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Spectroscopie moléculaire harmonique ultrarapide: accès aux structures et dynamiques moléculaires P. Salières Service des Photons, Atomes et Molécules CEA-Saclay La génération d harmoniques: spectroscopie

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Spectroscopie moléculaire harmonique ultrarapide: accès aux structures et dynamiques moléculaires P. Salières Service des Photons, Atomes et Molécules CEA-Saclay La génération d harmoniques: spectroscopie optique très NL Paquet d ondes électronique (chirpé): attoseconde R E Energie E q = 35 ev λ e 2Å R θ Photon émis: Energie E q ~5 ev Le paquet d ondes électronique peut sonder l orbitale moléculaire et encoder l information dans l émission harmonique Sonde de la structure moléculaire Sonde de la dynamique moléculaire vibrationelle rotationelle electronique Source d émission attoseconde λ q = hc E Itatani et al., Nature 432, 867 (24) Haessler et al., Nature Physics 6, 2 (21) Baker et al., Science 312, 424 (26) Wagner et al., PNAS 13, (26) Miyazaki et al., PRL 95, (25) Smirnova et al., Nature 46, 972 (29) q ~ 25nm Vozzi et al., Nature Physics 7, 822 (21) Boutu et al., Nature Physics 4, 545 (28) Harmonic signal D( ω, θ) = γ ( k) a ( k) d ( k) q Information encoded in the attosecond emission ion prop rec Complex amplitude of the free electron wave = ionization and continuum electron dynamics d rec ( k) Ψ r Ψ ( k) = Recombination dipole moment = molecular orbital structure c Harmonic signal D( ω, θ) = γ ( k) a ( k) d ( k) q Information encoded in the attosecond emission j ion prop rec Complex amplitude of the free electron wave = ionization and continuum electron dynamics d rec ( k) Ψ r Ψ ( k) = Recombination dipole moment = molecular orbital structure c j: multiple electron trajectories, multiple contributing orbitals = multi-channel dynamics Harmonic signal D( ω, θ, R) = γ ( k, R) a ( k) d ( k, R) q Information encoded in the attosecond emission j ion prop rec Complex amplitude of the free electron wave = ionization and continuum electron dynamics d rec ( k) Ψ r Ψ ( k) = Recombination dipole moment = molecular orbital structure c j: multiple electron trajectories, multiple contributing orbitals = multi-channel dynamics Strong influence of internuclear distance = nuclear configuration Attosecond nuclear dynamics during HHG H 2 / D 2 χ + ( τ q ) χ Nuclear autocorrelation function: C ( τ q ) = χ χ + ( τ q ) PACER Baker, Science 26 Harmonic signal Information encoded in the attosecond emission D ω q, θ, R) = γ ion( k, R) aprop( k) drec( k, R) χ ( R) χ+ ( R, τ ) ( q j Complex amplitude of the free electron wave = ionization and continuum electron dynamics d rec ( k) Ψ r Ψ ( k) = Recombination dipole moment = molecular orbital structure c j: multiple electron trajectories, multiple contributing orbitals = multi-channel dynamics Strong influence of internuclear distance = nuclear configuration and dynamics Probing proton dynamics in molecules on an attosecond time scale S. Baker, and J. P. Marangos, Science 312, 424 (26). The different harmonics probe the ion dynamics at different times Calibration of H 2 by D 2 possible reconstruction of the ion dynamics Harmonic signal Information encoded in the attosecond emission D ω q, θ, R) = γ ion( k, R) aprop( k) drec( k, R) χ ( R) χ+ ( R, τ ) ( q j Complex amplitude of the free electron wave = ionization and continuum electron dynamics d rec ( k) Ψ r Ψ ( k) = Recombination dipole moment = molecular orbital structure c j: multiple electron trajectories, multiple contributing orbitals = multi-channel