Wavepacket Rydberg

Another somewhat different example of coherence of electronic states is a radial electronic Rydberg wavepacket whose dynamics can be studied in pump-probe experiments. 

Fig. 2.11. Rydberg wavepackets after excitation by a 10 ps laser pulse tuned to a frequency around principal quantum number 85 in the Rydberg spectrum. The times chosen correspond to the first half of the orbit. They are indicated in ps above each wavepacket (after J.A. Yeazell and C.R. Stroud [52]).

The center of the Rydberg wavepacket, (r)t, undergoes periodic radial oscillations, analogous to the planetary motions (Kepler orbits). The Kepler period of (r)t for the Rydberg wavepacket with center-n, n enter, is... 

Once again, the quadrupole splittings are integer multiples of a common factor, and if several Z/j -components are excited at t — to, the Rydberg wavepacket will precess about N+ and exhibit grand rephasings. 

The computation of the time-dependent excitation of high-lying Rydberg wavepackets by laser pulses interacting with electrons via the full interaction Hamiltonian [55-57]... 

Th. Mercouris, Y. Komninos, C.A. Nicolaides, Electric dipole versus fuU interaction in the dynamics of laser excitation of Rydberg wavepackets, J. Phys. B 35 (2002) 1439. 

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

B. Kohler My question to T. Softley ties in to one of the major themes of the meeting, namely coherence. In your presentation you briefly mentioned that it may be important to consider an initially coherent superposition of states in the preparation step of experiments on highly excited Rydberg states. Several groups have now prepared coherent electronic wavepackets using picosecond (and shorter) pulses. Would this kind of an initial state be useful for any of the classes of pulsed-field ionization experiments that you have described ... 

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. 

Our purpose in mentioning negative ions here is to contrast their properties with those of systems which do exhibit Rydberg states. In particular, for negative ions, short pulse excitation is unable to produce narrow wavepackets of the kind described above, which arise by superposition of several Rydberg states. Thus, the response of negative ions to short pulses is markedly different from that of neutral atoms or positive ions, a matter which will be taken up again in chapter 9. 

In Section 4, we referred to the issue of the proper choice of the form of the EMF-atom interaction. In the example of this section, this issue is discussed in the context of the problem of processes of excitation and ionization involving directly high-lying Rydberg states and wavepackets. 

On- and off-resonance excitation of Rydberg states and the theme of angular momentum wavepackets... 

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