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) 409–547 531<br />
RESCALED ENERGY<br />
3<br />
2<br />
1<br />
0<br />
-1<br />
-2<br />
-3<br />
0.018 0.02 0.022<br />
F0 0.024 0.026<br />
Fig. 59. The quasi-energy spectrum of a two-dimensional hydrogen atom <strong>in</strong> a circularly polarized micro<strong>wave</strong> eld, as<br />
a function of the scaled micro<strong>wave</strong> amplitude F0 (for n0 = 60). In order to emphasize the dynamics of <strong>wave</strong>-packet<br />
states, the semiclassical prediction, Eq. (174) for the ground state <strong>wave</strong>-packet energy is substracted from the numerically<br />
calculated energies. Consequently, the ground state <strong>wave</strong> packet |0; 0〉 is represented by the almost horizontal l<strong>in</strong>e. The<br />
dashed l<strong>in</strong>e represents the semiclassical prediction for the |1; 4〉 <strong>wave</strong> packet. Although it is rather far from the exact<br />
result, the slope of the energy level is well reproduced. The size of the avoided cross<strong>in</strong>g between the “solitonic” levels<br />
|0; 0〉 and |1; 4〉 is a direct measure of the failure of the harmonic approximation.<br />
consecutive states and the simple solitonic model breaks down. In order to understand the variations<br />
of the (complex) energies of the resonances with F, a slightly more complicated model—level<br />
dynamics <strong>in</strong> the complex plane—should be used [15].<br />
8. Experimental preparation and detection of non-<strong>dispersive</strong> <strong>wave</strong> <strong>packets</strong><br />
In the preced<strong>in</strong>g sections, we have given an extensive theoretical description of the characteristic<br />
properties of non-<strong>dispersive</strong> <strong>wave</strong> <strong>packets</strong> <strong>in</strong> <strong>driven</strong> Rydberg <strong>systems</strong>. We have seen that these<br />
surpris<strong>in</strong>gly robust “<strong>quantum</strong> particles” are ubiquitous <strong>in</strong> the <strong>in</strong>teraction of electromagnetic radiation<br />
with matter. However, any theoretical analysis needs to be confronted with reality, and we have<br />
to deal with the question of creat<strong>in</strong>g and identify<strong>in</strong>g non-<strong>dispersive</strong> <strong>wave</strong> <strong>packets</strong> <strong>in</strong> a laboratory<br />
experiment. In our op<strong>in</strong>ion, none of the currently operational experiments on the <strong>in</strong>teraction of Rydberg<br />
atoms with micro<strong>wave</strong> elds allows for an unambiguous identi cation of non-<strong>dispersive</strong> <strong>wave</strong><br />
<strong>packets</strong>, although some of them [133] certa<strong>in</strong>ly have already populated such states. In the follow<strong>in</strong>g,<br />
we shall therefore start out with a brief description of the typical approach of state-of-the-art<br />
experiments, and subsequently extend on various alternatives to create and to probe non-<strong>dispersive</strong><br />
<strong>wave</strong> <strong>packets</strong> <strong>in</strong> a real experiment. We do not aim at a comprehensive review on the <strong>in</strong>teraction of<br />
Rydberg atoms with micro<strong>wave</strong> elds, but rather refer to [43,32,69,133,196] for a detailed treatment<br />
of various aspects of this <strong>in</strong>tricate problem. Here, we strictly focus on issues pert<strong>in</strong>ent to our speci c<br />
purpose.