Posts Tagged ‘XUV pulses’
H2+ in external XUV pulses. Calculations by using the exact prolate spheroidal coordinates
In recent years new and efficient numerical codes have been developed in order to solve the time-dependent Schrödinger equation (TDSE) for single or few-electron atomic and molecular systems. By applying the implemented algorithms on high performance computing platforms, exact solutions to the interaction of such systems with external and intense laser fields are obtained. For larger systems this laser field initiated dynamics is described in a simplified manner in the framework of the Born-Oppenheimer approach, where the nuclear dynamics is restricted to a few relevant electronic levels. A crucial part of these approaches is the calculation of high precision stationary electronic wave functions and the transition dipole moments between them.
The work of the STSM implied the development of an efficient algorithm for the calculation of the bound electronic eigenstates of H2+ for various internuclear distances. In the implemented approach we have discretized the electronic Hamiltonian in prolate spheroidal coordinates using finite difference (FD) discretization. The eigenstates were obtained via the direct diagonalization of the discretized Hamiltonian, and they were sorted according to their symmetry properties. The symmetry properties of each eigenstate was identified by counting the radial and angular nodal planes in prolate spheroidal coordinates (See figure below). After the convergence of the eigenstates (of the electronic wave functions) was carefully checked, the accurate transition dipole moments were also calculated.
In the next step the obtained ab initio electronic energy levels and transition moments will be included in the numerical code developed by the group of prof. Fernando Martin, and the combined electronic and nuclear dynamics of H2+ under the influence of ultrashort laser pulses will be studied.
In the existing approach of the host group the electronic wave functions are obtained by using one center partial wave expansion, which has the disadvantage of slow convergence, and low precision at large internuclear distances. During the present STSM this drawback was eliminated by the present approach.
STSM by Dr. Giuseppe Sansone and Dr. Michele Devetta, Politecnico Milano and CNR-IFN Politecnico (IT) with Prof. Jens Biegert, ICFO (ES)
On July 7th, 2014 (5 days)
From ITALY to SPAIN
Temporal characterization of attosecond pulses generated by mid-IR pulses
The purpose of the STSM was to investigate the feasibility of the temporal characterization of ultrashort extreme ultraviolet radiation (XUV) generated by the process of high-order harmonic generation by mid-infrared driving pulses. By using pulsese centered around 2.0 microns, XUV photon energies up to 500 eV can be reached enabling the investigation of femtosecond and attosecond dynamics in systems characterized by resonances in the water window. In spite of its fundamental interest for biological applications, no temporal characterization of XUV radiation generated in this spectral energy range has been reported so far.
The experiment was performed at ICFO combining the expertise of the Milano group in characterization of isolated attosecond pulses and the carrier-envelop-phase stable driving pulses centered at 1.8 microns available at ICFO. The temporal characterization was based on the so called attosecond streak camera principle by measuring using a time-of-flight spectrometer the photoelectron spectra generated by the attosecond XUV radiation in the presence of an intense synchronized infrared field. A first test measurement based on the cross-correlation between the two driving pulses evidenced an excellent stability of the laser source and of the interferometric setup used for the measurement (see Figure). Preliminary indication of a sub-cycle modulation of the photoelectron spectra as a function of the relative delay between the attosecond and mid-IR pulses was obtained.
The visit will lead to future common projects between the two groups. A new application is undergoing in order to improve the quality of the streaking effect observed so far and to implement the FROG-CRAB retrieving algorithm to the acquired data. The experimental results will be included in a future publication describing, for the first time to the best of our knowledge, the characterization of XUV pulses generated by mid-IR pulses.