Excitation of Rydberg states by very short pulses

22 Excitation of Rydberg states by very short pulses 

We can calculate their number simply by differentiating equation (2.8), 

After formation, the wavepacket travels outwards towards the classical turning point, where it becomes very narrow. Close to the turning point, such a wavepacket has an uncertainty product ArAp very close to the minimum allowed by Heisenberg s uncertainty principle (h/2). It then reverses direction and accelerates towards the core (or the nucleus, in the case of H), where it is dispersed. For a pure Coulomb potential, the classical period in a Kepler orbit with n 85 is about 93 ps. After a few periods, the wavepacket appears to disperse completely, although it can revive at later times. 

In the above example, the spatial localisation produced was in the radial coordinate. It is also possible, by using Rydberg states, to produce localisation in the angular coordinates, although the method of prepare tion of the wavepacket is then different. 

If such a wavepacket were formed in H, then the wavepacket would remain intact, with a fixed orientation in space, until some incoherent process (either spontaneous emission (see chapter 4) or collisions, discussed above) destroys the coherence. This arises because conservation of angular momentum for the excited electron applies strictly in this case. However, the experiment is performed in an alkali atom, which possesses a core, and there is a back reaction of the excited electron on this core (core polarisation), which depends on the degree of penetration of the excited electron into the core, i.e. on the quantum defect, which itself is a function of the angular momentum. Thus, the wavepacket precesses under the influence of a small potential due to the quantum defect of the alkali. It is found to follow a classical trajectory determined by the core polarisation potential. 

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