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New Light Sources New light sources of very high intensity and short duration allow us to carry out time resolved studies of atomic and molecular dynamics Femtosecond Lasers Attosecond Lasers 1 Characterized by a duration of a few to hundreds of femtoseconds (10-15 s). The peak intensity is high and the electric field of the laser is comparable to the electric field that a bound electron experiences from the nucleus. Compared to a laser field of long duration one needs an additional parameter, the carrier-envelope phase difference (CEPD), to characterize a few-cycle femtosecond pulse (see figure 1). 0.8 Normalized electric field 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1 0 Near-infrared (NIR), 1200-800 nm. 1013-1016W/cm2. High-order harmonic generation, tomography, coherent control, ablation, time-resolved chemical reactions. 2.5 5 7 .5 Realized by exploiting high-order harmonic generation (HHG) from atoms. Typical pulse length is hundreds of attoseconds (10-18 s). The intensity is low because of the low efficiency of the HHG process. A tool for time-resolved studies of electron dynamics in atoms, molecules and solids. Wavelength: Intensity: Applications: Fig. 1: Two few-cycle femtosecond pulses. The CEPD is the phase shift between the carrier-wave and the envelope of the pulse. UV-XUV, 10-1 nm. Low. Attoscience, biophysical and biomedical investigations, surgery. Wavelength: Intensity: Applications: Fig. 2: The HHG three-step model. Ionization at time t’ followed by propagation and recombination at time t. Different ionization instants lead to radiation at different frequencies. The basic principle of coherent control is to use laser sources to manipulate physical and chemical processes. One example of coherent control is laser induced alignment and orientation of molecules where the rotational motion is manipulated by one or more laser pulses of picoseconds (10-12s) or subpicoseconds duration to make the molecule point in a certain direction in space. Another example of coherent control is the use of the asymmetry of the electric field of a few-cycle femtosecond pulse to control the electron distribution in the dissociative ionization of molecules (see figure 3). Molecular-Orbital Tomography Fig. 3: Measured asymmetry of the D+ fragment in dissociative ionization of D2 molecules as a function of energy and CEPD [M. F. Kling et al. ,Science 2007]. The asymmetry in the signal is ascribed to a localization of the electron around one of the two nuclei in the singly ionized D2+ prior to dissociation, and the figure clearly demonstrates control of this localization as a function of the CEPD phase. Time-Resolved Studies of Nuclear Motion in Molecules y(Å) Molecule Laser Time y(Å) Electron x(Å) Fig. 4: (Top) The reconstructed N2 molecular-orbital in an experiment [Itatani et al., Nature 2004]. (Bottom) The theoretically calculated N2 molecular orbital. Harmonic intensity Attoscience Ioniz a tion yie ld (a rbitra ry units ) a) –1.0 380 as –0.5 0.0 0.5 1.0 Delay time, ∆ t (fs) b) V +V Coulomb Potential The characteristic time scale for electron motion in atoms and molecules is typically a few hundred attoseconds. Attosecond pulses extracted from the HHG process can be used to conduct time resolved measurements of this fast electron motion. Fast rearrangement of the electron is a fundamental part of a vast number of processes such as photosynthesis and vision. Several pioneering attoscience experiments are currently conducted. VCoulomb E−field Electron tunneling Distance Tunable from microwaves to x-rays. Up to 1022 W/cm2. Fast ignition of fusion, particle physics, biophysical and biomedical investigations and surgery. Coherent Control High-Order Harmonic Generation The HHG spectrum contains information about the orbital, since it is generated when the electron recombines with the ion under emission of a harmonic photon. The idea in molecular-orbital tomography is to use this information to reconstruct the molecular-orbital. Measurements of HHG spectra for a whole range of molecular orientations probes the Fourier transform of the dipole operator times the electron orbital, and from this the wave function is obtained from an inverse Fourier transform. Characterized by very energetic and potentially very intense laser beams. Lasing medium consists of highly relativistic electrons in an undulator (magnet array). A free electron laser is very expensive because the production of relativistic electrons requires a particle accelerator. 10 Time (femtoseconds) When matter interacts with an intense femtosecond laserpulse this may lead to the emision of coherent UV or XUV radiation. The production of radiation is understood in terms of a three-step model: 1. An electron is removed from the atom or molecule by absorption of k’ laser photons at a time t’ within a subfemtosecond around the peak of the femtosecond laser field. 2. The electron is accelerated in the laser field, initially away and then back towards the parent ion. 3. The electron recombines with the parent ion under the absorption of k laser photons at time t within a subfemtosecond interval around the minimum of the laser field. A photon of frequency k’+k times the laser frequency, a socalled harmonic photon, is emitted. Because the recombination takes place within a subfemtosecond interval, the harmonic radiation is emitted as a burst of attosocond duration. Free Electron Lasers Frequency Wavelength: Intensity: Applications: CEPD 0 CEPD π/2 Lundbeck Foundation Theoretical Center !!!!!!!!!!!!!! !!!! for !!!!!!!!!!!!!!!!! !!Quantum !!! !!System Research Fig. 5: Uiberacker et al. Nature 2007 used a pumpprobe experiment to study electron tunneling in neon ions, where the pump is an XUV attosecond pulse, and the probe is a near-infrared (NIR) femtosecond pulse. The two pulses are displaced by a variable delay ∆t. The XUV pulse ionizes neon, leaving neon in a number of excited ionic states. These states can be probed via tunnel ionization by the few-cycle NIR femtosecond pulse. Since the excited states are exposed to the NIR field from the moment they are made to the end of the NIR pulse, it is possible to probe different ionic states, by changing the delay ∆t. a) Experimental results. The steep part of the curve correspond to non-adiabatic tunneling ionization. b) The principle behind laser induced tunneling in atoms. Fig. 6: HHG can be used to study nuclear dynamics, e.g., in H2+. When an electron is removed from H2, the nuclei start to move apart due to the larger equlibrium separation in H2+, compared to H2. When the electron returns the recombination process is dependent on the overlap between the present nuclear wave function and the nuclear wave function in H2. If the nuclei have not moved far the overlap is close to unity, and a large amount of harmonic radiation is emitted. If, on the other hand, the nuclei have moved far apart, the overlap of the nuclear wave functions is small, and less harmonic radiation is emitted. Using, in addition, the fact that early returning electrons lead to high-order harmonic generation of low frequencies, while late returning electrons yield high frequencies one can reconstruct the nuclear motion by comparing results obtained from different isotopes. For light molecules nuclear dynamics is fast and has to be taken into account even on a femtosecond time scale. Simple physical models are necessary since the nuclear motion on top of the electronic motion would add at least add three dimensions to the problem if no approximations were made. A typical simplification of nuclear motion is to use the Born-Oppenheimer approximation, which has, e.g., been successfully employed to describe double ionization of H2. Experimentally the motion of nuclei can be studied with time resolution using high-order harmonic generation (See Fig. 6). The Lundbeck Foundation Theoretical Center for Quantum System Research (LTC) is concerned with the theory of quantum systems at the atomic level. The center merges research in quantum optics and information, cold atoms and matter waves, and atomic and molecular physics with new light sources, where immense experimental progress currently raises high demands on new theoretical ideas and analyses. www.phys.au.dk/ltc