dynamics Strong influence of internuclear distance = nuclear configuration and dynamics Outline I- Experimental techniques II- Structural interference in HHG - Continuum electron dynamics - Dipole extraction: molecular orbital tomography - Nuclear dynamics III- Dynamical interference in HHG - Multi-channel dynamics - Hole dynamics Alignement des molécules par laser Anisotropie de polarisabilité H ( θ ) α 2cos2 θ int 1 θ 2 α ε θ Le champ induit un dipôle couple de rotation Alignement transitoire des molécules par laser bref Alignement transitoire créé par un pulse laser de 5 fs, Wcm -2 Interaction Laser J, M, E = B J( J + 1) J Couplage Raman des états rotationnels J =, ± 2 M = Paquet cohérent d ondes rotationnelles: M Ψ ( t) = A ( t) J, M Ψ = J, M qui se rephase périodiquement J Alignement transitoire dit non-adiabatique N 2 Rosca-Pruna et al. PRL 87, (21) Alignement des molécules Simuls: S. Weber ( ) Ψθ, t 2 stat Jet supersonique (T 1K) t Génération Alignement 1 13 W/cm 2 - Intensity Characterization of the High-Harmonic emission - Phase: function of harmonic order = quantum interferometry (RABBIT) function of angle = optical interferometry 2-source interferometry Smirnova et al. Nature 29 - Polarization Transient-grating spectroscopy Mairesse et al. PRL 28 Measurement of the Harmonic relative phase: RABBIT Piezoelectric translation τ ~1as Laser Pulse 8 nm, 5 fs, 2 Hz up to 5mJ Generating gas jet Broadband toroidal mirror Target gas jet Diaphragm e - E DELAY LINE IR Time of flight spectrometer IR 2-photon XUV+IR photoionization = «sidebands» H q H q+2 S q+1 =C+A cos(2ωτ + Φ q Φ q+2 + φ at ) Photoelectron Spectrum Sideband amplitude oscillations Paul et al, Science 292, 1689 (21) Véniard et al., Phys. Rev. A 54, 721 (1996) Outline I- Experimental techniques II- Structural interference in HHG - Continuum electron dynamics - Dipole extraction: molecular orbital tomography - Nuclear dynamics III- Dynamical interference in HHG - Multi-channel dynamics - Hole dynamics Continuum electron dynamics D( ω, θ) = γ ( k) a ( k) d ( k) q ion prop rec t e (as) Argon t e Φ Φq+ Φ ω 2ω ( q + 1) = ( q + 1) Linear group delay 2 q 12 Phase (rad) Harmonic order Harmonic order,1,1 1E-3 Linear chirp : the atto-chirp Intensity (arb. unit) Different harmonic orders different traj. different recollision times Mairesse et al., Science (23) Extracting the N 2 recombination dipole moment Emission time [as] D( ω, θ) = γ ( k) a ( k) d ( k) q Argon N 2 ion prop rec mainly determined by I p and laser parameters I p (N 2 )=15.6 ev I p (Ar)=15.76 ev Group delay Phase difference N 2 - Ar (π rad) 1,,8,6,4,2 D N D ( ω ) q θ ( ω ) 2, Ar q = d d rec N rec Ar N2 N2 4 N2 8 N2 1 N2 5 N2 9 N2 2 N2 6 N2 3 N2 7 2 ( k ) ( k ) Haessler et al., Nature Physics 6, 2 (21) Phase difference N 2 - Ar Harmonic order, Harmonic order d rec k ( ) = Direct access to the spectral phase of (not accessible by PI) N 2 Quantum interference in recombination process M. Lein et al. Phys. Rev. A (22) 2 center-interference model R E θ symmetric combination: Emission from the 2 centers is dephased: 1) additional path length= R cos θ 2) symmetry of the orbital Ψ ( r - R 2) + Φ ( r + 2) Φ R Destructive interference for antisymmetric combination: Ψ Destructive interference for R cosθ = λ ( r - R 2) Φ ( r + 2) Φ R e R cosθ = λ e 2 More generally: = sign changes accross characteristic spatial frequencies of the orbital Structural interference in the Plane-Wave dipole N 2 HOMO (HF) PW dipole // laser field Cohen-Fano interferences = of the dipole = change of sign + - Molecular dipole contains Structural