory surface hopping calculations

III. HIGH HARMONIC TRANSIENT GRATING SPECTROSCOPY

A. Experimental setup

B. Experimental results

IV. INTERPRETATION

V. CONCLUSION

### Key Topics

- Diffraction efficiency
- 18.0
- Surface dynamics
- 15.0
- Electric dipole moments
- 13.0
- Diffraction gratings
- 11.0
- Transient grating spectroscopy
- 11.0

## Figures

Potential energy surfaces of the diabatic fundamental state 1^{2}A^{′} and first excited state 2^{2}A^{′} of NO_{2} as a function of the bending angle and NO stretch distance *R* _{1}. These diabatic states are referred to as 1 and 2 in the text, respectively. The second NO distance *R* _{2} is fixed to 1.19 Å.

Potential energy surfaces of the diabatic fundamental state 1^{2}A^{′} and first excited state 2^{2}A^{′} of NO_{2} as a function of the bending angle and NO stretch distance *R* _{1}. These diabatic states are referred to as 1 and 2 in the text, respectively. The second NO distance *R* _{2} is fixed to 1.19 Å.

Temporal evolution of the *P* _{2} diabatic population calculated with a batch of trajectories starting at the same time (green) or starting at Gaussian random time (red), in the case of a 30 fs pump pulse centered at 400 nm.

Temporal evolution of the *P* _{2} diabatic population calculated with a batch of trajectories starting at the same time (green) or starting at Gaussian random time (red), in the case of a 30 fs pump pulse centered at 400 nm.

Temporal evolution of the ground (blue) and first excited (red) diabatic state populations (a) and average bond angle (b) from TSH calculations, assuming a 100% excitation probability.

Temporal evolution of the ground (blue) and first excited (red) diabatic state populations (a) and average bond angle (b) from TSH calculations, assuming a 100% excitation probability.

Snapshots of the trajectories swarm and contour lines of the diabatic PES. The blue and red dots represent the coordinates of the trajectories on the ground and excited diabatic PESs, respectively. The contour lines are separated by 0.5 eV and the blue contour lines are below or equal to the O+NO dissociation limit. The crossing seam is represented by the thick red line. The PESs are represented as a function of the bending angle and the NO distance *R* _{1}, with the second NO distance *R* _{2} fixed to 1.19 Å. The snapshots are obtained by representing only two coordinates (bending angle and *R* _{1}) and ignoring the third one (*R* _{2}).

Snapshots of the trajectories swarm and contour lines of the diabatic PES. The blue and red dots represent the coordinates of the trajectories on the ground and excited diabatic PESs, respectively. The contour lines are separated by 0.5 eV and the blue contour lines are below or equal to the O+NO dissociation limit. The crossing seam is represented by the thick red line. The PESs are represented as a function of the bending angle and the NO distance *R* _{1}, with the second NO distance *R* _{2} fixed to 1.19 Å. The snapshots are obtained by representing only two coordinates (bending angle and *R* _{1}) and ignoring the third one (*R* _{2}).

Principle of high harmonic transient grating spectroscopy. In the case of one-photon excitation (a), the sinusoidal modulation of the pump intensity in the near field produces a sinusoidal modulation of the harmonic emission, which results in the appearance of first order diffracted light up and down the harmonics in the far field. The far field profile was experimentally recorded by using two pump pulses containing 20 μJ/p, at a pump-probe delay of 100 fs and with a probe pulse polarized orthogonally to the pump pulses. At higher pump intensity (35 μJ/p, (b)), second order diffraction peaks appear in the far field. They can result from two-photon transitions or from the saturation of the one-photon absorption, the two effects leading to anharmonicities of the near-field harmonic spatial modulation.

Principle of high harmonic transient grating spectroscopy. In the case of one-photon excitation (a), the sinusoidal modulation of the pump intensity in the near field produces a sinusoidal modulation of the harmonic emission, which results in the appearance of first order diffracted light up and down the harmonics in the far field. The far field profile was experimentally recorded by using two pump pulses containing 20 μJ/p, at a pump-probe delay of 100 fs and with a probe pulse polarized orthogonally to the pump pulses. At higher pump intensity (35 μJ/p, (b)), second order diffraction peaks appear in the far field. They can result from two-photon transitions or from the saturation of the one-photon absorption, the two effects leading to anharmonicities of the near-field harmonic spatial modulation.

First order diffraction efficiency for H15 as a function of the angle between pump and probe polarizations.

First order diffraction efficiency for H15 as a function of the angle between pump and probe polarizations.

