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) 409–547 455<br />
Fig. 10. Po<strong>in</strong>care surface of section for the dynamics of a 1D hydrogen atom <strong>driven</strong> by an external oscillatory electric<br />
eld, see Eq. (137). The driv<strong>in</strong>g frequency is chosen as ! =1=60 3 , such that the non-l<strong>in</strong>ear resonance island is centered at<br />
pr<strong>in</strong>cipal action (or e ective pr<strong>in</strong>cipal <strong>quantum</strong> number) n0=60. The scaled external eld amplitude is set to F0=Fn 4 0=0:01.<br />
Although the driv<strong>in</strong>g eld is much weaker than the Coulomb eld between the electron and the nucleus, it su ces to<br />
create a relatively large resonance island which supports several non-<strong>dispersive</strong> <strong>wave</strong> <strong>packets</strong>.<br />
Energy (10 −4 a.u.)<br />
−1.372<br />
−1.382<br />
−1.392<br />
−1.402<br />
−1.412<br />
0 0.02 0.04 0.06<br />
0 0.02 0.04 0.06<br />
F 0<br />
Fig. 11. Comparison of the exact quasi-energy spectrum of the 1D hydrogen atom <strong>driven</strong> by a l<strong>in</strong>early polarized micro<strong>wave</strong><br />
eld (right), Eq. (137), with the prediction of the pendulum approximation (left), Eq. (149). Because of the ˝! periodicity<br />
of the Floquet spectrum, the energy levels described by the pendulum approximation are folded <strong>in</strong>side one Floquet zone.<br />
The agreement between the exact <strong>quantum</strong> result and the pendulum approximation is very good. The lled circle shows the<br />
most localized non-<strong>dispersive</strong> <strong>wave</strong> packet N = 0 shown <strong>in</strong> Figs. 13–15, while the lled square represents the hyperbolic<br />
non-<strong>dispersive</strong> <strong>wave</strong> packet partly localized <strong>in</strong> the vic<strong>in</strong>ity of the unstable equilibrium po<strong>in</strong>t of the pendulum, shown <strong>in</strong><br />
Figs. 17 and 18. The open circle and square compare the exact location of the respective quasienergy values with the<br />
Mathieu prediction, which is considerably better for the ground state as compared to the separatrix state.