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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A. Buchleitner et al. / Physics Reports 368 (2002) 409–547 517<br />
con guration-<strong>in</strong>teraction is most pronounced) when the core is not <strong>in</strong> its ground state. Then these<br />
parts of the <strong>wave</strong> packet autoionize, and the rema<strong>in</strong><strong>in</strong>g Rydberg population is reshaped <strong>in</strong>to a localized<br />
<strong>wave</strong> packet, s<strong>in</strong>ce the spread<strong>in</strong>g tails have been chopped o . Hence, these <strong>wave</strong> <strong>packets</strong><br />
exhibit a rather rapid “melt<strong>in</strong>g” (on a time scale of at most some hundred Kepler periods)—to be<br />
compared to hundreds of thousands or even more Kepler cycles performed by non-<strong>dispersive</strong> <strong>wave</strong><br />
<strong>packets</strong> <strong>in</strong> micro<strong>wave</strong>-<strong>driven</strong> hydrogen atoms studied above (which also ionize, however very slowly,<br />
see Section 7.1).<br />
The present scenario is <strong>in</strong> some sense rem<strong>in</strong>iscent of the one <strong>in</strong> Section 6.1, with a (<strong>quantum</strong>)<br />
two-level core replac<strong>in</strong>g the rotat<strong>in</strong>g molecular core. As mentioned above, a two-level system alone<br />
can only exchange one <strong>quantum</strong> with the outer electron and thus cannot provide an exact phase<br />
lock<strong>in</strong>g mechanism for the highly excited Rydberg electron. However, the two-level core is here<br />
<strong>driven</strong> by an external electromagnetic eld and consequently ga<strong>in</strong>s an additional degree of freedom<br />
which can be used for the phase lock<strong>in</strong>g mechanism. The drawback is that this phase lock<strong>in</strong>g implies<br />
losses (through autoionization). Nevertheless, the quasi-classical evolution over ∼ 100 Kepler cycles<br />
is still quite impressive, and presumably stems from the relatively sharp con nement of e cient<br />
con guration-<strong>in</strong>teraction with<strong>in</strong> a spatial region close to the <strong>in</strong>ner turn<strong>in</strong>g po<strong>in</strong>t of the Rydberg<br />
<strong>wave</strong> packet.<br />
7. Characteristic properties of non-<strong>dispersive</strong> <strong>wave</strong> <strong>packets</strong><br />
After present<strong>in</strong>g several examples of non-<strong>dispersive</strong> <strong>wave</strong> <strong>packets</strong> <strong>in</strong> the previous chapters, we<br />
now study their speci c properties <strong>in</strong> more detail. Especially, several important physical processes<br />
which may a ect the existence of <strong>wave</strong> <strong>packets</strong> have so far been hidden under the carpet [177]. The<br />
two most important ones, at least for <strong>driven</strong> atoms, are ionization and spontaneous emission, and they<br />
will be discussed <strong>in</strong> detail below. First, let us brie y discuss the general properties of <strong>wave</strong>-packet<br />
eigenstates under the variation of various parameters of the <strong>driven</strong> system (e.g., micro<strong>wave</strong> amplitude<br />
and frequency, the strength of an external static eld, etc.).<br />
7.1. Ionization rates and chaos-assisted tunnel<strong>in</strong>g<br />
Atoms <strong>driven</strong> by micro<strong>wave</strong>s will eventually ionize. Therefore, the non-<strong>dispersive</strong> <strong>wave</strong>-packet<br />
states discussed up till now cannot be, rigorously speak<strong>in</strong>g, discrete states, they are rather resonances<br />
[23] with some nite lifetimes. Importantly, as we shall discuss <strong>in</strong> detail below, these lifetimes<br />
may be extremely long, of the order of millions of micro<strong>wave</strong> periods. In that sense, they are<br />
comparable to those of highly excited atomic Rydberg states, which also decay, by spontaneous<br />
emission, on time scales of few millions of classical periods. Even more importantly, the lifetimes<br />
of the non-<strong>dispersive</strong> <strong>wave</strong> <strong>packets</strong> are typically orders of magnitude larger than the lifetimes of<br />
other states <strong>in</strong> the Floquet spectrum: the <strong>wave</strong> <strong>packets</strong> are particularly resistant to ionization. This<br />
is due to the classical con nement of the electron <strong>in</strong>side the regular island. To ionize, the electron<br />
has no other option but to tunnel out of the classically con n<strong>in</strong>g island, before ga<strong>in</strong><strong>in</strong>g energy<br />
by di usive excitation [131]. The resonance island is strictly con n<strong>in</strong>g only for a one-dimensional<br />
system. For multi-dimensional <strong>systems</strong>, the tori <strong>in</strong> the resonance islands are not fully isolat<strong>in</strong>g and a<br />
very slow classical di usion process might eventually lead to ionization. This, however, takes place