Time dependency of the total harmonic signal (blue) and first order diffraction efficiency (red, multiplied by 20) for harmonics 15 (a), 17 (b), 19 (c), and 21 (d). The pump pulses are 20 μJ each, centered at 400 nm and polarized orthogonally to the probe. The cross correlation signal (panel (a): dots for the experimental points and green line for the Gaussian fit) from harmonic 16 allows an accurate determination of the zero delay.

Time dependency of the total harmonic signal (blue) and first order diffraction efficiency (red, multiplied by 20) for harmonics 15 (a), 17 (b), 19 (c), and 21 (d). The pump pulses are 20 μJ each, centered at 400 nm and polarized orthogonally to the probe. The cross correlation signal (panel (a): dots for the experimental points and green line for the Gaussian fit) from harmonic 16 allows an accurate determination of the zero delay.

Time dependency of the first order (light red) and second order (dark red, multiplied by 10) diffraction efficiency for harmonics 15 (a), 17 (b), 19 (c), and 21 (d). The pump pulses are 35 μJ each, are centered at 400 nm and polarized orthogonally to the probe.

Time dependency of the first order (light red) and second order (dark red, multiplied by 10) diffraction efficiency for harmonics 15 (a), 17 (b), 19 (c), and 21 (d). The pump pulses are 35 μJ each, are centered at 400 nm and polarized orthogonally to the probe.

First order diffraction efficiency in various excitation conditions. (a) Signal obtained using a warm (red) and cold (yellow) molecular beam. (b) Influence of the pump wavelength: 400 nm (red), 395 nm (blue), and 392 nm (purple). The signals are vertically shifted for the sake of clarity.

First order diffraction efficiency in various excitation conditions. (a) Signal obtained using a warm (red) and cold (yellow) molecular beam. (b) Influence of the pump wavelength: 400 nm (red), 395 nm (blue), and 392 nm (purple). The signals are vertically shifted for the sake of clarity.

Evolution of the calculated bending trajectory packet for the diabatic surfaces 1 (a) and 2 (b), in logarithmic scale. (c) Comparison between calculated (dark) and measured (light) high harmonic total signal (blue) and first order diffraction efficiency (red, multiplied by 20) for harmonic 15.

Evolution of the calculated bending trajectory packet for the diabatic surfaces 1 (a) and 2 (b), in logarithmic scale. (c) Comparison between calculated (dark) and measured (light) high harmonic total signal (blue) and first order diffraction efficiency (red, multiplied by 20) for harmonic 15.

Harmonic phase shift Δ*I* _{ p }τ in units of π, as a function of bending angle, for emission from PES 1 (1^{2}A′) (blue) and PES 2 (2^{2}A′)(red). The shaded areas correspond to the main part explored by the trajectories.

Harmonic phase shift Δ*I* _{ p }τ in units of π, as a function of bending angle, for emission from PES 1 (1^{2}A′) (blue) and PES 2 (2^{2}A′)(red). The shaded areas correspond to the main part explored by the trajectories.

Total harmonic signal (blue) and first order diffraction efficiency (red, multiplied by 20) obtained by imposing constant equal populations for the two diabatic states. The black dotted curves are the results of the full calculation.

Total harmonic signal (blue) and first order diffraction efficiency (red, multiplied by 20) obtained by imposing constant equal populations for the two diabatic states. The black dotted curves are the results of the full calculation.

(a) Partial contributions to the diffraction efficiency, considering only the trajectories on surface 1 (*P* _{1}(*t*) = 1, *P* _{2}(*t*) = 0, blue) or surface 2 (*P* _{1}(*t*) = 0, *P* _{2}(*t*) = 1, red). The black dashed line is the result of the full calculation. (b) Normalized diffraction efficiency as a function of the phase modulation Δ*I* _{ p }τ in units of π. The shaded areas correspond to the main part explored by the trajectories.

(a) Partial contributions to the diffraction efficiency, considering only the trajectories on surface 1 (*P* _{1}(*t*) = 1, *P* _{2}(*t*) = 0, blue) or surface 2 (*P* _{1}(*t*) = 0, *P* _{2}(*t*) = 1, red). The black dashed line is the result of the full calculation. (b) Normalized diffraction efficiency as a function of the phase modulation Δ*I* _{ p }τ in units of π. The shaded areas correspond to the main part explored by the trajectories.

Temporal evolution of the calculated trajectory packet on the excited diabatic surface 2 with (a) and without (b) the coupling to the ground state. (c) First order diffraction efficiency induced by the trajectories on surface 2, with (red) and without (blue) the coupling to the ground state. The black dashed line is the result of the full calculation.

Temporal evolution of the calculated trajectory packet on the excited diabatic surface 2 with (a) and without (b) the coupling to the ground state. (c) First order diffraction efficiency induced by the trajectories on surface 2, with (red) and without (blue) the coupling to the ground state. The black dashed line is the result of the full calculation.

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