information Principles of orbital tomographic imaging k Plane wave recombination dipole: Ψ r rr ikr = Ψ r e ( ) r e rr ik d r determined by recombination angle θ and Spatial Fourier transform of Ψ r k y 2 hk q hω = + 2 m Each order is associated to a spatial frequency of the orbital I p θ FT θθ k x Real Space Itatani et al., Nature (24) Fourier Space Crucial role of the phase in the reconstruction Experiment: N 2 : Molecular Orbital Tomography: HOMO Imaginary part of experimental dipole + symmetry of HOMO H17 positive - H31 negative Filtered Hartree simulations: Fock HOMOH17-H31 Good reconstruction, mainly limited by accessible spectral range! Haessler et al. Nature Physics 21 Playing around with the phases! All phases set to = only amplitudes used for the reconstruction The phase of the dipole is THE crucial element for the reconstruction Outline I- Experimental techniques II- Structural interference in HHG - Continuum electron dynamics - Dipole extraction: molecular orbital tomography - Nuclear dynamics III- Dynamical interference in HHG - Multi-channel dynamics - Hole dynamics Φ ( I L ) E τ q ( I L ) Harmonic signal D( ω, θ) = γ ( k) a ( k) d ( k) q Dynamic orbital imaging: snapshots of hole dynamics j ion prop j: multiple contributing orbitals ; ; rec 5 Energy (ev) % & '( *+, HOMO HOMO N 2 A 2 Π u X 2 + Σ g N 2 X 1 + Σ g 1 2 R(N-N) (Å) 4 4 Y (u.a.) 2-2 t fs Ionization t 1,5 fs Recombination Y (u.a.) X (u.a.) Haessler et al. Nature Physics X (u.a.) HOMO Multi-channel harmonic generation HOMO-1 D( ω, θ) = γ ( k) a ( k) d ( k) q j ion prop rec Energy (ev) Smirnova et al., Nature (29) McFarland, et al., Science (28) 5 Ionization from HOMO-1 A 2 Π u N 2 + E=1.4 ev N 2 X 2 + Σ g Ionization fromhomo X 1 Σ g + D D N Ar 2 = + α ( θ ) d β ( θ, I L X ( θ ) + ) e i Φ ( I L ) d A ( θ ) R(N-N) (a.u.) Φ ( I L ) E τ q ( I L ) How to identify multi-orbital contributions? = vary I L D D Intensity dependence of calibrated dipole N 2 i Φ ( I L ) = α ( θ ) d ( θ ) β ( θ, ) ( θ X + I L e d A Ar Little phase variation at low I Variation at high I and 9 ) Simulation for 9 o Calibrated phase (π rad) x 1 14 W/cm 2 x1 14 W/cm 2 Diveki et al., NJP (212) Attosecond nuclear dynamics in the A channel 2 5 A 2 Π u X 2 Σ g + Energy (ev) χ X + τ ( q ) N N 2 X 1 Σ g + χ Nuclear autocorrelation function: R ( N - N ) ( a. u. ) C = + χ ( τ ) χ C X 1 ; arg(c X ) C A.7 ; arg(c X ) π/3 q Influence of nuclear dynamics on calibrated phase D D N 2 i Φ ( I L ) = α ( θ ) d ( θ ) β ( θ, ) ( θ X + I L e d A Ar ) C A ( τ q ) Calibrated phase (π rad) x 1 14 W/cm 2 Simulation for 9 o x1 14 W/cm 2 = Phase increase at high orders may be due to ultrafast nuclear dynamics in the A channel Diveki et al., New J. Phys. (212) Conclusions Advanced characterization of attosecond emission from aligned molecules: = Molecular-frame recombination dipole = its spectral phase contains signature of structural interference = Tomographic reconstruction of the HOMO Angström resolution mainly limited by accessible spectral range = Dynamical interferences give access to the hole dynamics with attosecond resolution = Photo-chemical reactions already studied ex: NO2 dissociation through conical intersection Wörner et al., Science (211) Ruf et al., JCP (212) A. Camper, N. Lin, Z. Diveki, S. Haessler, B. Manschwetus, J. Rothhardt, E. English, T. Auguste, P. Breger, M. Géléoc, T. Ruchon, B. Carré, P. Salières CEA-Saclay, Service des Photons, Atomes et Molécules, France R. Guichard, J. Caillat, R. Taieb, A. Maquet Université Paris 6, LCP-MR, France
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