Attosecond dynamics

In this section, by applying the heterodyne interferometry to a mixed gas of H2 and D2 molecules, we probe attosecond dynamics of nuclear wavepackets in the molecules. We find that not only the single molecule responses but also the propagation effects of harmonics differ between the two isotopes and that to discuss dynamics of molecules in the single molecule responses, the propagation effects need to be excluded from the raw harmonic signals. The measured relative phase as well as intensity ratio are found to be monotonic functions of the harmonic order and are successfully reproduced by applying... 

Fig. 4.9. A schematic diagram illustrating the attosecond dynamics of the strongly correlated nuclear and electron wavepackets that lead to HHG in H2 and/or D2. When the internuclear distance is large, HHG is suppressed...

In summary, we investigated HHG in mixed gases both experimentally and theoretically. As the new nonlinear media for HHG, using mixed gases can serve as a new route not only to control and characterize harmonics but also to observe attosecond dynamics in atoms and molecules. 

Th. Mercouris, Y. Komninos, C.A. Nicolaides, Theory and computation of the attosecond dynamics of pairs of electrons excited by high-frequency short light pulses, Phys. Rev. A 69 (2004) 032502. 

Keywords Attosecond dynamics, neutron Compton scattering, electron-proton Compton... 

Keywords Attosecond dynamics, entanglement, decoherence, inelastic X-ray scattering,... 

Current technology is enabling pulses shorter in time scale than the nuclear dynamics [61, 76], opening up the field of attosecond dynamics for control the current focus is mostly on controlling the electron (recollision) dynamics [222]. 

Attosecond dynamics is now one of the most active fields in science [222, 476] (see also the introductory section of Ref. [499], which shows a concise list of the studies covering many phenomena and relevant studies). In particular, tracking electronic motions in chemical dynamics is a fundamentally important process. To monitor those electron wavepacket dynamics in an attosecond intense laser field [476], Bandrauk and his coworkers have developed the theory of attosecond-scale time-resolved photoelectron spectroscopy [499, 500], Photoionization dynamics of small molecules like has been studied so far, for which direct numerical integrations of the related (low-dimensional) time-dependent Schrodinger equations are possible. The photoelectron signals are extracted from those numerical solutions... 

Of course, even when the world s fastest laser pulses are available, there is always a feehng that what is really required is pulses that are faster still Laser pulses with durations in the attosecond regime would open up the possibility of observing the motions of electrons in atoms and molecules on their natural time scale and would enable phenomena such as atomic and molecular ionisation (Section 1.2) and the dynamics of electron orbits about nuclei to be captured in real time. 

In this section, we present the first experimental evidence of the destructive interference (DI) and the constructive interference (Cl) in a mixed gas of He and Ne, which prove the validity of the method. The observed interference modulation is, as discussed in Sect. 4.2, attributed to the difference between the phases of the intrinsically chirped harmonic pulses from He and Ne, which leads to the novel method for broadband measurement of the harmonic phases and for observing the underlying attosecond electron dynamics. 

We start our discussion of laser-controlled electron dynamics in an intuitive classical picture. Reminiscent of the Lorentz model [90, 91], which describes the electron dynamics with respect to the nuclei of a molecule as simple harmonic oscillations, we consider the electron system bound to the nuclei as a classical harmonic oscillator of resonance frequency co. Because the energies ha>r of electronic resonances in molecules are typically of the order 1-10 eV, the natural timescale of the electron dynamics is a few femtoseconds to several hundred attoseconds. The oscillator is driven by a linearly polarized shaped femtosecond... 

Because electrons are much lighter than nuclei, they move much faster. The intrinsic temporal regime for valence bond electron dynamics is the few femtosecond to several hundred attosecond timescale. Therefore, efficient and accurate control of electron dynamics requires extreme precision regarding the control field. Commonly attosecond techniques are considered to be the appropriate tools for efficient manipulation of electron motions [61-63, 111, 112]. However, attosecond pulses in the XUV region are not suited for efficient valence bond excitation (see Section 6.1). Here we demonstrate that ultrafast electron dynamics are controlled efficiently on the sub-10 as timescale employing a pair of femtosecond laser pulses with a temporal separation controllable down to zeptosecond precision [8]. 

S. Gilbertson, M. Chini, X. Feng, S. Khan, Y. Wu, Z. Chang, Monitoring and controlling the electron dynamics in helium with isolated attosecond pulses, Phys. Rev. Lett. 105 (26) (2010) 263003. 

E. Foumouo, P. Antoine, H. Bachau, B. Piraux, Attosecond timescale analysis of the dynamics of two-photon double ionization of helium, New J. Phys. 10 (2008) 025017. 

In the second part, we discuss possible applications of attosecond laser pulses to future studies of time-resolved electron dynamics in strongly driven systems. We discuss our current understanding of the time-dependent behaviour of non-perturbatively driven electrons in atoms, molecules and clusters. In Sect. 3.4 we discuss differences that arise when the generation of attosecond pulses is performed in different atomic media. This is followed in Sect. 3.5 by a description of the role of electron dynamics in dynamical alignment and enhanced ionization of molecules. Finally, in Sect. 3.6 the role of electron dynamics in laser heating of large clusters is discussed. 

Summarizing, the hitherto existing experimental results seem to be in contrast to well-established conventional expectations. In forthcoming work, we plan to investigate the possible connection and / or common origin of these IXS results with those obtained with NCS and ECS from protons in various systems [Chatzidimitriou-Dreismann 1997 (a) Chatzidimitriou-Dreismann 2003 (a) Physics News 2003 Physics Today 2003 Scientific American 2003], Novel aspects of attosecond quantum dynamics of hydrogen (and D), as well as hydrogen bonds, in molecules and condensed matter are expected to be revealed. 

The exploration of ultrafast molecular and cluster dynamics addressed herein unveiled novel facets of the analysis and control of ultrafast processes in clusters, which prevail on the femtosecond time scale of nuclear motion. Have we reached the temporal boarders of fundamental processes in chemical physics Ultrafast molecular and cluster dynamics is not limited on the time scale of the motion of nuclei, but is currently extended to the realm of electron dynamics [321]. Characteristic time scales for electron dynamics roughly involve the period of electron motion in atomic or molecular systems, which is characterized by x 1 a.u. (of time) = 24 attoseconds. Accordingly, the time scales for molecular and cluster dynamics are reduced (again ) by about three orders of magnitude from femtosecond nuclear dynamics to attosecond electron dynamics. Novel developments in the realm of electron dynamics of molecules in molecular clusters pertain to the coupling of clusters to ultraintense laser fields (peak intensity I = lO -lO W cm [322], where intracluster fragmentation and response of a nanoplasma occurs on the time scale of 100 attoseconds to femtoseconds [323]. 

Thus, information on attosecond jt-electron rotation can be obtained by detecting femtosecond molecular vibrations with spectroscopy, although this type of detection is not a direct imaging of ultrafast electron dynamics. 

Th. Schultz, M. VrakMng (eds.), Attosecond and XUV Spectroscopy Ultrafast Dynamics and Spectroscopy (Wiley/VCH, Weinheim, 2014)... 

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