Non-dispersive wave packets in periodically driven quantum systems

470 A. Buchleitner et al. / Physics Reports 368 (2002) 409–547
Fig. 25. Comparison of the numerically exact level dynamics (...) with the semiclassical prediction (—), for the
n0 =22(N = 1) manifold of a 3D hydrogen atom exposed to a microwave eld with frequency ! =1=(21) 3 , resonant
with the n0 = 21 manifold. For su ciently high F0, the quantum states originating at F0 = 0 from the unperturbed n0 =22
level are captured by the principal resonance island and then represent the rst excited state of the motion in the (Î; ˆ )
plane (i.e., N = 1 in Eq. (78)). Since the island’s size depends on the angular (L; ) motion (value of p in Eq. (163),
see also Fig. 20), states with large p enter the resonance zone rst. For these, the agreement between quantum and
semiclassical quasi-energies starts to be satisfactory at lower F0 values than for low-p states.
Finally note that, as already mentioned at the end of Section 3.3.1, all wave-packet eigenstates
have a nite decay rate which induces a slow, global reduction of the electronic density localized
on the resonantly driven classical periodic orbit. However, the time-scale of this decay is of the
order of thousands to millions of Kepler cycles, and therefore leaves our above conclusions unaffected.
However, some very intriguing consequences of the non-vanishing continuum coupling will
be discussed in Section 7.1.
3.4. Rydberg states in circularly polarized microwave elds
As shown in the preceding section, the use of a linearly polarized microwave eld is not su cient
to produce a non-dispersive wave packet fully localized in all three dimensions, due to the azimuthal
symmetry around the microwave polarization axis. To get more exibility, one may consider the case
of arbitrary polarization. It turns out that the results are especially simple in circular polarization.
They are the subject of this section.
In most experiments on microwave driven Rydberg atoms, linearly polarized (LP) microwaves
have been used [132,133,135–137]. For circular polarization (CP), rst experiments were performed
for alkali atoms in the late eighties [138,139], with hydrogen atoms following only recently [134].
The latter experiments also studied the general case of elliptic polarization (EP). While, at least
theoretically, di erent frequency regimes were considered for CP microwaves (for a review, see
[140])—we shall restrict our discussion here to resonant driving. Given a di erent microwave