10 research outputs found
Reconstruction and control of a time-dependent two-electron wave packet
The concerted motion of two or more bound electrons governs atomic1 and molecular2,3 non-equilibrium processes including chemical reactions, and hence there is much interest in developing a detailed understanding of such electron dynamics in the quantum regime. However, there is no exact solution for the quantumthree-body problem, and as a result even the minimal system of two active electrons and a nucleus is analytically intractable4. This makes experimental measurements of the dynamics of two bound and correlated electrons, as found in the helium atom, an attractive prospect.However, although the motion of single active electrons and holes has been observed with attosecond time resolution5-7, comparable experiments on two-electron motion have so far remained out of reach. Here we showthat a correlated two-electron wave packet can be reconstructed froma 1.2-femtosecondquantumbeatamong low-lying doubly excited states in helium.The beat appears in attosecond transient-absorption spectra5,7-9 measured with unprecedentedly high spectral resolution and in the presence of an intensity-tunable visible laser field.Wetune the coupling10-12 between the two low-lying quantum states by adjusting the visible laser intensity, and use the Fano resonance as a phase-sensitive quantum interferometer13 to achieve coherent control of the two correlated electrons. Given the excellent agreement with large-scalequantum-mechanical calculations for thehelium atom, we anticipate thatmultidimensional spectroscopy experiments of the type we report here will provide benchmark data for testing fundamental few-body quantumdynamics theory in more complex systems. Theymight also provide a route to the site-specificmeasurement and control of metastable electronic transition states that are at the heart of fundamental chemical reactionsWe thank E. Lindroth for calculating the dipole moment (2p2|r|sp2,3+), and also A. Voitkiv, Z.-H. Loh, and R. Moshammer for helpful discussions. We acknowledge financial support by the Max-Planck Research Group Program of the Max-Planck Gesellschaft (MPG) and the European COST Action CM1204 XLIC. L. A. and F. M. acknowledge computer time from the CCC-UAM and Mare Nostrum supercomputer centers and financial support by the European Research Council under the ERC Advanced Grant no. 290853 XCHEM, the Ministerio de EconomÃa y Competitividad projects FIS2010-15127, FIS2013-42002-R and ERA-Chemistry PIM2010EEC-00751, and the European grant MC-ITN CORIN
Complex energies and the polyelectronic Stark problem: II. The Li n=4 levels for weak and strong fields
Quantum-mechanical versus semiclassical calculations of dc-field-induced tunneling rates of Li 1s(2)2s S-2, 1s(2)2p P-2(0), and 1s(2)3d D-2
Quantum-mechanical versus semiclassical calculations of dc-field-induced tunneling rates of Li 1s22s2S, 1s22p2P0, and 1s23d2D
Properties of doubly excited states of H- and He associated with the manifolds from N=6 up to N=25
This paper discusses theory and results on 1P0 doubly excited states (DES) in He and in H- of
very high excitation, up to the N=25 manifold. Our calculations employed full configuration
interaction (CI) with large hydrogenic basis sets and produced correlated wavefunctions for
the four lowest roots at each hydrogenic manifold by excluding open channels and the small
contribution of series belonging to lower thresholds. The suitability of the hydrogenic basis
sets for such calculations is justified, apart from their practicality, by the fact that, by
computing from them natural orbitals, the results were shown to be the same with those of
earlier multiconfigurational Hartree-Fock (MCHF) calculations on low-lying DES. In total,
160Â states were computed, most of them for the first time. Their energy spectrum should be of
use to possible future photoabsorption experiments. For certain low-lying DES up to N=13,
for which previous reliable results are available, comparison of the calculated energies shows
good agreement. The correlated wavefunctions contain systematically chosen single and
double excitations from each hydrogenic manifold of interest. From their analysis, we
determined the “goodness" of different quantum numbers and the geometry (average angles
and radii) as a function of excitation. For the Sinanolu-Herrick (K, T) classification scheme,
whose basis is a restricted CI with hydrogenic functions and which has thus far been tested
only on low-lying DES, we established that, whereas T remains a good index as energy
increases, K does not. Consequently, a more flexible than K quantum number is needed in
order to account for most of the additional correlation. This number, represented by ,
where N and K are not good numbers anymore, produces consistently a much higher degree
of purity than the (K, T) scheme does, especially as N increases and as the relative
significance of various virtual excitations due to electron correlation increases. Among the
four states of each manifold, in all cases in H- and in most cases in He, the three are of the
intrashell type and one is of the intershell type with (F, T)=(0,0). The lowest intrashell states
and the lowest intershell states exhibit a wide angle geometry tending to 180 as