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