Non-dispersive wave packets in periodically driven quantum systems

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