Quasi Landau resonances

While direct diagonalization of the Hamiltonian matrix works well for situations in which there is a finite number of states, as in Fig. 9.1, it is clearly hopeless to try it in this case. A useful WKB approach was proposed by Edmonds12 and refined by Starace.13 Using the fact that azimuthal symmetry exists, Starace writes the wavefunction of the spinless Rydberg electron in cylindrical coordinates as13 

Using this wavefunction in the Schroedinger equation leads to an equation for 

As pointed out by Edmonds and Starace,12,13 the atoms are excited near the origin and can only escape in the z directions. The motion in the x,y plane is bound and is most likely to be the source of the quasi Landau resonances. To find the locations of the resonances it is adequate to ignore the z motion entirely and simply compute the energy spectrum of the motion in x,y plane. Applying the Bohr-Sommerfeld quantization condition leads to 

Evaluating Eq. (9.13) to obtain the resonance spacing, AW = dW/dn, shows that 

These experiments showed clearly that n states evolve into the quasi-Landau resonances. In higher resolution experiments, Gay et a/.18 and Castro et al.19 showed that it was in fact the highest energy diamagnetic states which evolved into 

It is convenient to represent a constant and uniform magnetic field B pointing in the z direction by a vector potential 

It is in this intermediate region (roughly outlined with dashed curves in fig. 10.8) that quantum chaos develops. The classical analogue of this motion is a pendulum-like motion (the Rydberg orbit) in an applied magnetic field, and is chaotic. 

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When they observed final states of m = 0, with both lasers polarized along the field direction, they observed the familiar quasi-Landau resonances spaced at 3a> J2. In contrast, when they excited the m = 1 final state via the intermediate 2p m = 1 state these resonances were absent. Only resonances spaced by 0.64clearly evident if the data are smoothed over 2 cm-1. The periodicity is even more apparent in the Fourier transform of the spectrum, shown in Fig. 9.7. In Fig. 9.7(b) the peak corresponding to the resonance spacing of 0.64[Pg.153]

Main, J., Holle, A., Wiebusch, G., and Welge, K.H. (1987). Semiclassical quantization of three-dimensional quasi-Landau resonances under strong-field mixing, Z. Phys. D 6, 295-302. 

Although Garton and Tomkins discovered -mixing, n-mixing and the quasi-Landau resonances in the spectrum of Ba, from the standpoint of quantum chaology the asymptotically Coulombic nature of the atomic... 

For large fields, the separation between Coulomb states becomes much smaller than the separation between quasi-Landau resonances, and one observes sequences of overlapping Rydberg channels distinguished by the... 

In the strong field problem, much effort and attention has been given to situations where the quantum defects m are nearly integral, i.e. the solutions are quasihydrogenic. An example is the spectrum of Li, which was investigated in considerable detail [569]. In the quasi-Landau resonance range, it had been noticed quite early that the spacings observed in photoabsorption experiments do not follow the usual rule but... 

G. Raithel, M. Fauth, H. Walther, Quasi-Landau resonances in the spectra of rubidium Rydberg atoms in crossed electric and magnetic fields. Phys. Rev. A 44, 1898 (1991)... 

J. Neukammer, H. Rinneberg, K. Vietzke, A. Kdnig, H. Hieronymus, M. Kohl, H.-J. Grabka Spectroscopy of Rydberg atoms at n 500 Observation of quasi-Landau resonances in low magnetic fields. Phys. Rev. Lett. 59, 2947 (1987)... 

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