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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γ /∆ σ/∆<br />
10 -1<br />
10 -2<br />
10 -3<br />
0.2<br />
0.1<br />
(a)<br />
(b)<br />
0.0<br />
20 40 60 80 100<br />
Pr<strong>in</strong>cipal Quantum Number n 0<br />
A. Buchleitner et al. / Physics Reports 368 (2002) 409–547 521<br />
10 -1<br />
10 -2<br />
10 -3<br />
10 -1<br />
10 -3<br />
10 -5<br />
10 -7<br />
0.02 0.04 0.06<br />
Fig. 53. E ective tunnel<strong>in</strong>g rate = of the <strong>wave</strong> packet (a), as a function of the e ective <strong>quantum</strong> number n0 = ! −1=3<br />
(the <strong>in</strong>verse of the e ective Planck constant), for xed classical dynamics, F0 =0:0426. Note the exponential decrease for<br />
su ciently high n0 (the vertical scale is logarithmic). The correspond<strong>in</strong>g e ective chaotic ionization rate = (b) smoothly<br />
<strong>in</strong>creases with n0, approximately as n 2 0.<br />
Fig. 54. The tunnel<strong>in</strong>g rate = (panel (a)) and the chaotic ionization rate = (panel (b)), as a function of the scaled<br />
micro<strong>wave</strong> amplitude F0, for <strong>wave</strong>-packet eigenstates of a two-dimensional hydrogen atom <strong>in</strong> a circularly polarized<br />
micro<strong>wave</strong> eld. Observe the oscillatory behavior of the tunnel<strong>in</strong>g rate. The bumps are due to secondary nonl<strong>in</strong>ear<br />
resonances <strong>in</strong> the classical dynamics of the system.<br />
order of 10 5 Kepler periods, for n0 60. This may be used for their possible experimental detection,<br />
see Section 8.4.<br />
7.2. Radiative properties<br />
So far, we have considered the <strong>in</strong>teraction of the atom with the coherent driv<strong>in</strong>g eld only. However,<br />
this is not the full story. S<strong>in</strong>ce the driv<strong>in</strong>g eld couples excited atomic states, it rema<strong>in</strong>s to be<br />
seen to which extent spontaneous emission (or, more precisely, the coupl<strong>in</strong>g to other, <strong>in</strong>itially unoccupied<br />
modes of the electromagnetic eld) a ects the <strong>wave</strong> packet properties. This is very important,<br />
s<strong>in</strong>ce the non-<strong>dispersive</strong> <strong>wave</strong> <strong>packets</strong> are supposed to be long liv<strong>in</strong>g objects, and spontaneous emission<br />
obviously limits their lifetime. Furthermore, we have here an example of decoherence e ects due<br />
to <strong>in</strong>teraction with the environment. More generally, the <strong>in</strong>teraction of non-<strong>dispersive</strong> <strong>wave</strong> <strong>packets</strong><br />
with an additional weak external electromagnetic eld may provide a useful tool to probe their properties.<br />
In particular, their localization with<strong>in</strong> the resonance island implies that an external probe will<br />
couple them e ciently only to neighbor<strong>in</strong>g states with<strong>in</strong> the island. In turn, that should make their<br />
experimental characterization easy and unambiguous. Of course, external drive (micro<strong>wave</strong> eld)<br />
and probe must not be treated on the same foot<strong>in</strong>g. One should rather consider the atom dressed<br />
γ/∆ σ/∆<br />
F 0<br />
(b)<br />
(a)