Non-dispersive wave packets in periodically driven quantum systems
Non-dispersive wave packets in periodically driven quantum systems
Non-dispersive wave packets in periodically driven quantum systems
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494 A. Buchleitner et al. / Physics Reports 368 (2002) 409–547<br />
Fig. 38. Temporal dynamics of the non-<strong>dispersive</strong> <strong>wave</strong> packet of a three-dimensional hydrogen atom exposed to a l<strong>in</strong>early<br />
polarized, resonant micro<strong>wave</strong> eld, <strong>in</strong> the presence of a parallel static electric eld. F0 =0:03, Fs;0 =0:009, Fs;0=F0 =0:3,<br />
n0 = 60. Driv<strong>in</strong>g eld phases at the di erent stages of the <strong>wave</strong>-packet’s evolution: !t = 0 (top left), =2 (top right), 3 =4<br />
(bottom left), (bottom right). It is well localized <strong>in</strong> the three dimensions of space and repeats its shape <strong>periodically</strong> (cf.<br />
Fig. 13 for the analogous dynamics <strong>in</strong> the restricted 1D model, where no additional static electric eld is needed). The<br />
nucleus is at the center of the plot which extends over ±8000 Bohr radii. The micro<strong>wave</strong> polarization axis and the static<br />
eld are oriented along the vertical axis.<br />
papers [144,44,46,54,62,30,151]. The Hamiltonian of the system <strong>in</strong> the coord<strong>in</strong>ate frame corotat<strong>in</strong>g<br />
with the CP eld reads (compare with Eq. (184), for the pure CP case)<br />
H = p2 x + p 2 y + p 2 z<br />
2<br />
− 1<br />
r − (! − !c=2)Lz + Fx + !2 c<br />
8 (x2 + y 2 ) ; (214)<br />
where !c is the cyclotron frequency. In atomic units, the cyclotron frequency !c = −qB=m equals<br />
the magnetic eld value. It can be both positive or negative, depend<strong>in</strong>g on the direction of the<br />
magnetic eld. 23 This additional parameter modi es the dynamical properties which characterize<br />
the equilibrium po<strong>in</strong>ts, the analysis of which may be carried out alike the pure CP case treated <strong>in</strong><br />
23<br />
A di erent convention is used (quantization axis de ned by the orientation of the magnetic eld) <strong>in</strong> many papers on<br />
this subject. It leads to unnecessarily complicated equations.